{"id":919953,"date":"2026-10-07T23:26:22","date_gmt":"2026-10-07T23:26:22","guid":{"rendered":"https:\/\/www.newsbeep.com\/au\/919953\/"},"modified":"2026-10-07T23:26:22","modified_gmt":"2026-10-07T23:26:22","slug":"non-reciprocity-in-quantum-technologies-nature-physics","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/au\/919953\/","title":{"rendered":"Non-reciprocity in quantum technologies | Nature Physics"},"content":{"rendered":"<p class=\"c-article-references__text\" id=\"ref-CR1\">De\u00e1k, L. &amp; F\u00fcl\u00f6p, T. Reciprocity in quantum, electromagnetic and other wave scattering. Ann. Phys. 327, 1050 <a href=\"https:\/\/doi.org\/10.1016\/j.aop.2011.10.013\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1016\/j.aop.2011.10.013\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1016\/j.aop.2011.10.013<\/a> (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.aop.2011.10.013\" data-track-item_id=\"10.1016\/j.aop.2011.10.013\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.aop.2011.10.013\" aria-label=\"Article reference 1\" data-doi=\"10.1016\/j.aop.2011.10.013\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2012AnPhy.327.1050D\" aria-label=\"ADS reference 1\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=2887248\" aria-label=\"MathSciNet reference 1\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 1\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Reciprocity%20in%20quantum%2C%20electromagnetic%20and%20other%20wave%20scattering&amp;journal=Ann.%20Phys.&amp;doi=10.1016%2Fj.aop.2011.10.013&amp;volume=327&amp;publication_year=2012&amp;author=De%C3%A1k%2CL&amp;author=F%C3%BCl%C3%B6p%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR2\">Jalas, D. et al. What is \u2014 and what is not \u2014 an optical isolator. Nat. Photon. 7, 579 <a href=\"https:\/\/doi.org\/10.1038\/nphoton.2013.185\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphoton.2013.185\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphoton.2013.185<\/a> (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphoton.2013.185\" data-track-item_id=\"10.1038\/nphoton.2013.185\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphoton.2013.185\" aria-label=\"Article reference 2\" data-doi=\"10.1038\/nphoton.2013.185\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2013NaPho...7..579J\" aria-label=\"ADS reference 2\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 2\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=What%20is%20%E2%80%94%20and%20what%20is%20not%20%E2%80%94%20an%20optical%20isolator&amp;journal=Nat.%20Photon.&amp;doi=10.1038%2Fnphoton.2013.185&amp;volume=7&amp;publication_year=2013&amp;author=Jalas%2CD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR3\">Caloz, C. et al. Electromagnetic nonreciprocity. Phys. Rev. Appl. 10, 047001 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevApplied.10.047001\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevApplied.10.047001\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevApplied.10.047001<\/a> (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevApplied.10.047001\" data-track-item_id=\"10.1103\/PhysRevApplied.10.047001\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevApplied.10.047001\" aria-label=\"Article reference 3\" data-doi=\"10.1103\/PhysRevApplied.10.047001\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018PhRvP..10d7001C\" aria-label=\"ADS reference 3\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 3\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Electromagnetic%20nonreciprocity&amp;journal=Phys.%20Rev.%20Appl.&amp;doi=10.1103%2FPhysRevApplied.10.047001&amp;volume=10&amp;publication_year=2018&amp;author=Caloz%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR4\">Yao, N. Y. et al. Topologically protected quantum state transfer in a chiral spin liquid. Nat. Commun. 4, 1585 <a href=\"https:\/\/doi.org\/10.1038\/ncomms2531\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/ncomms2531\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/ncomms2531<\/a> (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/ncomms2531\" data-track-item_id=\"10.1038\/ncomms2531\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fncomms2531\" aria-label=\"Article reference 4\" data-doi=\"10.1038\/ncomms2531\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2013NatCo...4.1585Y\" aria-label=\"ADS reference 4\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 4\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topologically%20protected%20quantum%20state%20transfer%20in%20a%20chiral%20spin%20liquid&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fncomms2531&amp;volume=4&amp;publication_year=2013&amp;author=Yao%2CNY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR5\">Lemonde, M.-A., Peano, V., Rabl, P. &amp; Angelakis, D. G. Quantum state transfer via acoustic edge states in a 2D optomechanical array. N. J. Phys. 21, 113030 <a href=\"https:\/\/doi.org\/10.1088\/1367-2630\/ab51f5\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/1367-2630\/ab51f5\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/1367-2630\/ab51f5<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/1367-2630\/ab51f5\" data-track-item_id=\"10.1088\/1367-2630\/ab51f5\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1367-2630%2Fab51f5\" aria-label=\"Article reference 5\" data-doi=\"10.1088\/1367-2630\/ab51f5\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4171081\" aria-label=\"MathSciNet reference 5\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 5\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20state%20transfer%20via%20acoustic%20edge%20states%20in%20a%202D%20optomechanical%20array&amp;journal=N.%20J.%20Phys.&amp;doi=10.1088%2F1367-2630%2Fab51f5&amp;volume=21&amp;publication_year=2019&amp;author=Lemonde%2CM-A&amp;author=Peano%2CV&amp;author=Rabl%2CP&amp;author=Angelakis%2CDG\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR6\">Owens, J. et al. Chiral cavity quantum electrodynamics. Nat. Phys. 18, 1048\u20131052 <a href=\"https:\/\/doi.org\/10.1038\/s41567-022-01671-3\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41567-022-01671-3\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41567-022-01671-3<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-022-01671-3\" data-track-item_id=\"10.1038\/s41567-022-01671-3\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-022-01671-3\" aria-label=\"Article reference 6\" data-doi=\"10.1038\/s41567-022-01671-3\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 6\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20cavity%20quantum%20electrodynamics&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-022-01671-3&amp;volume=18&amp;pages=1048-1052&amp;publication_year=2022&amp;author=Owens%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR7\">Lodahl, P. et al. Chiral quantum optics. Nature 541, 473 <a href=\"https:\/\/doi.org\/10.1038\/nature21037\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nature21037\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nature21037<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature21037\" data-track-item_id=\"10.1038\/nature21037\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature21037\" aria-label=\"Article reference 7\" data-doi=\"10.1038\/nature21037\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017Natur.541..473L\" aria-label=\"ADS reference 7\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 7\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20quantum%20optics&amp;journal=Nature&amp;doi=10.1038%2Fnature21037&amp;volume=541&amp;publication_year=2017&amp;author=Lodahl%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR8\">De Bernardis, D., Piccioli, F. S., Rabl, P. &amp; Carusotto, I. Chiral quantum optics in the bulk of photonic quantum hall systems. PRX Quantum 4, 030306 <a href=\"https:\/\/doi.org\/10.1103\/PRXQuantum.4.030306\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PRXQuantum.4.030306\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PRXQuantum.4.030306<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PRXQuantum.4.030306\" data-track-item_id=\"10.1103\/PRXQuantum.4.030306\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPRXQuantum.4.030306\" aria-label=\"Article reference 8\" data-doi=\"10.1103\/PRXQuantum.4.030306\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 8\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20quantum%20optics%20in%20the%20bulk%20of%20photonic%20quantum%20hall%20systems&amp;journal=PRX%20Quantum&amp;doi=10.1103%2FPRXQuantum.4.030306&amp;volume=4&amp;publication_year=2023&amp;author=Bernardis%2CD&amp;author=Piccioli%2CFS&amp;author=Rabl%2CP&amp;author=Carusotto%2CI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR9\">Kamal, A., Clarke, J. &amp; Devoret, M. H. Noiseless non-reciprocity in a parametric active device. Nat. Phys. 7, 311 <a href=\"https:\/\/doi.org\/10.1038\/nphys1893\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphys1893\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphys1893<\/a> (2011).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys1893\" data-track-item_id=\"10.1038\/nphys1893\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys1893\" aria-label=\"Article reference 9\" data-doi=\"10.1038\/nphys1893\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 9\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Noiseless%20non-reciprocity%20in%20a%20parametric%20active%20device&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys1893&amp;volume=7&amp;publication_year=2011&amp;author=Kamal%2CA&amp;author=Clarke%2CJ&amp;author=Devoret%2CMH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR10\">Lau, H.-K. &amp; Clerk, A. A. Fundamental limits and non-reciprocal approaches in non-Hermitian quantum sensing. Nat. Commun. 9, 4320 <a href=\"https:\/\/doi.org\/10.1038\/s41467-018-06477-7\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41467-018-06477-7\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41467-018-06477-7<\/a> (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-018-06477-7\" data-track-item_id=\"10.1038\/s41467-018-06477-7\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-018-06477-7\" aria-label=\"Article reference 10\" data-doi=\"10.1038\/s41467-018-06477-7\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018NatCo...9.4320L\" aria-label=\"ADS reference 10\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 10\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Fundamental%20limits%20and%20non-reciprocal%20approaches%20in%20non-Hermitian%20quantum%20sensing&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-018-06477-7&amp;volume=9&amp;publication_year=2018&amp;author=Lau%2CH-K&amp;author=Clerk%2CAA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR11\">Chen, C., Jin, L. &amp; Liu, R.-B. Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system. N. J. Phys. 21, 083002 <a href=\"https:\/\/doi.org\/10.1088\/1367-2630\/ab32ab\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/1367-2630\/ab32ab\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/1367-2630\/ab32ab<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/1367-2630\/ab32ab\" data-track-item_id=\"10.1088\/1367-2630\/ab32ab\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1367-2630%2Fab32ab\" aria-label=\"Article reference 11\" data-doi=\"10.1088\/1367-2630\/ab32ab\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4170961\" aria-label=\"MathSciNet reference 11\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 11\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Sensitivity%20of%20parameter%20estimation%20near%20the%20exceptional%20point%20of%20a%20non-Hermitian%20system&amp;journal=N.%20J.%20Phys.&amp;doi=10.1088%2F1367-2630%2Fab32ab&amp;volume=21&amp;publication_year=2019&amp;author=Chen%2CC&amp;author=Jin%2CL&amp;author=Liu%2CR-B\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR12\">McDonald, A. &amp; Clerk, A. A. Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics. Nat. Commun. 11, 5382 <a href=\"https:\/\/doi.org\/10.1038\/s41467-020-19090-4\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41467-020-19090-4\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41467-020-19090-4<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-020-19090-4\" data-track-item_id=\"10.1038\/s41467-020-19090-4\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-020-19090-4\" aria-label=\"Article reference 12\" data-doi=\"10.1038\/s41467-020-19090-4\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020NatCo..11.5382M\" aria-label=\"ADS reference 12\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 12\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Exponentially-enhanced%20quantum%20sensing%20with%20non-Hermitian%20lattice%20dynamics&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-020-19090-4&amp;volume=11&amp;publication_year=2020&amp;author=McDonald%2CA&amp;author=Clerk%2CAA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR13\">Hafezi, M., Demler, E. A., Lukin, M. D. &amp; Taylor, J. M. Robust optical delay lines with topological protection. Nat. Phys. 7, 907 <a href=\"https:\/\/doi.org\/10.1038\/nphys2063\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphys2063\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphys2063<\/a> (2011).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys2063\" data-track-item_id=\"10.1038\/nphys2063\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys2063\" aria-label=\"Article reference 13\" data-doi=\"10.1038\/nphys2063\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 13\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Robust%20optical%20delay%20lines%20with%20topological%20protection&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys2063&amp;volume=7&amp;publication_year=2011&amp;author=Hafezi%2CM&amp;author=Demler%2CEA&amp;author=Lukin%2CMD&amp;author=Taylor%2CJM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR14\">Ringel, M., Pletyukhov, M. &amp; Gritsev, V. Topologically protected strongly correlated states of photons. N. J. Phys. 16, 113030 <a href=\"https:\/\/doi.org\/10.1088\/1367-2630\/16\/11\/113030\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/1367-2630\/16\/11\/113030\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/1367-2630\/16\/11\/113030<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/1367-2630\/16\/11\/113030\" data-track-item_id=\"10.1088\/1367-2630\/16\/11\/113030\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1367-2630%2F16%2F11%2F113030\" aria-label=\"Article reference 14\" data-doi=\"10.1088\/1367-2630\/16\/11\/113030\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 14\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topologically%20protected%20strongly%20correlated%20states%20of%20photons&amp;journal=N.%20J.%20Phys.&amp;doi=10.1088%2F1367-2630%2F16%2F11%2F113030&amp;volume=16&amp;publication_year=2014&amp;author=Ringel%2CM&amp;author=Pletyukhov%2CM&amp;author=Gritsev%2CV\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR15\">Peano, V., Houde, M., Marquardt, F. &amp; Clerk, A. A. Topological quantum fluctuations and traveling wave amplifiers. Phys. Rev. X 6, 041026 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.6.041026\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.6.041026\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.6.041026<\/a> (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.6.041026\" data-track-item_id=\"10.1103\/PhysRevX.6.041026\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.6.041026\" aria-label=\"Article reference 15\" data-doi=\"10.1103\/PhysRevX.6.041026\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 15\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20quantum%20fluctuations%20and%20traveling%20wave%20amplifiers&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.6.041026&amp;volume=6&amp;publication_year=2016&amp;author=Peano%2CV&amp;author=Houde%2CM&amp;author=Marquardt%2CF&amp;author=Clerk%2CAA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR16\">Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 <a href=\"https:\/\/doi.org\/10.1103\/RevModPhys.91.015006\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/RevModPhys.91.015006\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/RevModPhys.91.015006<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.91.015006\" data-track-item_id=\"10.1103\/RevModPhys.91.015006\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.91.015006\" aria-label=\"Article reference 16\" data-doi=\"10.1103\/RevModPhys.91.015006\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019RvMP...91a5006O\" aria-label=\"ADS reference 16\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3942981\" aria-label=\"MathSciNet reference 16\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 16\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20photonics&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.91.015006&amp;volume=91&amp;publication_year=2019&amp;author=Ozawa%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR17\">Wang, Y.-P. et al. Nonreciprocity and unidirectional invisibility in cavity magnonics. Phys. Rev. Lett. 123, 127202 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.123.127202\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.123.127202\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.123.127202<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.123.127202\" data-track-item_id=\"10.1103\/PhysRevLett.123.127202\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.123.127202\" aria-label=\"Article reference 17\" data-doi=\"10.1103\/PhysRevLett.123.127202\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019PhRvL.123l7202W\" aria-label=\"ADS reference 17\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 17\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocity%20and%20unidirectional%20invisibility%20in%20cavity%20magnonics&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.123.127202&amp;volume=123&amp;publication_year=2019&amp;author=Wang%2CY-P\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR18\">Zhu, N., Han, X., Zou, C.-L., Xu, M. &amp; Tang, H. X. Magnon\u2013photon strong coupling for tunable microwave circulators. Phys. Rev. A 101, 043842 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.101.043842\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevA.101.043842\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevA.101.043842<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.101.043842\" data-track-item_id=\"10.1103\/PhysRevA.101.043842\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.101.043842\" aria-label=\"Article reference 18\" data-doi=\"10.1103\/PhysRevA.101.043842\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PhRvA.101d3842Z\" aria-label=\"ADS reference 18\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 18\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Magnon%E2%80%93photon%20strong%20coupling%20for%20tunable%20microwave%20circulators&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.101.043842&amp;volume=101&amp;publication_year=2020&amp;author=Zhu%2CN&amp;author=Han%2CX&amp;author=Zou%2CC-L&amp;author=Xu%2CM&amp;author=Tang%2CHX\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR19\">Sounas, D. L. &amp; Al\u00f9, A. Non-reciprocal photonics based on time modulation. Nat. Photon. 11, 774 <a href=\"https:\/\/doi.org\/10.1038\/s41566-017-0051-x\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41566-017-0051-x\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41566-017-0051-x<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41566-017-0051-x\" data-track-item_id=\"10.1038\/s41566-017-0051-x\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41566-017-0051-x\" aria-label=\"Article reference 19\" data-doi=\"10.1038\/s41566-017-0051-x\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017NaPho..11..774S\" aria-label=\"ADS reference 19\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 19\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Non-reciprocal%20photonics%20based%20on%20time%20modulation&amp;journal=Nat.%20Photon.&amp;doi=10.1038%2Fs41566-017-0051-x&amp;volume=11&amp;publication_year=2017&amp;author=Sounas%2CDL&amp;author=Al%C3%B9%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR20\">Estep, N. A., Sounas, D. L., Soric, J. &amp; Al\u00fa, A. Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops. Nat. Phys. 10, 923 <a href=\"https:\/\/doi.org\/10.1038\/nphys3134\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphys3134\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphys3134<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys3134\" data-track-item_id=\"10.1038\/nphys3134\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys3134\" aria-label=\"Article reference 20\" data-doi=\"10.1038\/nphys3134\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 20\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Magnetic-free%20non-reciprocity%20and%20isolation%20based%20on%20parametrically%20modulated%20coupled-resonator%20loops&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys3134&amp;volume=10&amp;publication_year=2014&amp;author=Estep%2CNA&amp;author=Sounas%2CDL&amp;author=Soric%2CJ&amp;author=Al%C3%BA%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR21\">Tzuang, L. D., Fang, K., Nussenzveig, P., Fan, S. &amp; Lipson, M. Non-reciprocal phase shift induced by an effective magnetic flux for light. Nat. Photon. 8, 701 <a href=\"https:\/\/doi.org\/10.1038\/nphoton.2014.177\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphoton.2014.177\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphoton.2014.177<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphoton.2014.177\" data-track-item_id=\"10.1038\/nphoton.2014.177\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphoton.2014.177\" aria-label=\"Article reference 21\" data-doi=\"10.1038\/nphoton.2014.177\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014NaPho...8..701T\" aria-label=\"ADS reference 21\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 21\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Non-reciprocal%20phase%20shift%20induced%20by%20an%20effective%20magnetic%20flux%20for%20light&amp;journal=Nat.%20Photon.&amp;doi=10.1038%2Fnphoton.2014.177&amp;volume=8&amp;publication_year=2014&amp;author=Tzuang%2CLD&amp;author=Fang%2CK&amp;author=Nussenzveig%2CP&amp;author=Fan%2CS&amp;author=Lipson%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR22\">Fang, K., Yu, Z. &amp; Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photon. 6, 782 <a href=\"https:\/\/doi.org\/10.1038\/nphoton.2012.236\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphoton.2012.236\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphoton.2012.236<\/a> (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphoton.2012.236\" data-track-item_id=\"10.1038\/nphoton.2012.236\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphoton.2012.236\" aria-label=\"Article reference 22\" data-doi=\"10.1038\/nphoton.2012.236\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2012NaPho...6..782F\" aria-label=\"ADS reference 22\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 22\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Realizing%20effective%20magnetic%20field%20for%20photons%20by%20controlling%20the%20phase%20of%20dynamic%20modulation&amp;journal=Nat.%20Photon.&amp;doi=10.1038%2Fnphoton.2012.236&amp;volume=6&amp;publication_year=2012&amp;author=Fang%2CK&amp;author=Yu%2CZ&amp;author=Fan%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR23\">Roushan, P. et al. Chiral ground-state currents of interacting photons in a synthetic magnetic field. Nat. Phys. 13, 146\u2013151 <a href=\"https:\/\/doi.org\/10.1038\/nphys3930\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphys3930\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphys3930<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys3930\" data-track-item_id=\"10.1038\/nphys3930\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys3930\" aria-label=\"Article reference 23\" data-doi=\"10.1038\/nphys3930\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 23\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20ground-state%20currents%20of%20interacting%20photons%20in%20a%20synthetic%20magnetic%20field&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys3930&amp;volume=13&amp;pages=146-151&amp;publication_year=2017&amp;author=Roushan%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR24\">Rosen, I. et al. A synthetic magnetic vector potential in a 2D superconducting qubit array. Nat. Phys. 20, 1881\u20131887 <a href=\"https:\/\/doi.org\/10.1038\/s41567-024-02661-3\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41567-024-02661-3\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41567-024-02661-3<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-024-02661-3\" data-track-item_id=\"10.1038\/s41567-024-02661-3\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-024-02661-3\" aria-label=\"Article reference 24\" data-doi=\"10.1038\/s41567-024-02661-3\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 24\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20synthetic%20magnetic%20vector%20potential%20in%20a%202D%20superconducting%20qubit%20array&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-024-02661-3&amp;volume=20&amp;pages=1881-1887&amp;publication_year=2024&amp;author=Rosen%2CI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR25\">Regensburger, A. et al. Parity-time synthetic photonic lattices. Nature 488, 167 <a href=\"https:\/\/doi.org\/10.1038\/nature11298\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nature11298\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nature11298<\/a> (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature11298\" data-track-item_id=\"10.1038\/nature11298\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature11298\" aria-label=\"Article reference 25\" data-doi=\"10.1038\/nature11298\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2012Natur.488..167R\" aria-label=\"ADS reference 25\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 25\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Parity-time%20synthetic%20photonic%20lattices&amp;journal=Nature&amp;doi=10.1038%2Fnature11298&amp;volume=488&amp;publication_year=2012&amp;author=Regensburger%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR26\">Miri, M.-A. &amp; Al\u00fa, A. Exceptional points in optics and photonics. Science 363, eaar7709 <a href=\"https:\/\/doi.org\/10.1126\/science.aar7709\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1126\/science.aar7709\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1126\/science.aar7709<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.aar7709\" data-track-item_id=\"10.1126\/science.aar7709\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.aar7709\" aria-label=\"Article reference 26\" data-doi=\"10.1126\/science.aar7709\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3889190\" aria-label=\"MathSciNet reference 26\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 26\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Exceptional%20points%20in%20optics%20and%20photonics&amp;journal=Science&amp;doi=10.1126%2Fscience.aar7709&amp;volume=363&amp;publication_year=2019&amp;author=Miri%2CM-A&amp;author=Al%C3%BA%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR27\">Hua, S. et al. Demonstration of a chip-based optical isolator with parametric amplification. Nat. Commun. 7, 13657 <a href=\"https:\/\/doi.org\/10.1038\/ncomms13657\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/ncomms13657\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/ncomms13657<\/a> (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/ncomms13657\" data-track-item_id=\"10.1038\/ncomms13657\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fncomms13657\" aria-label=\"Article reference 27\" data-doi=\"10.1038\/ncomms13657\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016NatCo...713657H\" aria-label=\"ADS reference 27\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 27\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Demonstration%20of%20a%20chip-based%20optical%20isolator%20with%20parametric%20amplification&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fncomms13657&amp;volume=7&amp;publication_year=2016&amp;author=Hua%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR28\">Huang, X., Lu, C., Liang, C., Tao, H. &amp; Liu, Y.-C. Loss-induced nonreciprocity. Light Sci. Appl. 10, 30 <a href=\"https:\/\/doi.org\/10.1038\/s41377-021-00464-2\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41377-021-00464-2\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41377-021-00464-2<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41377-021-00464-2\" data-track-item_id=\"10.1038\/s41377-021-00464-2\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41377-021-00464-2\" aria-label=\"Article reference 28\" data-doi=\"10.1038\/s41377-021-00464-2\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021LSA....10...30H\" aria-label=\"ADS reference 28\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 28\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Loss-induced%20nonreciprocity&amp;journal=Light%20Sci.%20Appl.&amp;doi=10.1038%2Fs41377-021-00464-2&amp;volume=10&amp;publication_year=2021&amp;author=Huang%2CX&amp;author=Lu%2CC&amp;author=Liang%2CC&amp;author=Tao%2CH&amp;author=Liu%2CY-C\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR29\">Barzanjeh, S. et al. Mechanical on-chip microwave circulator. Nat. Commun. 8, 953 <a href=\"https:\/\/doi.org\/10.1038\/s41467-017-01304-x\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41467-017-01304-x\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41467-017-01304-x<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-017-01304-x\" data-track-item_id=\"10.1038\/s41467-017-01304-x\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-017-01304-x\" aria-label=\"Article reference 29\" data-doi=\"10.1038\/s41467-017-01304-x\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017NatCo...8..953B\" aria-label=\"ADS reference 29\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 29\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Mechanical%20on-chip%20microwave%20circulator&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-017-01304-x&amp;volume=8&amp;publication_year=2017&amp;author=Barzanjeh%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR30\">Bernier, N. R. et al. Nonreciprocal reconfigurable microwave optomechanical circuit. Nat. Commun. 8, 604 <a href=\"https:\/\/doi.org\/10.1038\/s41467-017-00447-1\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41467-017-00447-1\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41467-017-00447-1<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-017-00447-1\" data-track-item_id=\"10.1038\/s41467-017-00447-1\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-017-00447-1\" aria-label=\"Article reference 30\" data-doi=\"10.1038\/s41467-017-00447-1\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017NatCo...8..604B\" aria-label=\"ADS reference 30\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 30\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocal%20reconfigurable%20microwave%20optomechanical%20circuit&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-017-00447-1&amp;volume=8&amp;publication_year=2017&amp;author=Bernier%2CNR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR31\">Malz, D. et al. Quantum-limited directional amplifiers with optomechanics. Phys. Rev. Lett. 120, 023601 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.120.023601\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.120.023601\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.120.023601<\/a> (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.120.023601\" data-track-item_id=\"10.1103\/PhysRevLett.120.023601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.120.023601\" aria-label=\"Article reference 31\" data-doi=\"10.1103\/PhysRevLett.120.023601\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018PhRvL.120b3601M\" aria-label=\"ADS reference 31\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 31\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum-limited%20directional%20amplifiers%20with%20optomechanics&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.120.023601&amp;volume=120&amp;publication_year=2018&amp;author=Malz%2CD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR32\">Mirhosseini, M., Sipahigil, A., Kalaee, M. &amp; Painter, O. Superconducting qubit to optical photon transduction. Nature 588, 599 <a href=\"https:\/\/doi.org\/10.1038\/s41586-020-3038-6\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41586-020-3038-6\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41586-020-3038-6<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-020-3038-6\" data-track-item_id=\"10.1038\/s41586-020-3038-6\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-020-3038-6\" aria-label=\"Article reference 32\" data-doi=\"10.1038\/s41586-020-3038-6\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020Natur.588..599M\" aria-label=\"ADS reference 32\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 32\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Superconducting%20qubit%20to%20optical%20photon%20transduction&amp;journal=Nature&amp;doi=10.1038%2Fs41586-020-3038-6&amp;volume=588&amp;publication_year=2020&amp;author=Mirhosseini%2CM&amp;author=Sipahigil%2CA&amp;author=Kalaee%2CM&amp;author=Painter%2CO\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR33\">Kamal, A., Roy, A., Clarke, J. &amp; Devoret, M. H. Asymmetric frequency conversion in nonlinear systems driven by a biharmonic pump. Phys. Rev. Lett. 113, 247003 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.113.247003\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.113.247003\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.113.247003<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.113.247003\" data-track-item_id=\"10.1103\/PhysRevLett.113.247003\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.113.247003\" aria-label=\"Article reference 33\" data-doi=\"10.1103\/PhysRevLett.113.247003\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvL.113x7003K\" aria-label=\"ADS reference 33\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 33\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Asymmetric%20frequency%20conversion%20in%20nonlinear%20systems%20driven%20by%20a%20biharmonic%20pump&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.113.247003&amp;volume=113&amp;publication_year=2014&amp;author=Kamal%2CA&amp;author=Roy%2CA&amp;author=Clarke%2CJ&amp;author=Devoret%2CMH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR34\">Su\u00e1rez-Forero, D., Jalali Mehrabad, M., Vega, C., Gonz\u00e1lez-Tudela, A. &amp; Hafezi, M. Chiral quantum optics: recent developments and future directions. PRX Quantum 6, 020101 <a href=\"https:\/\/doi.org\/10.1103\/PRXQuantum.6.020101\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PRXQuantum.6.020101\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PRXQuantum.6.020101<\/a> (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PRXQuantum.6.020101\" data-track-item_id=\"10.1103\/PRXQuantum.6.020101\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPRXQuantum.6.020101\" aria-label=\"Article reference 34\" data-doi=\"10.1103\/PRXQuantum.6.020101\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2025PRXQ....6b0101S\" aria-label=\"ADS reference 34\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 34\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20quantum%20optics%3A%20recent%20developments%20and%20future%20directions&amp;journal=PRX%20Quantum&amp;doi=10.1103%2FPRXQuantum.6.020101&amp;volume=6&amp;publication_year=2025&amp;author=Su%C3%A1rez-Forero%2CD&amp;author=Jalali%20Mehrabad%2CM&amp;author=Vega%2CC&amp;author=Gonz%C3%A1lez-Tudela%2CA&amp;author=Hafezi%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR35\">Aspelmeyer, M., Kippenberg, T. J. &amp; Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391 <a href=\"https:\/\/doi.org\/10.1103\/RevModPhys.86.1391\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/RevModPhys.86.1391\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/RevModPhys.86.1391<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.86.1391\" data-track-item_id=\"10.1103\/RevModPhys.86.1391\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.86.1391\" aria-label=\"Article reference 35\" data-doi=\"10.1103\/RevModPhys.86.1391\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014RvMP...86.1391A\" aria-label=\"ADS reference 35\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 35\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Cavity%20optomechanics&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.86.1391&amp;volume=86&amp;publication_year=2014&amp;author=Aspelmeyer%2CM&amp;author=Kippenberg%2CTJ&amp;author=Marquardt%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR36\">Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. &amp; Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.69.062320\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevA.69.062320\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevA.69.062320<\/a> (2004).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.69.062320\" data-track-item_id=\"10.1103\/PhysRevA.69.062320\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.69.062320\" aria-label=\"Article reference 36\" data-doi=\"10.1103\/PhysRevA.69.062320\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2004PhRvA..69f2320B\" aria-label=\"ADS reference 36\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 36\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Cavity%20quantum%20electrodynamics%20for%20superconducting%20electrical%20circuits%3A%20an%20architecture%20for%20quantum%20computation&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.69.062320&amp;volume=69&amp;publication_year=2004&amp;author=Blais%2CA&amp;author=Huang%2CR-S&amp;author=Wallraff%2CA&amp;author=Girvin%2CSM&amp;author=Schoelkopf%2CRJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR37\">Gu, X., Kockum, A. F., Miranowicz, A., xi Liu, Y. &amp; Nori, F. Microwave photonics with superconducting quantum circuits. Phys. Rep. 718\u2013719, 1 <a href=\"https:\/\/doi.org\/10.1016\/j.physrep.2017.10.002\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1016\/j.physrep.2017.10.002\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1016\/j.physrep.2017.10.002<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.physrep.2017.10.002\" data-track-item_id=\"10.1016\/j.physrep.2017.10.002\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.physrep.2017.10.002\" aria-label=\"Article reference 37\" data-doi=\"10.1016\/j.physrep.2017.10.002\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhR...718....1G\" aria-label=\"ADS reference 37\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=3732441\" aria-label=\"MathSciNet reference 37\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 37\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Microwave%20photonics%20with%20superconducting%20quantum%20circuits&amp;journal=Phys.%20Rep.&amp;doi=10.1016%2Fj.physrep.2017.10.002&amp;volume=718%E2%80%93719&amp;publication_year=2017&amp;author=Gu%2CX&amp;author=Kockum%2CAF&amp;author=Miranowicz%2CA&amp;author=xi%20Liu%2CY&amp;author=Nori%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR38\">Blais, A., Grimsmo, A. L., Girvin, S. M. &amp; Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 <a href=\"https:\/\/doi.org\/10.1103\/RevModPhys.93.025005\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/RevModPhys.93.025005\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/RevModPhys.93.025005<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/RevModPhys.93.025005\" data-track-item_id=\"10.1103\/RevModPhys.93.025005\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.93.025005\" aria-label=\"Article reference 38\" data-doi=\"10.1103\/RevModPhys.93.025005\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021RvMP...93b5005B\" aria-label=\"ADS reference 38\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4290949\" aria-label=\"MathSciNet reference 38\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 38\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Circuit%20quantum%20electrodynamics&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.93.025005&amp;volume=93&amp;publication_year=2021&amp;author=Blais%2CA&amp;author=Grimsmo%2CAL&amp;author=Girvin%2CSM&amp;author=Wallraff%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR39\">Zhang, X., Galda, A., Han, X., Jin, D. &amp; Vinokur, V. M. Broadband nonreciprocity enabled by strong coupling of magnons and microwave photons. Phys. Rev. Appl. 13, 044039 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevApplied.13.044039\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevApplied.13.044039\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevApplied.13.044039<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevApplied.13.044039\" data-track-item_id=\"10.1103\/PhysRevApplied.13.044039\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevApplied.13.044039\" aria-label=\"Article reference 39\" data-doi=\"10.1103\/PhysRevApplied.13.044039\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PhRvP..13d4039Z\" aria-label=\"ADS reference 39\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 39\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Broadband%20nonreciprocity%20enabled%20by%20strong%20coupling%20of%20magnons%20and%20microwave%20photons&amp;journal=Phys.%20Rev.%20Appl.&amp;doi=10.1103%2FPhysRevApplied.13.044039&amp;volume=13&amp;publication_year=2020&amp;author=Zhang%2CX&amp;author=Galda%2CA&amp;author=Han%2CX&amp;author=Jin%2CD&amp;author=Vinokur%2CVM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR40\">Kim, M., Tabesh, A., Zegray, T., Barzanjeh, S. &amp; Hu, C.-M. Nonreciprocity in cavity magnonics at millikelvin temperature. J. Appl. Phys. 135, 063904 <a href=\"https:\/\/doi.org\/10.1063\/5.0176462\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1063\/5.0176462\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1063\/5.0176462<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1063\/5.0176462\" data-track-item_id=\"10.1063\/5.0176462\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1063%2F5.0176462\" aria-label=\"Article reference 40\" data-doi=\"10.1063\/5.0176462\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024JAP...135f3904K\" aria-label=\"ADS reference 40\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 40\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocity%20in%20cavity%20magnonics%20at%20millikelvin%20temperature&amp;journal=J.%20Appl.%20Phys.&amp;doi=10.1063%2F5.0176462&amp;volume=135&amp;publication_year=2024&amp;author=Kim%2CM&amp;author=Tabesh%2CA&amp;author=Zegray%2CT&amp;author=Barzanjeh%2CS&amp;author=Hu%2CC-M\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR41\">Koch, J., Houck, A. A., Hur, K. L. &amp; Girvin, S. M. Time-reversal-symmetry breaking in circuit-QED-based photon lattices. Phys. Rev. A 82, 043811 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.82.043811\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevA.82.043811\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevA.82.043811<\/a> (2010).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.82.043811\" data-track-item_id=\"10.1103\/PhysRevA.82.043811\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.82.043811\" aria-label=\"Article reference 41\" data-doi=\"10.1103\/PhysRevA.82.043811\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2010PhRvA..82d3811K\" aria-label=\"ADS reference 41\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 41\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Time-reversal-symmetry%20breaking%20in%20circuit-QED-based%20photon%20lattices&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.82.043811&amp;volume=82&amp;publication_year=2010&amp;author=Koch%2CJ&amp;author=Houck%2CAA&amp;author=Hur%2CKL&amp;author=Girvin%2CSM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR42\">Navarathna, R. et al. Passive superconducting circulator on a chip. Phys. Rev. Lett. 130, 037001 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.130.037001\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.130.037001\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.130.037001<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.130.037001\" data-track-item_id=\"10.1103\/PhysRevLett.130.037001\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.130.037001\" aria-label=\"Article reference 42\" data-doi=\"10.1103\/PhysRevLett.130.037001\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023PhRvL.130c7001N\" aria-label=\"ADS reference 42\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4613314\" aria-label=\"MathSciNet reference 42\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 42\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Passive%20superconducting%20circulator%20on%20a%20chip&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.130.037001&amp;volume=130&amp;publication_year=2023&amp;author=Navarathna%2CR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR43\">Landgraf, J., Peano, V. &amp; Marquardt, F. Automated discovery of coupled-mode setups. Phys. Rev. X 15, 021038 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.15.021038\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.15.021038\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.15.021038<\/a> (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.15.021038\" data-track-item_id=\"10.1103\/PhysRevX.15.021038\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.15.021038\" aria-label=\"Article reference 43\" data-doi=\"10.1103\/PhysRevX.15.021038\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 43\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Automated%20discovery%20of%20coupled-mode%20setups&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.15.021038&amp;volume=15&amp;publication_year=2025&amp;author=Landgraf%2CJ&amp;author=Peano%2CV&amp;author=Marquardt%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR44\">Metelmann, A. &amp; Clerk, A. A. Nonreciprocal photon transmission and amplification via reservoir engineering. Phys. Rev. X 5, 021025 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.5.021025\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.5.021025\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.5.021025<\/a> (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.5.021025\" data-track-item_id=\"10.1103\/PhysRevX.5.021025\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.5.021025\" aria-label=\"Article reference 44\" data-doi=\"10.1103\/PhysRevX.5.021025\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 44\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocal%20photon%20transmission%20and%20amplification%20via%20reservoir%20engineering&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.5.021025&amp;volume=5&amp;publication_year=2015&amp;author=Metelmann%2CA&amp;author=Clerk%2CAA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR45\">Metelmann, A. &amp; Clerk, A. A. Quantum-limited amplification via reservoir engineering. Phys. Rev. Lett. 112, 133904 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.112.133904\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.112.133904\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.112.133904<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.112.133904\" data-track-item_id=\"10.1103\/PhysRevLett.112.133904\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.112.133904\" aria-label=\"Article reference 45\" data-doi=\"10.1103\/PhysRevLett.112.133904\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvL.112m3904M\" aria-label=\"ADS reference 45\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 45\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum-limited%20amplification%20via%20reservoir%20engineering&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.112.133904&amp;volume=112&amp;publication_year=2014&amp;author=Metelmann%2CA&amp;author=Clerk%2CAA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR46\">Wang, Y.-X. &amp; Clerk, A. A. Non-Hermitian dynamics without dissipation in quantum systems. Phys. Rev. A 99, 063834 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.99.063834\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevA.99.063834\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevA.99.063834<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.99.063834\" data-track-item_id=\"10.1103\/PhysRevA.99.063834\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.99.063834\" aria-label=\"Article reference 46\" data-doi=\"10.1103\/PhysRevA.99.063834\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019PhRvA..99f3834W\" aria-label=\"ADS reference 46\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 46\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Non-Hermitian%20dynamics%20without%20dissipation%20in%20quantum%20systems&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.99.063834&amp;volume=99&amp;publication_year=2019&amp;author=Wang%2CY-X&amp;author=Clerk%2CAA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR47\">Kerckhoff, J., Lalumi\u00e8re, K., Chapman, B. J., Blais, A. &amp; Lehnert, K. W. On-chip superconducting microwave circulator from synthetic rotation. Phys. Rev. Appl. 4, 034002 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevApplied.4.034002\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevApplied.4.034002\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevApplied.4.034002<\/a> (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevApplied.4.034002\" data-track-item_id=\"10.1103\/PhysRevApplied.4.034002\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevApplied.4.034002\" aria-label=\"Article reference 47\" data-doi=\"10.1103\/PhysRevApplied.4.034002\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015PhRvP...4c4002K\" aria-label=\"ADS reference 47\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 47\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=On-chip%20superconducting%20microwave%20circulator%20from%20synthetic%20rotation&amp;journal=Phys.%20Rev.%20Appl.&amp;doi=10.1103%2FPhysRevApplied.4.034002&amp;volume=4&amp;publication_year=2015&amp;author=Kerckhoff%2CJ&amp;author=Lalumi%C3%A8re%2CK&amp;author=Chapman%2CBJ&amp;author=Blais%2CA&amp;author=Lehnert%2CKW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR48\">Rosenthal, E. I., Chapman, B. J., Higginbotham, A. P., Kerckhoff, J. &amp; Lehnert, K. W. Breaking Lorentz reciprocity with frequency conversion and delay. Phys. Rev. Lett. 119, 147703 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.119.147703\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.119.147703\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.119.147703<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.119.147703\" data-track-item_id=\"10.1103\/PhysRevLett.119.147703\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.119.147703\" aria-label=\"Article reference 48\" data-doi=\"10.1103\/PhysRevLett.119.147703\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhRvL.119n7703R\" aria-label=\"ADS reference 48\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 48\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Breaking%20Lorentz%20reciprocity%20with%20frequency%20conversion%20and%20delay&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.119.147703&amp;volume=119&amp;publication_year=2017&amp;author=Rosenthal%2CEI&amp;author=Chapman%2CBJ&amp;author=Higginbotham%2CAP&amp;author=Kerckhoff%2CJ&amp;author=Lehnert%2CKW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR49\">Lecocq, F. et al. Nonreciprocal microwave signal processing with a field-programmable Josephson amplifier. Phys. Rev. Appl. 7, 024028 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevApplied.7.024028\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevApplied.7.024028\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevApplied.7.024028<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevApplied.7.024028\" data-track-item_id=\"10.1103\/PhysRevApplied.7.024028\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevApplied.7.024028\" aria-label=\"Article reference 49\" data-doi=\"10.1103\/PhysRevApplied.7.024028\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhRvP...7b4028L\" aria-label=\"ADS reference 49\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 49\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocal%20microwave%20signal%20processing%20with%20a%20field-programmable%20Josephson%20amplifier&amp;journal=Phys.%20Rev.%20Appl.&amp;doi=10.1103%2FPhysRevApplied.7.024028&amp;volume=7&amp;publication_year=2017&amp;author=Lecocq%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR50\">Abdo, B., Sliwa, K., Frunzio, L. &amp; Devoret, M. Directional amplification with a Josephson circuit. Phys. Rev. X 3, 031001 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.3.031001\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.3.031001\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.3.031001<\/a> (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.3.031001\" data-track-item_id=\"10.1103\/PhysRevX.3.031001\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.3.031001\" aria-label=\"Article reference 50\" data-doi=\"10.1103\/PhysRevX.3.031001\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 50\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Directional%20amplification%20with%20a%20Josephson%20circuit&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.3.031001&amp;volume=3&amp;publication_year=2013&amp;author=Abdo%2CB&amp;author=Sliwa%2CK&amp;author=Frunzio%2CL&amp;author=Devoret%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR51\">Fang, K. et al. Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering. Nat. Phys. 13, 465 <a href=\"https:\/\/doi.org\/10.1038\/nphys4009\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphys4009\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphys4009<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys4009\" data-track-item_id=\"10.1038\/nphys4009\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys4009\" aria-label=\"Article reference 51\" data-doi=\"10.1038\/nphys4009\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 51\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Generalized%20non-reciprocity%20in%20an%20optomechanical%20circuit%20via%20synthetic%20magnetism%20and%20reservoir%20engineering&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys4009&amp;volume=13&amp;publication_year=2017&amp;author=Fang%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR52\">Ranzani, L. &amp; Aumentado, J. Graph-based analysis of nonreciprocity in coupled-mode systems. N. J. Phys. 17, 023024 <a href=\"https:\/\/doi.org\/10.1088\/1367-2630\/17\/2\/023024\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/1367-2630\/17\/2\/023024\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/1367-2630\/17\/2\/023024<\/a> (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/1367-2630\/17\/2\/023024\" data-track-item_id=\"10.1088\/1367-2630\/17\/2\/023024\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1367-2630%2F17%2F2%2F023024\" aria-label=\"Article reference 52\" data-doi=\"10.1088\/1367-2630\/17\/2\/023024\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 52\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Graph-based%20analysis%20of%20nonreciprocity%20in%20coupled-mode%20systems&amp;journal=N.%20J.%20Phys.&amp;doi=10.1088%2F1367-2630%2F17%2F2%2F023024&amp;volume=17&amp;publication_year=2015&amp;author=Ranzani%2CL&amp;author=Aumentado%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR53\">Sliwa, K. M. et al. Reconfigurable Josephson circulator\/directional amplifier. Phys. Rev. X 5, 041020 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.5.041020\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.5.041020\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.5.041020<\/a> (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.5.041020\" data-track-item_id=\"10.1103\/PhysRevX.5.041020\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.5.041020\" aria-label=\"Article reference 53\" data-doi=\"10.1103\/PhysRevX.5.041020\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 53\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Reconfigurable%20Josephson%20circulator%2Fdirectional%20amplifier&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.5.041020&amp;volume=5&amp;publication_year=2015&amp;author=Sliwa%2CKM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR54\">Naaman, O. &amp; Aumentado, J. Synthesis of parametrically coupled networks. PRX Quantum 3, 020201 <a href=\"https:\/\/doi.org\/10.1103\/PRXQuantum.3.020201\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PRXQuantum.3.020201\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PRXQuantum.3.020201<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PRXQuantum.3.020201\" data-track-item_id=\"10.1103\/PRXQuantum.3.020201\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPRXQuantum.3.020201\" aria-label=\"Article reference 54\" data-doi=\"10.1103\/PRXQuantum.3.020201\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022PRXQ....3b0201N\" aria-label=\"ADS reference 54\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 54\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Synthesis%20of%20parametrically%20coupled%20networks&amp;journal=PRX%20Quantum&amp;doi=10.1103%2FPRXQuantum.3.020201&amp;volume=3&amp;publication_year=2022&amp;author=Naaman%2CO&amp;author=Aumentado%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR55\">Kwende, R., White, T. &amp; Naaman, O. Josephson parametric circulator with same-frequency signal ports, 200 mHz bandwidth, and high dynamic range. Appl. Phys. Lett. 122, 224001 <a href=\"https:\/\/doi.org\/10.1063\/5.0150427\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1063\/5.0150427\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1063\/5.0150427<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1063\/5.0150427\" data-track-item_id=\"10.1063\/5.0150427\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1063%2F5.0150427\" aria-label=\"Article reference 55\" data-doi=\"10.1063\/5.0150427\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023ApPhL.122v4001K\" aria-label=\"ADS reference 55\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 55\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Josephson%20parametric%20circulator%20with%20same-frequency%20signal%20ports%2C%20200%20mHz%20bandwidth%2C%20and%20high%20dynamic%20range&amp;journal=Appl.%20Phys.%20Lett.&amp;doi=10.1063%2F5.0150427&amp;volume=122&amp;publication_year=2023&amp;author=Kwende%2CR&amp;author=White%2CT&amp;author=Naaman%2CO\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR56\">Carmichael, H. J. Quantum trajectory theory for cascaded open systems. Phys. Rev. Lett. 70, 2273 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.70.2273\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.70.2273\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.70.2273<\/a> (1993).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.70.2273\" data-track-item_id=\"10.1103\/PhysRevLett.70.2273\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.70.2273\" aria-label=\"Article reference 56\" data-doi=\"10.1103\/PhysRevLett.70.2273\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1993PhRvL..70.2273C\" aria-label=\"ADS reference 56\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 56\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20trajectory%20theory%20for%20cascaded%20open%20systems&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.70.2273&amp;volume=70&amp;publication_year=1993&amp;author=Carmichael%2CHJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR57\">Stannigel, K., Rabl, P. &amp; Zoller, P. Driven-dissipative preparation of entangled states in cascaded quantum-optical networks. N. J. Phys. 14, 06301 <a href=\"https:\/\/doi.org\/10.1088\/1367-2630\/14\/6\/063014\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/1367-2630\/14\/6\/063014\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/1367-2630\/14\/6\/063014<\/a> (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/1367-2630\/14\/6\/063014\" data-track-item_id=\"10.1088\/1367-2630\/14\/6\/063014\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1367-2630%2F14%2F6%2F063014\" aria-label=\"Article reference 57\" data-doi=\"10.1088\/1367-2630\/14\/6\/063014\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 57\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Driven-dissipative%20preparation%20of%20entangled%20states%20in%20cascaded%20quantum-optical%20networks&amp;journal=N.%20J.%20Phys.&amp;doi=10.1088%2F1367-2630%2F14%2F6%2F063014&amp;volume=14&amp;publication_year=2012&amp;author=Stannigel%2CK&amp;author=Rabl%2CP&amp;author=Zoller%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR58\">Peano, V., Brendel, C., Schmidt, M. &amp; Marquardt, F. Topological phases of sound and light. Phys. Rev. X 5, 031011 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.5.031011\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.5.031011\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.5.031011<\/a> (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.5.031011\" data-track-item_id=\"10.1103\/PhysRevX.5.031011\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.5.031011\" aria-label=\"Article reference 58\" data-doi=\"10.1103\/PhysRevX.5.031011\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 58\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20phases%20of%20sound%20and%20light&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.5.031011&amp;volume=5&amp;publication_year=2015&amp;author=Peano%2CV&amp;author=Brendel%2CC&amp;author=Schmidt%2CM&amp;author=Marquardt%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR59\">Hafezi, M. &amp; Rabl, P. Optomechanically induced non-reciprocity in microring resonators. Opt. Express 20, 7672 <a href=\"https:\/\/doi.org\/10.1364\/OE.20.007672\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1364\/OE.20.007672\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1364\/OE.20.007672<\/a> (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1364\/OE.20.007672\" data-track-item_id=\"10.1364\/OE.20.007672\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1364%2FOE.20.007672\" aria-label=\"Article reference 59\" data-doi=\"10.1364\/OE.20.007672\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2012OExpr..20.7672H\" aria-label=\"ADS reference 59\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 59\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optomechanically%20induced%20non-reciprocity%20in%20microring%20resonators&amp;journal=Opt.%20Express&amp;doi=10.1364%2FOE.20.007672&amp;volume=20&amp;publication_year=2012&amp;author=Hafezi%2CM&amp;author=Rabl%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR60\">Ruesink, F., Miri, M.-A., Al\u00f9, A. &amp; Verhagen, E. Nonreciprocity and magnetic-free isolation based on optomechanical interactions. Nat. Commun. 7, 13662 <a href=\"https:\/\/doi.org\/10.1038\/ncomms13662\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/ncomms13662\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/ncomms13662<\/a> (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/ncomms13662\" data-track-item_id=\"10.1038\/ncomms13662\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fncomms13662\" aria-label=\"Article reference 60\" data-doi=\"10.1038\/ncomms13662\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016NatCo...713662R\" aria-label=\"ADS reference 60\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 60\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocity%20and%20magnetic-free%20isolation%20based%20on%20optomechanical%20interactions&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fncomms13662&amp;volume=7&amp;publication_year=2016&amp;author=Ruesink%2CF&amp;author=Miri%2CM-A&amp;author=Al%C3%B9%2CA&amp;author=Verhagen%2CE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR61\">Kim, J., Kuzyk, M. C., Han, K., Wang, H. &amp; Bahl, G. Non-reciprocal Brillouin scattering induced transparency. Nat. Phys. 11, 275 <a href=\"https:\/\/doi.org\/10.1038\/nphys3236\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphys3236\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphys3236<\/a> (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphys3236\" data-track-item_id=\"10.1038\/nphys3236\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphys3236\" aria-label=\"Article reference 61\" data-doi=\"10.1038\/nphys3236\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 61\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Non-reciprocal%20Brillouin%20scattering%20induced%20transparency&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fnphys3236&amp;volume=11&amp;publication_year=2015&amp;author=Kim%2CJ&amp;author=Kuzyk%2CMC&amp;author=Han%2CK&amp;author=Wang%2CH&amp;author=Bahl%2CG\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR62\">Shen, Z. et al. Experimental realization of optomechanically induced non-reciprocity. Nat. Photon. 10, 657 <a href=\"https:\/\/doi.org\/10.1038\/nphoton.2016.161\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nphoton.2016.161\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nphoton.2016.161<\/a> (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nphoton.2016.161\" data-track-item_id=\"10.1038\/nphoton.2016.161\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnphoton.2016.161\" aria-label=\"Article reference 62\" data-doi=\"10.1038\/nphoton.2016.161\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016NaPho..10..657S\" aria-label=\"ADS reference 62\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 62\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Experimental%20realization%20of%20optomechanically%20induced%20non-reciprocity&amp;journal=Nat.%20Photon.&amp;doi=10.1038%2Fnphoton.2016.161&amp;volume=10&amp;publication_year=2016&amp;author=Shen%2CZ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR63\">Wanjura, C. C. et al. Quadrature nonreciprocity in bosonic networks without breaking time-reversal symmetry. Nat. Phys. 19, 1429 <a href=\"https:\/\/doi.org\/10.1038\/s41567-023-02128-x\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41567-023-02128-x\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41567-023-02128-x<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-023-02128-x\" data-track-item_id=\"10.1038\/s41567-023-02128-x\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-023-02128-x\" aria-label=\"Article reference 63\" data-doi=\"10.1038\/s41567-023-02128-x\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 63\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quadrature%20nonreciprocity%20in%20bosonic%20networks%20without%20breaking%20time-reversal%20symmetry&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-023-02128-x&amp;volume=19&amp;publication_year=2023&amp;author=Wanjura%2CCC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR64\">Slim, J. J. et al. Optomechanical realization of the bosonic Kitaev chain. Nature 627, 767 <a href=\"https:\/\/doi.org\/10.1038\/s41586-024-07174-w\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41586-024-07174-w\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41586-024-07174-w<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-024-07174-w\" data-track-item_id=\"10.1038\/s41586-024-07174-w\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-024-07174-w\" aria-label=\"Article reference 64\" data-doi=\"10.1038\/s41586-024-07174-w\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024Natur.627..767S\" aria-label=\"ADS reference 64\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 64\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optomechanical%20realization%20of%20the%20bosonic%20Kitaev%20chain&amp;journal=Nature&amp;doi=10.1038%2Fs41586-024-07174-w&amp;volume=627&amp;publication_year=2024&amp;author=Slim%2CJJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR65\">Busnaina J. H. et al. Quantum simulation of the bosonic Kitaev chain. Nat. Commun. 15, 3065 <a href=\"https:\/\/doi.org\/10.1038\/s41467-024-47186-8\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41467-024-47186-8\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41467-024-47186-8<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-024-47186-8\" data-track-item_id=\"10.1038\/s41467-024-47186-8\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-024-47186-8\" aria-label=\"Article reference 65\" data-doi=\"10.1038\/s41467-024-47186-8\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024NatCo..15.3065B\" aria-label=\"ADS reference 65\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 65\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20simulation%20of%20the%20bosonic%20Kitaev%20chain&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-024-47186-8&amp;volume=15&amp;publication_year=2024&amp;author=Busnaina%2CJH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR66\">S\u00f6llner, I. et al. Deterministic photon-emitter coupling in chiral photonic circuits. Nat. Nanotechnol. 10, 775\u2013778 <a href=\"https:\/\/doi.org\/10.1038\/nnano.2015.159\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nnano.2015.159\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nnano.2015.159<\/a> (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nnano.2015.159\" data-track-item_id=\"10.1038\/nnano.2015.159\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnnano.2015.159\" aria-label=\"Article reference 66\" data-doi=\"10.1038\/nnano.2015.159\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015NatNa..10..775S\" aria-label=\"ADS reference 66\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 66\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Deterministic%20photon-emitter%20coupling%20in%20chiral%20photonic%20circuits&amp;journal=Nat.%20Nanotechnol.&amp;doi=10.1038%2Fnnano.2015.159&amp;volume=10&amp;pages=775-778&amp;publication_year=2015&amp;author=S%C3%B6llner%2CI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR67\">Petersen, J., Volz, J. &amp; Rauschenbeutel, A. Chiral nanophotonic waveguide interface based on spin\u2013orbit interaction of light. Science 346, 67 <a href=\"https:\/\/doi.org\/10.1126\/science.1257671\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1126\/science.1257671\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1126\/science.1257671<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.1257671\" data-track-item_id=\"10.1126\/science.1257671\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.1257671\" aria-label=\"Article reference 67\" data-doi=\"10.1126\/science.1257671\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014Sci...346...67P\" aria-label=\"ADS reference 67\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 67\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20nanophotonic%20waveguide%20interface%20based%20on%20spin%E2%80%93orbit%20interaction%20of%20light&amp;journal=Science&amp;doi=10.1126%2Fscience.1257671&amp;volume=346&amp;publication_year=2014&amp;author=Petersen%2CJ&amp;author=Volz%2CJ&amp;author=Rauschenbeutel%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR68\">Mitsch, R., Sayrin, C., Albrecht, B., Schneeweiss, P. &amp; Rauschenbeutel, A. Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide. Nat. Commun. 5, 5713 <a href=\"https:\/\/doi.org\/10.1038\/ncomms6713\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/ncomms6713\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/ncomms6713<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/ncomms6713\" data-track-item_id=\"10.1038\/ncomms6713\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fncomms6713\" aria-label=\"Article reference 68\" data-doi=\"10.1038\/ncomms6713\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014NatCo...5.5713M\" aria-label=\"ADS reference 68\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 68\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20state-controlled%20directional%20spontaneous%20emission%20of%20photons%20into%20a%20nanophotonic%20waveguide&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fncomms6713&amp;volume=5&amp;publication_year=2014&amp;author=Mitsch%2CR&amp;author=Sayrin%2CC&amp;author=Albrecht%2CB&amp;author=Schneeweiss%2CP&amp;author=Rauschenbeutel%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR69\">Scheucher, M., Hilico, A., Will, E., Volz, J. &amp; Rauschenbeutel, A. Quantum optical circulator controlled by a single chirally coupled atom. Science 354, 1577 <a href=\"https:\/\/doi.org\/10.1126\/science.aaj2118\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1126\/science.aaj2118\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1126\/science.aaj2118<\/a> (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.aaj2118\" data-track-item_id=\"10.1126\/science.aaj2118\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.aaj2118\" aria-label=\"Article reference 69\" data-doi=\"10.1126\/science.aaj2118\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2016Sci...354.1577S\" aria-label=\"ADS reference 69\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 69\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20optical%20circulator%20controlled%20by%20a%20single%20chirally%20coupled%20atom&amp;journal=Science&amp;doi=10.1126%2Fscience.aaj2118&amp;volume=354&amp;publication_year=2016&amp;author=Scheucher%2CM&amp;author=Hilico%2CA&amp;author=Will%2CE&amp;author=Volz%2CJ&amp;author=Rauschenbeutel%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR70\">Potton, R. J. Reciprocity in optics. Rep. Prog. Phys. 67, 717 <a href=\"https:\/\/doi.org\/10.1088\/0034-4885\/67\/5\/R03\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/0034-4885\/67\/5\/R03\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/0034-4885\/67\/5\/R03<\/a> (2004).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/0034-4885\/67\/5\/R03\" data-track-item_id=\"10.1088\/0034-4885\/67\/5\/R03\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F0034-4885%2F67%2F5%2FR03\" aria-label=\"Article reference 70\" data-doi=\"10.1088\/0034-4885\/67\/5\/R03\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2004RPPh...67..717P\" aria-label=\"ADS reference 70\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 70\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Reciprocity%20in%20optics&amp;journal=Rep.%20Prog.%20Phys.&amp;doi=10.1088%2F0034-4885%2F67%2F5%2FR03&amp;volume=67&amp;publication_year=2004&amp;author=Potton%2CRJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR71\">Fratini, F. et al. Fabry\u2013Perot interferometer with quantum mirrors: nonlinear light transport and rectification. Phys. Rev. Lett. 113, 243601 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.113.243601\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.113.243601\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.113.243601<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.113.243601\" data-track-item_id=\"10.1103\/PhysRevLett.113.243601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.113.243601\" aria-label=\"Article reference 71\" data-doi=\"10.1103\/PhysRevLett.113.243601\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvL.113x3601F\" aria-label=\"ADS reference 71\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 71\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Fabry%E2%80%93Perot%20interferometer%20with%20quantum%20mirrors%3A%20nonlinear%20light%20transport%20and%20rectification&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.113.243601&amp;volume=113&amp;publication_year=2014&amp;author=Fratini%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR72\">M\u00fcller, C., Combes, J., Hamann, A. R., Fedorov, A. &amp; Stace, T. M. Nonreciprocal atomic scattering: a saturable, quantum yagi-uda antenna. Phys. Rev. A 96, 053817 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.96.053817\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevA.96.053817\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevA.96.053817<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.96.053817\" data-track-item_id=\"10.1103\/PhysRevA.96.053817\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.96.053817\" aria-label=\"Article reference 72\" data-doi=\"10.1103\/PhysRevA.96.053817\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhRvA..96e3817M\" aria-label=\"ADS reference 72\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 72\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocal%20atomic%20scattering%3A%20a%20saturable%2C%20quantum%20yagi-uda%20antenna&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.96.053817&amp;volume=96&amp;publication_year=2017&amp;author=M%C3%BCller%2CC&amp;author=Combes%2CJ&amp;author=Hamann%2CAR&amp;author=Fedorov%2CA&amp;author=Stace%2CTM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR73\">Nefedkin, N., Cotrufo, M., Krasnok, A. &amp; Al\u00fa, A. Dark-state induced quantum nonreciprocity. Adv. Quantum Technol. 5, 2100112 <a href=\"https:\/\/doi.org\/10.1002\/qute.202100112\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1002\/qute.202100112\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1002\/qute.202100112<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1002\/qute.202100112\" data-track-item_id=\"10.1002\/qute.202100112\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1002%2Fqute.202100112\" aria-label=\"Article reference 73\" data-doi=\"10.1002\/qute.202100112\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 73\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Dark-state%20induced%20quantum%20nonreciprocity&amp;journal=Adv.%20Quantum%20Technol.&amp;doi=10.1002%2Fqute.202100112&amp;volume=5&amp;publication_year=2022&amp;author=Nefedkin%2CN&amp;author=Cotrufo%2CM&amp;author=Krasnok%2CA&amp;author=Al%C3%BA%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR74\">Rosario Hamann, A. et al. Nonreciprocity realized with quantum nonlinearity. Phys. Rev. Lett. 121, 123601 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.121.123601\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.121.123601\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.121.123601<\/a> (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.121.123601\" data-track-item_id=\"10.1103\/PhysRevLett.121.123601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.121.123601\" aria-label=\"Article reference 74\" data-doi=\"10.1103\/PhysRevLett.121.123601\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018PhRvL.121l3601R\" aria-label=\"ADS reference 74\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 74\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocity%20realized%20with%20quantum%20nonlinearity&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.121.123601&amp;volume=121&amp;publication_year=2018&amp;author=Rosario%20Hamann%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR75\">Rieser, J. et al. Tunable light-induced dipole\u2013dipole interaction between optically levitated nanoparticles. Science 377, 987 <a href=\"https:\/\/doi.org\/10.1126\/science.abp9941\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1126\/science.abp9941\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1126\/science.abp9941<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.abp9941\" data-track-item_id=\"10.1126\/science.abp9941\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.abp9941\" aria-label=\"Article reference 75\" data-doi=\"10.1126\/science.abp9941\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022Sci...377..987R\" aria-label=\"ADS reference 75\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4479673\" aria-label=\"MathSciNet reference 75\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 75\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Tunable%20light-induced%20dipole%E2%80%93dipole%20interaction%20between%20optically%20levitated%20nanoparticles&amp;journal=Science&amp;doi=10.1126%2Fscience.abp9941&amp;volume=377&amp;publication_year=2022&amp;author=Rieser%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR76\">Herrmann, J. F. et al. Mirror symmetric on-chip frequency circulation of light. Nat. Photon. 16, 603 <a href=\"https:\/\/doi.org\/10.1038\/s41566-022-01026-7\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41566-022-01026-7\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41566-022-01026-7<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41566-022-01026-7\" data-track-item_id=\"10.1038\/s41566-022-01026-7\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41566-022-01026-7\" aria-label=\"Article reference 76\" data-doi=\"10.1038\/s41566-022-01026-7\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022NaPho..16..603H\" aria-label=\"ADS reference 76\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 76\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Mirror%20symmetric%20on-chip%20frequency%20circulation%20of%20light&amp;journal=Nat.%20Photon.&amp;doi=10.1038%2Fs41566-022-01026-7&amp;volume=16&amp;publication_year=2022&amp;author=Herrmann%2CJF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR77\">Zare Rameshti, B. et al. Cavity magnonics. Phys. Rep. 979, 1 <a href=\"https:\/\/doi.org\/10.1016\/j.physrep.2022.06.001\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1016\/j.physrep.2022.06.001\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1016\/j.physrep.2022.06.001<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.physrep.2022.06.001\" data-track-item_id=\"10.1016\/j.physrep.2022.06.001\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.physrep.2022.06.001\" aria-label=\"Article reference 77\" data-doi=\"10.1016\/j.physrep.2022.06.001\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022PhR...979....1Z\" aria-label=\"ADS reference 77\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4456842\" aria-label=\"MathSciNet reference 77\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 77\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Cavity%20magnonics&amp;journal=Phys.%20Rep.&amp;doi=10.1016%2Fj.physrep.2022.06.001&amp;volume=979&amp;publication_year=2022&amp;author=Zare%20Rameshti%2CB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR78\">Wang, Y.-Y. et al. Low-loss ferrite circulator as a tunable chiral quantum system. Phys. Rev. Appl. 16, 064066 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevApplied.16.064066\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevApplied.16.064066\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevApplied.16.064066<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevApplied.16.064066\" data-track-item_id=\"10.1103\/PhysRevApplied.16.064066\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevApplied.16.064066\" aria-label=\"Article reference 78\" data-doi=\"10.1103\/PhysRevApplied.16.064066\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhRvP..16f4066W\" aria-label=\"ADS reference 78\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 78\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Low-loss%20ferrite%20circulator%20as%20a%20tunable%20chiral%20quantum%20system&amp;journal=Phys.%20Rev.%20Appl.&amp;doi=10.1103%2FPhysRevApplied.16.064066&amp;volume=16&amp;publication_year=2021&amp;author=Wang%2CY-Y\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR79\">Nefedkin, N., Cotrufo, M. &amp; Al\u00fa, A. Nonreciprocal total cross section of quantum metasurfaces. Nanophotonics 12, 589 <a href=\"https:\/\/doi.org\/10.1515\/nanoph-2022-0596\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1515\/nanoph-2022-0596\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1515\/nanoph-2022-0596<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1515\/nanoph-2022-0596\" data-track-item_id=\"10.1515\/nanoph-2022-0596\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1515%2Fnanoph-2022-0596\" aria-label=\"Article reference 79\" data-doi=\"10.1515\/nanoph-2022-0596\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023Nanop..12..589N\" aria-label=\"ADS reference 79\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 79\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocal%20total%20cross%20section%20of%20quantum%20metasurfaces&amp;journal=Nanophotonics&amp;doi=10.1515%2Fnanoph-2022-0596&amp;volume=12&amp;publication_year=2023&amp;author=Nefedkin%2CN&amp;author=Cotrufo%2CM&amp;author=Al%C3%BA%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR80\">Bergeal, N. et al. Phase-preserving amplification near the quantum limit with a Josephson ring modulator. Nature 465, 64 <a href=\"https:\/\/doi.org\/10.1038\/nature09035\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nature09035\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nature09035<\/a> (2010).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature09035\" data-track-item_id=\"10.1038\/nature09035\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature09035\" aria-label=\"Article reference 80\" data-doi=\"10.1038\/nature09035\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2010Natur.465...64B\" aria-label=\"ADS reference 80\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 80\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Phase-preserving%20amplification%20near%20the%20quantum%20limit%20with%20a%20Josephson%20ring%20modulator&amp;journal=Nature&amp;doi=10.1038%2Fnature09035&amp;volume=465&amp;publication_year=2010&amp;author=Bergeal%2CN\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR81\">Macklin, C. et al. A near-quantum-limited Josephson traveling-wave parametric amplifier. Science 350, 307 <a href=\"https:\/\/doi.org\/10.1126\/science.aaa8525\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1126\/science.aaa8525\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1126\/science.aaa8525<\/a> (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/science.aaa8525\" data-track-item_id=\"10.1126\/science.aaa8525\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.aaa8525\" aria-label=\"Article reference 81\" data-doi=\"10.1126\/science.aaa8525\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2015Sci...350..307M\" aria-label=\"ADS reference 81\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 81\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20near-quantum-limited%20Josephson%20traveling-wave%20parametric%20amplifier&amp;journal=Science&amp;doi=10.1126%2Fscience.aaa8525&amp;volume=350&amp;publication_year=2015&amp;author=Macklin%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR82\">Naghiloo, M., Abbasi, M., Joglekar, Y. N. &amp; Murch, K. W. Quantum state tomography across the exceptional point in a single dissipative qubit. Nat. Phys. 15, 1232 <a href=\"https:\/\/doi.org\/10.1038\/s41567-019-0652-z\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41567-019-0652-z\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41567-019-0652-z<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-019-0652-z\" data-track-item_id=\"10.1038\/s41567-019-0652-z\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-019-0652-z\" aria-label=\"Article reference 82\" data-doi=\"10.1038\/s41567-019-0652-z\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 82\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20state%20tomography%20across%20the%20exceptional%20point%20in%20a%20single%20dissipative%20qubit&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-019-0652-z&amp;volume=15&amp;publication_year=2019&amp;author=Naghiloo%2CM&amp;author=Abbasi%2CM&amp;author=Joglekar%2CYN&amp;author=Murch%2CKW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR83\">Abdo, B. et al. Josephson directional amplifier for quantum measurement of superconducting circuits. Phys. Rev. Lett. 112, 167701 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.112.167701\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.112.167701\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.112.167701<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.112.167701\" data-track-item_id=\"10.1103\/PhysRevLett.112.167701\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.112.167701\" aria-label=\"Article reference 83\" data-doi=\"10.1103\/PhysRevLett.112.167701\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2014PhRvL.112p7701A\" aria-label=\"ADS reference 83\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 83\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Josephson%20directional%20amplifier%20for%20quantum%20measurement%20of%20superconducting%20circuits&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.112.167701&amp;volume=112&amp;publication_year=2014&amp;author=Abdo%2CB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR84\">Aumentado, J. Superconducting parametric amplifiers: the state of the art in Josephson parametric amplifiers. IEEE Microw. Mag. 21, 45 <a href=\"https:\/\/doi.org\/10.1109\/MMM.2020.2993476\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1109\/MMM.2020.2993476\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1109\/MMM.2020.2993476<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1109\/MMM.2020.2993476\" data-track-item_id=\"10.1109\/MMM.2020.2993476\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1109%2FMMM.2020.2993476\" aria-label=\"Article reference 84\" data-doi=\"10.1109\/MMM.2020.2993476\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 84\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Superconducting%20parametric%20amplifiers%3A%20the%20state%20of%20the%20art%20in%20Josephson%20parametric%20amplifiers&amp;journal=IEEE%20Microw.%20Mag.&amp;doi=10.1109%2FMMM.2020.2993476&amp;volume=21&amp;publication_year=2020&amp;author=Aumentado%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR85\">Esposito, M., Ranadive, A., Planat, L. &amp; Roch, N. Perspective on traveling wave microwave parametric amplifiers. Appl. Phys. Lett. 119, 120501 <a href=\"https:\/\/doi.org\/10.1063\/5.0064892\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1063\/5.0064892\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1063\/5.0064892<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1063\/5.0064892\" data-track-item_id=\"10.1063\/5.0064892\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1063%2F5.0064892\" aria-label=\"Article reference 85\" data-doi=\"10.1063\/5.0064892\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021ApPhL.119l0501E\" aria-label=\"ADS reference 85\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 85\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Perspective%20on%20traveling%20wave%20microwave%20parametric%20amplifiers&amp;journal=Appl.%20Phys.%20Lett.&amp;doi=10.1063%2F5.0064892&amp;volume=119&amp;publication_year=2021&amp;author=Esposito%2CM&amp;author=Ranadive%2CA&amp;author=Planat%2CL&amp;author=Roch%2CN\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR86\">Ranadive, A. et al. A travelling-wave parametric amplifier isolator. Nat. Electron. 8, 1089 <a href=\"https:\/\/doi.org\/10.1038\/s41928-025-01489-w\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41928-025-01489-w\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41928-025-01489-w<\/a> (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41928-025-01489-w\" data-track-item_id=\"10.1038\/s41928-025-01489-w\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41928-025-01489-w\" aria-label=\"Article reference 86\" data-doi=\"10.1038\/s41928-025-01489-w\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 86\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20travelling-wave%20parametric%20amplifier%20isolator&amp;journal=Nat.%20Electron.&amp;doi=10.1038%2Fs41928-025-01489-w&amp;volume=8&amp;publication_year=2025&amp;author=Ranadive%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR87\">Abdo, B., Jinka, O., Bronn, N. T., Olivadese, S. &amp; Brink, M. High-fidelity qubit readout using interferometric directional Josephson devices. PRX Quantum 2, 040360 <a href=\"https:\/\/doi.org\/10.1103\/PRXQuantum.2.040360\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PRXQuantum.2.040360\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PRXQuantum.2.040360<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PRXQuantum.2.040360\" data-track-item_id=\"10.1103\/PRXQuantum.2.040360\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPRXQuantum.2.040360\" aria-label=\"Article reference 87\" data-doi=\"10.1103\/PRXQuantum.2.040360\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PRXQ....2d0360A\" aria-label=\"ADS reference 87\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 87\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-fidelity%20qubit%20readout%20using%20interferometric%20directional%20Josephson%20devices&amp;journal=PRX%20Quantum&amp;doi=10.1103%2FPRXQuantum.2.040360&amp;volume=2&amp;publication_year=2021&amp;author=Abdo%2CB&amp;author=Jinka%2CO&amp;author=Bronn%2CNT&amp;author=Olivadese%2CS&amp;author=Brink%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR88\">Lecocq, F. et al. Efficient qubit measurement with a nonreciprocal microwave amplifier. Phys. Rev. Lett. 126, 020502 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.126.020502\" data-track-item_id=\"10.1103\/PhysRevLett.126.020502\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.126.020502\" aria-label=\"Article reference 88\" data-doi=\"10.1103\/PhysRevLett.126.020502\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhRvL.126b0502L\" aria-label=\"ADS reference 88\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 88\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Efficient%20qubit%20measurement%20with%20a%20nonreciprocal%20microwave%20amplifier&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.126.020502&amp;volume=126&amp;publication_year=2021&amp;author=Lecocq%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR89\">Mittal, S., Goldschmidt, E. A. &amp; Hafezi, M. A topological source of quantum light. Nature 561, 502 <a href=\"https:\/\/doi.org\/10.1038\/s41586-018-0478-3\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41586-018-0478-3\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41586-018-0478-3<\/a> (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-018-0478-3\" data-track-item_id=\"10.1038\/s41586-018-0478-3\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-018-0478-3\" aria-label=\"Article reference 89\" data-doi=\"10.1038\/s41586-018-0478-3\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018Natur.561..502M\" aria-label=\"ADS reference 89\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 89\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20topological%20source%20of%20quantum%20light&amp;journal=Nature&amp;doi=10.1038%2Fs41586-018-0478-3&amp;volume=561&amp;publication_year=2018&amp;author=Mittal%2CS&amp;author=Goldschmidt%2CEA&amp;author=Hafezi%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR90\">Porras, D. &amp; Fern\u00e1ndez-Lorenzo, S. Topological amplification in photonic lattices. Phys. Rev. Lett. 122, 143901 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.122.143901\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.122.143901\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.122.143901<\/a> (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.122.143901\" data-track-item_id=\"10.1103\/PhysRevLett.122.143901\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.122.143901\" aria-label=\"Article reference 90\" data-doi=\"10.1103\/PhysRevLett.122.143901\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2019PhRvL.122n3901P\" aria-label=\"ADS reference 90\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 90\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20amplification%20in%20photonic%20lattices&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.122.143901&amp;volume=122&amp;publication_year=2019&amp;author=Porras%2CD&amp;author=Fern%C3%A1ndez-Lorenzo%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR91\">Wanjura, C. C., Brunelli, M. &amp; Nunnenkamp, A. Topological framework for directional amplification in driven-dissipative cavity arrays. Nat. Commun. 11, 3149 <a href=\"https:\/\/doi.org\/10.1038\/s41467-020-16863-9\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41467-020-16863-9\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41467-020-16863-9<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41467-020-16863-9\" data-track-item_id=\"10.1038\/s41467-020-16863-9\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-020-16863-9\" aria-label=\"Article reference 91\" data-doi=\"10.1038\/s41467-020-16863-9\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020NatCo..11.3149W\" aria-label=\"ADS reference 91\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 91\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20framework%20for%20directional%20amplification%20in%20driven-dissipative%20cavity%20arrays&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-020-16863-9&amp;volume=11&amp;publication_year=2020&amp;author=Wanjura%2CCC&amp;author=Brunelli%2CM&amp;author=Nunnenkamp%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR92\">Wanjura, C. C., Brunelli, M. &amp; Nunnenkamp, A. Correspondence between non-Hermitian topology and directional amplification in the presence of disorder. Phys. Rev. Lett. 127, 213601 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.127.213601\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.127.213601\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.127.213601<\/a> (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.127.213601\" data-track-item_id=\"10.1103\/PhysRevLett.127.213601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.127.213601\" aria-label=\"Article reference 92\" data-doi=\"10.1103\/PhysRevLett.127.213601\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2021PhRvL.127u3601W\" aria-label=\"ADS reference 92\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4344928\" aria-label=\"MathSciNet reference 92\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 92\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Correspondence%20between%20non-Hermitian%20topology%20and%20directional%20amplification%20in%20the%20presence%20of%20disorder&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.127.213601&amp;volume=127&amp;publication_year=2021&amp;author=Wanjura%2CCC&amp;author=Brunelli%2CM&amp;author=Nunnenkamp%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR93\">Cirac, J. I., Zoller, P., Kimble, H. J. &amp; Mabuchi, H. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.78.3221\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.78.3221\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.78.3221<\/a> (1997).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.78.3221\" data-track-item_id=\"10.1103\/PhysRevLett.78.3221\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.78.3221\" aria-label=\"Article reference 93\" data-doi=\"10.1103\/PhysRevLett.78.3221\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=1997PhRvL..78.3221C\" aria-label=\"ADS reference 93\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 93\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20state%20transfer%20and%20entanglement%20distribution%20among%20distant%20nodes%20in%20a%20quantum%20network&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.78.3221&amp;volume=78&amp;publication_year=1997&amp;author=Cirac%2CJI&amp;author=Zoller%2CP&amp;author=Kimble%2CHJ&amp;author=Mabuchi%2CH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR94\">Gheeraert, N., Kono, S. &amp; Nakamura, Y. Programmable directional emitter and receiver of itinerant microwave photons in a waveguide. Phys. Rev. A 102, 053720 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.102.053720\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevA.102.053720\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevA.102.053720<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.102.053720\" data-track-item_id=\"10.1103\/PhysRevA.102.053720\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.102.053720\" aria-label=\"Article reference 94\" data-doi=\"10.1103\/PhysRevA.102.053720\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020PhRvA.102e3720G\" aria-label=\"ADS reference 94\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 94\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Programmable%20directional%20emitter%20and%20receiver%20of%20itinerant%20microwave%20photons%20in%20a%20waveguide&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.102.053720&amp;volume=102&amp;publication_year=2020&amp;author=Gheeraert%2CN&amp;author=Kono%2CS&amp;author=Nakamura%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR95\">Guimond, P. et al. A unidirectional on-chip photonic interface for superconducting circuits. npj Quantum Inf. 6, 32 <a href=\"https:\/\/doi.org\/10.1038\/s41534-020-0261-9\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41534-020-0261-9\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41534-020-0261-9<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41534-020-0261-9\" data-track-item_id=\"10.1038\/s41534-020-0261-9\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41534-020-0261-9\" aria-label=\"Article reference 95\" data-doi=\"10.1038\/s41534-020-0261-9\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020npjQI...6...32G\" aria-label=\"ADS reference 95\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 95\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20unidirectional%20on-chip%20photonic%20interface%20for%20superconducting%20circuits&amp;journal=npj%20Quantum%20Inf.&amp;doi=10.1038%2Fs41534-020-0261-9&amp;volume=6&amp;publication_year=2020&amp;author=Guimond%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR96\">Kannan, B. et al. On-demand directional microwave photon emission using waveguide quantum electrodynamics. Nat. Phys. 19, 394 <a href=\"https:\/\/doi.org\/10.1038\/s41567-022-01869-5\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41567-022-01869-5\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41567-022-01869-5<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-022-01869-5\" data-track-item_id=\"10.1038\/s41567-022-01869-5\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-022-01869-5\" aria-label=\"Article reference 96\" data-doi=\"10.1038\/s41567-022-01869-5\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 96\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=On-demand%20directional%20microwave%20photon%20emission%20using%20waveguide%20quantum%20electrodynamics&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-022-01869-5&amp;volume=19&amp;publication_year=2023&amp;author=Kannan%2CB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR97\">Joshi, C., Yang, F. &amp; Mirhosseini, M. Resonance fluorescence of a chiral artificial atom. Phys. Rev. X 13, 021039 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.13.021039\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.13.021039\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.13.021039<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.13.021039\" data-track-item_id=\"10.1103\/PhysRevX.13.021039\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.13.021039\" aria-label=\"Article reference 97\" data-doi=\"10.1103\/PhysRevX.13.021039\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 97\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Resonance%20fluorescence%20of%20a%20chiral%20artificial%20atom&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.13.021039&amp;volume=13&amp;publication_year=2023&amp;author=Joshi%2CC&amp;author=Yang%2CF&amp;author=Mirhosseini%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR98\">Wang, X. &amp; Li, H.-R. Chiral quantum network with giant atoms. Quantum Sci. Technol. 7, 035007 <a href=\"https:\/\/doi.org\/10.1088\/2058-9565\/ac6a04\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1088\/2058-9565\/ac6a04\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1088\/2058-9565\/ac6a04<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/2058-9565\/ac6a04\" data-track-item_id=\"10.1088\/2058-9565\/ac6a04\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F2058-9565%2Fac6a04\" aria-label=\"Article reference 98\" data-doi=\"10.1088\/2058-9565\/ac6a04\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022QS%26T....7c5007W\" aria-label=\"ADS reference 98\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 98\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20quantum%20network%20with%20giant%20atoms&amp;journal=Quantum%20Sci.%20Technol.&amp;doi=10.1088%2F2058-9565%2Fac6a04&amp;volume=7&amp;publication_year=2022&amp;author=Wang%2CX&amp;author=Li%2CH-R\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR99\">Soro, A. &amp; Kockum, A. F. Chiral quantum optics with giant atoms. Phys. Rev. A 105, 023712 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.105.023712\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevA.105.023712\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevA.105.023712<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.105.023712\" data-track-item_id=\"10.1103\/PhysRevA.105.023712\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.105.023712\" aria-label=\"Article reference 99\" data-doi=\"10.1103\/PhysRevA.105.023712\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2022PhRvA.105b3712S\" aria-label=\"ADS reference 99\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4390405\" aria-label=\"MathSciNet reference 99\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 99\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Chiral%20quantum%20optics%20with%20giant%20atoms&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.105.023712&amp;volume=105&amp;publication_year=2022&amp;author=Soro%2CA&amp;author=Kockum%2CAF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR100\">Chen, Y.-T. et al. Nonreciprocal and chiral single-photon scattering for giant atoms. Commun. Phys. 5, 215 <a href=\"https:\/\/doi.org\/10.1038\/s42005-022-00991-3\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s42005-022-00991-3\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s42005-022-00991-3<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s42005-022-00991-3\" data-track-item_id=\"10.1038\/s42005-022-00991-3\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs42005-022-00991-3\" aria-label=\"Article reference 100\" data-doi=\"10.1038\/s42005-022-00991-3\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 100\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocal%20and%20chiral%20single-photon%20scattering%20for%20giant%20atoms&amp;journal=Commun.%20Phys.&amp;doi=10.1038%2Fs42005-022-00991-3&amp;volume=5&amp;publication_year=2022&amp;author=Chen%2CY-T\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR101\">Almanakly, A. et al. Deterministic remote entanglement using a chiral quantum interconnect. Nat. Phys. 21, 825 <a href=\"https:\/\/doi.org\/10.1038\/s41567-025-02811-1\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41567-025-02811-1\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41567-025-02811-1<\/a> (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41567-025-02811-1\" data-track-item_id=\"10.1038\/s41567-025-02811-1\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-025-02811-1\" aria-label=\"Article reference 101\" data-doi=\"10.1038\/s41567-025-02811-1\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 101\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Deterministic%20remote%20entanglement%20using%20a%20chiral%20quantum%20interconnect&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-025-02811-1&amp;volume=21&amp;publication_year=2025&amp;author=Almanakly%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR102\">Chen, W., Kaya \u00d6zdemir, \u015e, Zhao, G., Wiersig, J. &amp; Yang, L. Exceptional points enhance sensing in an optical microcavity. Nature 548, 192 <a href=\"https:\/\/doi.org\/10.1038\/nature23281\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/nature23281\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/nature23281<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/nature23281\" data-track-item_id=\"10.1038\/nature23281\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature23281\" aria-label=\"Article reference 102\" data-doi=\"10.1038\/nature23281\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017Natur.548..192C\" aria-label=\"ADS reference 102\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 102\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Exceptional%20points%20enhance%20sensing%20in%20an%20optical%20microcavity&amp;journal=Nature&amp;doi=10.1038%2Fnature23281&amp;volume=548&amp;publication_year=2017&amp;author=Chen%2CW&amp;author=Kaya%20%C3%96zdemir%2C%C5%9E&amp;author=Zhao%2CG&amp;author=Wiersig%2CJ&amp;author=Yang%2CL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR103\">Mao, W., Fu, Z., Li, Y., Li, F. &amp; Yang, L. Exceptional-point-enhanced phase sensing. Sci. Adv. 10, eadl5037 <a href=\"https:\/\/doi.org\/10.1126\/sciadv.adl5037\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1126\/sciadv.adl5037\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1126\/sciadv.adl5037<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/sciadv.adl5037\" data-track-item_id=\"10.1126\/sciadv.adl5037\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fsciadv.adl5037\" aria-label=\"Article reference 103\" data-doi=\"10.1126\/sciadv.adl5037\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024SciA...10L5037M\" aria-label=\"ADS reference 103\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 103\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Exceptional-point-enhanced%20phase%20sensing&amp;journal=Sci.%20Adv.&amp;doi=10.1126%2Fsciadv.adl5037&amp;volume=10&amp;publication_year=2024&amp;author=Mao%2CW&amp;author=Fu%2CZ&amp;author=Li%2CY&amp;author=Li%2CF&amp;author=Yang%2CL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR104\">Langbein, W. No exceptional precision of exceptional-point sensors. Phys. Rev. A 98, 023805 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.98.023805\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevA.98.023805\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevA.98.023805<\/a> (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.98.023805\" data-track-item_id=\"10.1103\/PhysRevA.98.023805\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.98.023805\" aria-label=\"Article reference 104\" data-doi=\"10.1103\/PhysRevA.98.023805\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2018PhRvA..98b3805L\" aria-label=\"ADS reference 104\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 104\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=No%20exceptional%20precision%20of%20exceptional-point%20sensors&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.98.023805&amp;volume=98&amp;publication_year=2018&amp;author=Langbein%2CW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR105\">Duggan, R., Mann, S. A. &amp; Al\u00f9, A. Limitations of sensing at an exceptional point. ACS Photon. 9, 1554 <a href=\"https:\/\/doi.org\/10.1021\/acsphotonics.1c01535\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1021\/acsphotonics.1c01535\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1021\/acsphotonics.1c01535<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1021\/acsphotonics.1c01535\" data-track-item_id=\"10.1021\/acsphotonics.1c01535\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1021%2Facsphotonics.1c01535\" aria-label=\"Article reference 105\" data-doi=\"10.1021\/acsphotonics.1c01535\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 105\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Limitations%20of%20sensing%20at%20an%20exceptional%20point&amp;journal=ACS%20Photon.&amp;doi=10.1021%2Facsphotonics.1c01535&amp;volume=9&amp;publication_year=2022&amp;author=Duggan%2CR&amp;author=Mann%2CSA&amp;author=Al%C3%B9%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR106\">Ding, W., Wang, X. &amp; Chen, S. Fundamental sensitivity limits for non-Hermitian quantum sensors. Phys. Rev. Lett. 131, 160801 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.131.160801\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.131.160801\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.131.160801<\/a> (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.131.160801\" data-track-item_id=\"10.1103\/PhysRevLett.131.160801\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.131.160801\" aria-label=\"Article reference 106\" data-doi=\"10.1103\/PhysRevLett.131.160801\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023PhRvL.131p0801D\" aria-label=\"ADS reference 106\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4661095\" aria-label=\"MathSciNet reference 106\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 106\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Fundamental%20sensitivity%20limits%20for%20non-Hermitian%20quantum%20sensors&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.131.160801&amp;volume=131&amp;publication_year=2023&amp;author=Ding%2CW&amp;author=Wang%2CX&amp;author=Chen%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR107\">Montenegro, V. et al. Quantum metrology and sensing with many-body systems. Phys. Rep. 1134, 1 <a href=\"https:\/\/doi.org\/10.1016\/j.physrep.2025.05.005\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1016\/j.physrep.2025.05.005\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1016\/j.physrep.2025.05.005<\/a> (2025).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/j.physrep.2025.05.005\" data-track-item_id=\"10.1016\/j.physrep.2025.05.005\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2Fj.physrep.2025.05.005\" aria-label=\"Article reference 107\" data-doi=\"10.1016\/j.physrep.2025.05.005\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2025PhR..1134....1M\" aria-label=\"ADS reference 107\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4916939\" aria-label=\"MathSciNet reference 107\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 107\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20metrology%20and%20sensing%20with%20many-body%20systems&amp;journal=Phys.%20Rep.&amp;doi=10.1016%2Fj.physrep.2025.05.005&amp;volume=1134&amp;publication_year=2025&amp;author=Montenegro%2CV\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR108\">Huang, J., Zhuang, M. &amp; Lee, C. Entanglement-enhanced quantum metrology: from standard quantum limit to Heisenberg limit. Appl. Phys. Rev. 11, 031302 <a href=\"https:\/\/doi.org\/10.1063\/5.0204102\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1063\/5.0204102\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1063\/5.0204102<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1063\/5.0204102\" data-track-item_id=\"10.1063\/5.0204102\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1063%2F5.0204102\" aria-label=\"Article reference 108\" data-doi=\"10.1063\/5.0204102\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024ApPRv..11c1302H\" aria-label=\"ADS reference 108\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 108\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Entanglement-enhanced%20quantum%20metrology%3A%20from%20standard%20quantum%20limit%20to%20Heisenberg%20limit&amp;journal=Appl.%20Phys.%20Rev.&amp;doi=10.1063%2F5.0204102&amp;volume=11&amp;publication_year=2024&amp;author=Huang%2CJ&amp;author=Zhuang%2CM&amp;author=Lee%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR109\">Xiao, L. et al. Non-Hermitian sensing in the absence of exceptional points. Phys. Rev. Lett. 133, 180801 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.133.180801\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.133.180801\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.133.180801<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.133.180801\" data-track-item_id=\"10.1103\/PhysRevLett.133.180801\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.133.180801\" aria-label=\"Article reference 109\" data-doi=\"10.1103\/PhysRevLett.133.180801\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024PhRvL.133r0801X\" aria-label=\"ADS reference 109\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 109\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Non-Hermitian%20sensing%20in%20the%20absence%20of%20exceptional%20points&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.133.180801&amp;volume=133&amp;publication_year=2024&amp;author=Xiao%2CL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR110\">Gardiner, C. W. &amp; Zoller, P. Quantum Noise (Springer, 2004).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR111\">Wang, Y.-Y. et al. Dispersive nonreciprocity between a qubit and a cavity. Sci. Adv. 10, eadj8796 <a href=\"https:\/\/doi.org\/10.1126\/sciadv.adj8796\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1126\/sciadv.adj8796\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1126\/sciadv.adj8796<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1126\/sciadv.adj8796\" data-track-item_id=\"10.1126\/sciadv.adj8796\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fsciadv.adj8796\" aria-label=\"Article reference 111\" data-doi=\"10.1126\/sciadv.adj8796\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 111\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Dispersive%20nonreciprocity%20between%20a%20qubit%20and%20a%20cavity&amp;journal=Sci.%20Adv.&amp;doi=10.1126%2Fsciadv.adj8796&amp;volume=10&amp;publication_year=2024&amp;author=Wang%2CY-Y\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR112\">Metelmann, A. &amp; Clerk, A. A. Nonreciprocal quantum interactions and devices via autonomous feedforward. Phys. Rev. A 95, 013837 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevA.95.013837\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevA.95.013837\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevA.95.013837<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevA.95.013837\" data-track-item_id=\"10.1103\/PhysRevA.95.013837\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.95.013837\" aria-label=\"Article reference 112\" data-doi=\"10.1103\/PhysRevA.95.013837\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2017PhRvA..95a3837M\" aria-label=\"ADS reference 112\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 112\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocal%20quantum%20interactions%20and%20devices%20via%20autonomous%20feedforward&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.95.013837&amp;volume=95&amp;publication_year=2017&amp;author=Metelmann%2CA&amp;author=Clerk%2CAA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR113\">Ahmadi, B., Mazurek, P., Horodecki, P. &amp; Barzanjeh, S. Nonreciprocal quantum batteries. Phys. Rev. Lett. 132, 210402 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevLett.132.210402\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevLett.132.210402\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevLett.132.210402<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevLett.132.210402\" data-track-item_id=\"10.1103\/PhysRevLett.132.210402\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.132.210402\" aria-label=\"Article reference 113\" data-doi=\"10.1103\/PhysRevLett.132.210402\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2024PhRvL.132u0402A\" aria-label=\"ADS reference 113\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"mathscinet reference\" data-track-action=\"mathscinet reference\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=4752094\" aria-label=\"MathSciNet reference 113\" target=\"_blank\">MathSciNet<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 113\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocal%20quantum%20batteries&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.132.210402&amp;volume=132&amp;publication_year=2024&amp;author=Ahmadi%2CB&amp;author=Mazurek%2CP&amp;author=Horodecki%2CP&amp;author=Barzanjeh%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR114\">Nagaosa, N. &amp; Yanase, Y. Nonreciprocal transport and optical phenomena in quantum materials. Annu. Rev. Condensed Matter Phys. 15, 63 <a href=\"https:\/\/doi.org\/10.1146\/annurev-conmatphys-032822-033734\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1146\/annurev-conmatphys-032822-033734\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1146\/annurev-conmatphys-032822-033734<\/a> (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1146\/annurev-conmatphys-032822-033734\" data-track-item_id=\"10.1146\/annurev-conmatphys-032822-033734\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1146%2Fannurev-conmatphys-032822-033734\" aria-label=\"Article reference 114\" data-doi=\"10.1146\/annurev-conmatphys-032822-033734\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2023ARCMP..15...63N\" aria-label=\"ADS reference 114\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 114\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonreciprocal%20transport%20and%20optical%20phenomena%20in%20quantum%20materials&amp;journal=Annu.%20Rev.%20Condensed%20Matter%20Phys.&amp;doi=10.1146%2Fannurev-conmatphys-032822-033734&amp;volume=15&amp;publication_year=2024&amp;author=Nagaosa%2CN&amp;author=Yanase%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR115\">Ando, F. et al. Observation of superconducting diode effect. Nature 584, 373 <a href=\"https:\/\/doi.org\/10.1038\/s41586-020-2590-4\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1038\/s41586-020-2590-4\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1038\/s41586-020-2590-4<\/a> (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/s41586-020-2590-4\" data-track-item_id=\"10.1038\/s41586-020-2590-4\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-020-2590-4\" aria-label=\"Article reference 115\" data-doi=\"10.1038\/s41586-020-2590-4\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"ads reference\" data-track-action=\"ads reference\" href=\"http:\/\/adsabs.harvard.edu\/cgi-bin\/nph-data_query?link_type=ABSTRACT&amp;bibcode=2020Natur.584..373A\" aria-label=\"ADS reference 115\" target=\"_blank\">ADS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 115\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20superconducting%20diode%20effect&amp;journal=Nature&amp;doi=10.1038%2Fs41586-020-2590-4&amp;volume=584&amp;publication_year=2020&amp;author=Ando%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR116\">Zhang, H. et al. A Josephson diode. Phys. Rev. X 12, 041013 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.12.041013\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.12.041013\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.12.041013<\/a> (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.12.041013\" data-track-item_id=\"10.1103\/PhysRevX.12.041013\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.12.041013\" aria-label=\"Article reference 116\" data-doi=\"10.1103\/PhysRevX.12.041013\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 116\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20Josephson%20diode&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.12.041013&amp;volume=12&amp;publication_year=2022&amp;author=Zhang%2CH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR117\">Viola, G. &amp; DiVincenzo, D. P. Hall effect gyrators and circulators. Phys. Rev. X 4, 021019 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.4.021019\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.4.021019\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.4.021019<\/a> (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.4.021019\" data-track-item_id=\"10.1103\/PhysRevX.4.021019\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.4.021019\" aria-label=\"Article reference 117\" data-doi=\"10.1103\/PhysRevX.4.021019\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 117\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Hall%20effect%20gyrators%20and%20circulators&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.4.021019&amp;volume=4&amp;publication_year=2014&amp;author=Viola%2CG&amp;author=DiVincenzo%2CDP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR118\">Mahoney, A. C. et al. On-chip microwave quantum Hall circulator. Phys. Rev. X 7, 011007 <a href=\"https:\/\/doi.org\/10.1103\/PhysRevX.7.011007\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.1103\/PhysRevX.7.011007\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.1103\/PhysRevX.7.011007<\/a> (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevX.7.011007\" data-track-item_id=\"10.1103\/PhysRevX.7.011007\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.7.011007\" aria-label=\"Article reference 118\" data-doi=\"10.1103\/PhysRevX.7.011007\" target=\"_blank\">Article<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 118\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=On-chip%20microwave%20quantum%20Hall%20circulator&amp;journal=Phys.%20Rev.%20X&amp;doi=10.1103%2FPhysRevX.7.011007&amp;volume=7&amp;publication_year=2017&amp;author=Mahoney%2CAC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n","protected":false},"excerpt":{"rendered":"De\u00e1k, L. &amp; F\u00fcl\u00f6p, T. Reciprocity in quantum, electromagnetic and other wave scattering. Ann. Phys. 327, 1050 https:\/\/doi.org\/10.1016\/j.aop.2011.10.013&hellip;\n","protected":false},"author":2,"featured_media":919954,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[7265,64,63,7264,7269,7268,1325,7263,7266,7267,292,4638,28229,7568,128,7262],"class_list":["post-919953","post","type-post","status-publish","format-standard","has-post-thumbnail","category-physics","tag-atomic","tag-au","tag-australia","tag-classical-and-continuum-physics","tag-complex-systems","tag-condensed-matter-physics","tag-general","tag-mathematical-and-computational-physics","tag-molecular","tag-optical-and-plasma-physics","tag-physics","tag-quantum-information","tag-quantum-simulation","tag-qubits","tag-science","tag-theoretical"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/posts\/919953","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/comments?post=919953"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/posts\/919953\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/media\/919954"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/media?parent=919953"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/categories?post=919953"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/tags?post=919953"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}