{"id":618559,"date":"2026-06-03T08:23:16","date_gmt":"2026-06-03T08:23:16","guid":{"rendered":"https:\/\/www.newsbeep.com\/uk\/618559\/"},"modified":"2026-06-03T08:23:16","modified_gmt":"2026-06-03T08:23:16","slug":"suppression-of-coherent-light-scattering-in-a-three-dimensional-atomic-array","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/uk\/618559\/","title":{"rendered":"Suppression of coherent light scattering in a three-dimensional atomic array"},"content":{"rendered":"<p class=\"c-article-references__text\" id=\"ref-CR1\">Dicke, R. H. Coherence in spontaneous radiation processes. Phys. Rev. 93, 99\u2013110 (1954).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRev.93.99\" data-track-item_id=\"10.1103\/PhysRev.93.99\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRev.93.99\" aria-label=\"Article reference 1\" data-doi=\"10.1103\/PhysRev.93.99\" 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=1954PhRv...93...99D\" aria-label=\"ADS reference 1\" 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 1\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Coherence%20in%20spontaneous%20radiation%20processes&amp;journal=Phys.%20Rev.&amp;doi=10.1103%2FPhysRev.93.99&amp;volume=93&amp;pages=99-110&amp;publication_year=1954&amp;author=Dicke%2CRH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR2\">Lehmberg, R. H. Radiation from an n-atom system. I. General formalism. Phys. Rev. A 2, 883\u2013888 (1970).<\/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.2.883\" data-track-item_id=\"10.1103\/PhysRevA.2.883\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.2.883\" aria-label=\"Article reference 2\" data-doi=\"10.1103\/PhysRevA.2.883\" 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=1970PhRvA...2..883L\" 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=Radiation%20from%20an%20n-atom%20system.%20I.%20General%20formalism&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.2.883&amp;volume=2&amp;pages=883-888&amp;publication_year=1970&amp;author=Lehmberg%2CRH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR3\">Gross, M. &amp; Haroche, S. Superradiance: an essay on the theory of collective spontaneous emission. Phys. Rep. 93, 301\u2013396 (1982).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1016\/0370-1573(82)90102-8\" data-track-item_id=\"10.1016\/0370-1573(82)90102-8\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1016%2F0370-1573%2882%2990102-8\" aria-label=\"Article reference 3\" data-doi=\"10.1016\/0370-1573(82)90102-8\" 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=1982PhR....93..301G\" 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=Superradiance%3A%20an%20essay%20on%20the%20theory%20of%20collective%20spontaneous%20emission&amp;journal=Phys.%20Rep.&amp;doi=10.1016%2F0370-1573%2882%2990102-8&amp;volume=93&amp;pages=301-396&amp;publication_year=1982&amp;author=Gross%2CM&amp;author=Haroche%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR4\">Gross, C. &amp; Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995\u20131001 (2017).<\/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.aal3837\" data-track-item_id=\"10.1126\/science.aal3837\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1126%2Fscience.aal3837\" aria-label=\"Article reference 4\" data-doi=\"10.1126\/science.aal3837\" 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=2017Sci...357..995G\" 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=Quantum%20simulations%20with%20ultracold%20atoms%20in%20optical%20lattices&amp;journal=Science&amp;doi=10.1126%2Fscience.aal3837&amp;volume=357&amp;pages=995-1001&amp;publication_year=2017&amp;author=Gross%2CC&amp;author=Bloch%2CI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR5\">Kaufman, A. M. &amp; Ni, K.-K. Quantum science with optical tweezer arrays of ultracold atoms and molecules. Nat. Phys. 17, 1324\u20131333 (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\/s41567-021-01357-2\" data-track-item_id=\"10.1038\/s41567-021-01357-2\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-021-01357-2\" aria-label=\"Article reference 5\" data-doi=\"10.1038\/s41567-021-01357-2\" 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 5\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20science%20with%20optical%20tweezer%20arrays%20of%20ultracold%20atoms%20and%20molecules&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-021-01357-2&amp;volume=17&amp;pages=1324-1333&amp;publication_year=2021&amp;author=Kaufman%2CAM&amp;author=Ni%2CK-K\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR6\">Glicenstein, A. et al. Collective shift in resonant light scattering by a one-dimensional atomic chain. Phys. Rev. Lett. 124, 253602 (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\/PhysRevLett.124.253602\" data-track-item_id=\"10.1103\/PhysRevLett.124.253602\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.124.253602\" aria-label=\"Article reference 6\" data-doi=\"10.1103\/PhysRevLett.124.253602\" 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=2020PhRvL.124y3602G\" aria-label=\"ADS reference 6\" 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 6\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Collective%20shift%20in%20resonant%20light%20scattering%20by%20a%20one-dimensional%20atomic%20chain&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.124.253602&amp;volume=124&amp;publication_year=2020&amp;author=Glicenstein%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR7\">Corzo, N. V. et al. Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide. Phys. Rev. Lett. 117, 133603 (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\/PhysRevLett.117.133603\" data-track-item_id=\"10.1103\/PhysRevLett.117.133603\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.117.133603\" aria-label=\"Article reference 7\" data-doi=\"10.1103\/PhysRevLett.117.133603\" 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=2016PhRvL.117m3603C\" 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=Large%20Bragg%20reflection%20from%20one-dimensional%20chains%20of%20trapped%20atoms%20near%20a%20nanoscale%20waveguide&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.117.133603&amp;volume=117&amp;publication_year=2016&amp;author=Corzo%2CNV\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR8\">S\u00f8rensen, H. L. et al. Coherent backscattering of light off one-dimensional atomic strings. Phys. Rev. Lett. 117, 133604 (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\/PhysRevLett.117.133604\" data-track-item_id=\"10.1103\/PhysRevLett.117.133604\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.117.133604\" aria-label=\"Article reference 8\" data-doi=\"10.1103\/PhysRevLett.117.133604\" 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=2016PhRvL.117m3604S\" aria-label=\"ADS reference 8\" 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 8\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Coherent%20backscattering%20of%20light%20off%20one-dimensional%20atomic%20strings&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.117.133604&amp;volume=117&amp;publication_year=2016&amp;author=S%C3%B8rensen%2CHL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR9\">Yan, Z. et al. Superradiant and subradiant cavity scattering by atom arrays. Phys. Rev. Lett. 131, 253603 (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.131.253603\" data-track-item_id=\"10.1103\/PhysRevLett.131.253603\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.131.253603\" aria-label=\"Article reference 9\" data-doi=\"10.1103\/PhysRevLett.131.253603\" 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.131y3603Y\" aria-label=\"ADS reference 9\" 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 9\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Superradiant%20and%20subradiant%20cavity%20scattering%20by%20atom%20arrays&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.131.253603&amp;volume=131&amp;publication_year=2023&amp;author=Yan%2CZ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR10\">Weitenberg, C. et al. Coherent light scattering from a two-dimensional Mott insulator. Phys. Rev. Lett. 106, 215301 (2011).<\/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.106.215301\" data-track-item_id=\"10.1103\/PhysRevLett.106.215301\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.106.215301\" aria-label=\"Article reference 10\" data-doi=\"10.1103\/PhysRevLett.106.215301\" 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=2011PhRvL.106u5301W\" 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=Coherent%20light%20scattering%20from%20a%20two-dimensional%20Mott%20insulator&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.106.215301&amp;volume=106&amp;publication_year=2011&amp;author=Weitenberg%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR11\">Rui, J. et al. A subradiant optical mirror formed by a single structured atomic layer. Nature 583, 369\u2013374 (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\/s41586-020-2463-x\" data-track-item_id=\"10.1038\/s41586-020-2463-x\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-020-2463-x\" aria-label=\"Article reference 11\" data-doi=\"10.1038\/s41586-020-2463-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=2020Natur.583..369R\" aria-label=\"ADS reference 11\" 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 11\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=A%20subradiant%20optical%20mirror%20formed%20by%20a%20single%20structured%20atomic%20layer&amp;journal=Nature&amp;doi=10.1038%2Fs41586-020-2463-x&amp;volume=583&amp;pages=369-374&amp;publication_year=2020&amp;author=Rui%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR12\">Birkl, G., Gatzke, M., Deutsch, I. H., Rolston, S. L. &amp; Phillips, W. D. Bragg scattering from atoms in optical lattices. Phys. Rev. Lett. 75, 2823\u20132826 (1995).<\/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.75.2823\" data-track-item_id=\"10.1103\/PhysRevLett.75.2823\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.75.2823\" aria-label=\"Article reference 12\" data-doi=\"10.1103\/PhysRevLett.75.2823\" 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=1995PhRvL..75.2823B\" 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=Bragg%20scattering%20from%20atoms%20in%20optical%20lattices&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.75.2823&amp;volume=75&amp;pages=2823-2826&amp;publication_year=1995&amp;author=Birkl%2CG&amp;author=Gatzke%2CM&amp;author=Deutsch%2CIH&amp;author=Rolston%2CSL&amp;author=Phillips%2CWD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR13\">Weidem\u00fcller, M., Hemmerich, A., G\u00f6rlitz, A., Esslinger, T. &amp; H\u00e4nsch, T. W. Bragg diffraction in an atomic lattice bound by light. Phys. Rev. Lett. 75, 4583\u20134586 (1995).<\/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.75.4583\" data-track-item_id=\"10.1103\/PhysRevLett.75.4583\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.75.4583\" aria-label=\"Article reference 13\" data-doi=\"10.1103\/PhysRevLett.75.4583\" 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=1995PhRvL..75.4583W\" aria-label=\"ADS reference 13\" 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 13\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Bragg%20diffraction%20in%20an%20atomic%20lattice%20bound%20by%20light&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.75.4583&amp;volume=75&amp;pages=4583-4586&amp;publication_year=1995&amp;author=Weidem%C3%BCller%2CM&amp;author=Hemmerich%2CA&amp;author=G%C3%B6rlitz%2CA&amp;author=Esslinger%2CT&amp;author=H%C3%A4nsch%2CTW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR14\">Miyake, H. et al. Bragg scattering as a probe of atomic wave functions and quantum phase transitions in optical lattices. Phys. Rev. Lett. 107, 175302 (2011).<\/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.107.175302\" data-track-item_id=\"10.1103\/PhysRevLett.107.175302\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.107.175302\" aria-label=\"Article reference 14\" data-doi=\"10.1103\/PhysRevLett.107.175302\" 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=2011PhRvL.107q5302M\" aria-label=\"ADS reference 14\" 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 14\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Bragg%20scattering%20as%20a%20probe%20of%20atomic%20wave%20functions%20and%20quantum%20phase%20transitions%20in%20optical%20lattices&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.107.175302&amp;volume=107&amp;publication_year=2011&amp;author=Miyake%2CH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR15\">Hart, R. A. et al. Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms. Nature 519, 211\u2013214 (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\/nature14223\" data-track-item_id=\"10.1038\/nature14223\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fnature14223\" aria-label=\"Article reference 15\" data-doi=\"10.1038\/nature14223\" 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=2015Natur.519..211H\" aria-label=\"ADS reference 15\" 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 15\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20antiferromagnetic%20correlations%20in%20the%20Hubbard%20model%20with%20ultracold%20atoms&amp;journal=Nature&amp;doi=10.1038%2Fnature14223&amp;volume=519&amp;pages=211-214&amp;publication_year=2015&amp;author=Hart%2CRA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR16\">Shao, H.-J. et al. Antiferromagnetic phase transition in a 3d fermionic Hubbard model. Nature 632, 267\u2013272 (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\/s41586-024-07689-2\" data-track-item_id=\"10.1038\/s41586-024-07689-2\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-024-07689-2\" aria-label=\"Article reference 16\" data-doi=\"10.1038\/s41586-024-07689-2\" 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=2024Natur.632..261S\" aria-label=\"ADS reference 16\" 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 16\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Antiferromagnetic%20phase%20transition%20in%20a%203d%20fermionic%20Hubbard%20model&amp;journal=Nature&amp;doi=10.1038%2Fs41586-024-07689-2&amp;volume=632&amp;pages=267-272&amp;publication_year=2024&amp;author=Shao%2CH-J\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR17\">Mewton, C. &amp; Ficek, Z. Radiative properties of a linear chain of coupled qubits. J. Phys. B: At. Mol. Opt. Phys. 40, S181\u2013S197 (2007).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/0953-4075\/40\/9\/S11\" data-track-item_id=\"10.1088\/0953-4075\/40\/9\/S11\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F0953-4075%2F40%2F9%2FS11\" aria-label=\"Article reference 17\" data-doi=\"10.1088\/0953-4075\/40\/9\/S11\" 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=2007JPhB...40..181M\" aria-label=\"ADS reference 17\" 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=2317276\" aria-label=\"MathSciNet reference 17\" 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 17\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Radiative%20properties%20of%20a%20linear%20chain%20of%20coupled%20qubits&amp;journal=J.%20Phys.%20B%3A%20At.%20Mol.%20Opt.%20Phys.&amp;doi=10.1088%2F0953-4075%2F40%2F9%2FS11&amp;volume=40&amp;pages=S181-S197&amp;publication_year=2007&amp;author=Mewton%2CC&amp;author=Ficek%2CZ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR18\">Zoubi, H. &amp; Ritsch, H. Metastability and directional emission characteristics of excitons in 1D optical lattices. Europhys. Lett. 90, 23001 (2010).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1209\/0295-5075\/90\/23001\" data-track-item_id=\"10.1209\/0295-5075\/90\/23001\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1209%2F0295-5075%2F90%2F23001\" aria-label=\"Article reference 18\" data-doi=\"10.1209\/0295-5075\/90\/23001\" 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=2010EL.....9023001Z\" 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=Metastability%20and%20directional%20emission%20characteristics%20of%20excitons%20in%201D%20optical%20lattices&amp;journal=Europhys.%20Lett.&amp;doi=10.1209%2F0295-5075%2F90%2F23001&amp;volume=90&amp;publication_year=2010&amp;author=Zoubi%2CH&amp;author=Ritsch%2CH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR19\">Sutherland, R. &amp; Robicheaux, F. Collective dipole-dipole interactions in an atomic array. Phys. Rev. A 94, 013847 (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\/PhysRevA.94.013847\" data-track-item_id=\"10.1103\/PhysRevA.94.013847\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.94.013847\" aria-label=\"Article reference 19\" data-doi=\"10.1103\/PhysRevA.94.013847\" 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=2016PhRvA..94a3847S\" 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=Collective%20dipole-dipole%20interactions%20in%20an%20atomic%20array&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.94.013847&amp;volume=94&amp;publication_year=2016&amp;author=Sutherland%2CR&amp;author=Robicheaux%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR20\">Rubies-Bigorda, O. &amp; Yelin, S. F. Superradiance and subradiance in inverted atomic arrays. Phys. Rev. A 106, 053717 (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.106.053717\" data-track-item_id=\"10.1103\/PhysRevA.106.053717\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.106.053717\" aria-label=\"Article reference 20\" data-doi=\"10.1103\/PhysRevA.106.053717\" 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.106e3717R\" aria-label=\"ADS reference 20\" 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 20\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Superradiance%20and%20subradiance%20in%20inverted%20atomic%20arrays&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.106.053717&amp;volume=106&amp;publication_year=2022&amp;author=Rubies-Bigorda%2CO&amp;author=Yelin%2CSF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR21\">Sierra, E., Masson, S. J. &amp; Asenjo-Garcia, A. Dicke superradiance in ordered lattices: dimensionality matters. Phys. Rev. Res. 4, 023207 (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\/PhysRevResearch.4.023207\" data-track-item_id=\"10.1103\/PhysRevResearch.4.023207\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevResearch.4.023207\" aria-label=\"Article reference 21\" data-doi=\"10.1103\/PhysRevResearch.4.023207\" 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 21\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Dicke%20superradiance%20in%20ordered%20lattices%3A%20dimensionality%20matters&amp;journal=Phys.%20Rev.%20Res.&amp;doi=10.1103%2FPhysRevResearch.4.023207&amp;volume=4&amp;publication_year=2022&amp;author=Sierra%2CE&amp;author=Masson%2CSJ&amp;author=Asenjo-Garcia%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR22\">Masson, S. J. &amp; Asenjo-Garcia, A. Universality of Dicke superradiance in arrays of quantum emitters. Nat. Commun. 13, 2285 (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\/s41467-022-29805-4\" data-track-item_id=\"10.1038\/s41467-022-29805-4\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41467-022-29805-4\" aria-label=\"Article reference 22\" data-doi=\"10.1038\/s41467-022-29805-4\" 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=2022NatCo..13.2285M\" 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=Universality%20of%20Dicke%20superradiance%20in%20arrays%20of%20quantum%20emitters&amp;journal=Nat.%20Commun.&amp;doi=10.1038%2Fs41467-022-29805-4&amp;volume=13&amp;publication_year=2022&amp;author=Masson%2CSJ&amp;author=Asenjo-Garcia%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR23\">Fayard, N., Ferrier-Barbut, I., Browaeys, A. &amp; Greffet, J.-J. Optical control of collective states in one-dimensional ordered atomic chains beyond the linear regime. Phys. Rev. A 108, 023116 (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\/PhysRevA.108.023116\" data-track-item_id=\"10.1103\/PhysRevA.108.023116\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.108.023116\" aria-label=\"Article reference 23\" data-doi=\"10.1103\/PhysRevA.108.023116\" 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=2023PhRvA.108b3116F\" aria-label=\"ADS reference 23\" 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 23\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optical%20control%20of%20collective%20states%20in%20one-dimensional%20ordered%20atomic%20chains%20beyond%20the%20linear%20regime&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.108.023116&amp;volume=108&amp;publication_year=2023&amp;author=Fayard%2CN&amp;author=Ferrier-Barbut%2CI&amp;author=Browaeys%2CA&amp;author=Greffet%2CJ-J\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR24\">Masson, S. J., Covey, J. P., Will, S. &amp; Asenjo-Garcia, A. Dicke superradiance in ordered arrays of multilevel atoms. PRX Quantum 5, 010344 (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\/PRXQuantum.5.010344\" data-track-item_id=\"10.1103\/PRXQuantum.5.010344\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPRXQuantum.5.010344\" aria-label=\"Article reference 24\" data-doi=\"10.1103\/PRXQuantum.5.010344\" 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=2024PRXQ....5a0344M\" aria-label=\"ADS reference 24\" 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 24\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Dicke%20superradiance%20in%20ordered%20arrays%20of%20multilevel%20atoms&amp;journal=PRX%20Quantum&amp;doi=10.1103%2FPRXQuantum.5.010344&amp;volume=5&amp;publication_year=2024&amp;author=Masson%2CSJ&amp;author=Covey%2CJP&amp;author=Will%2CS&amp;author=Asenjo-Garcia%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR25\">Bettles, R. J., Gardiner, S. A. &amp; Adams, C. S. Enhanced optical cross section via collective coupling of atomic dipoles in a 2D array. Phys. Rev. Lett. 116, 103602 (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\/PhysRevLett.116.103602\" data-track-item_id=\"10.1103\/PhysRevLett.116.103602\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.116.103602\" aria-label=\"Article reference 25\" data-doi=\"10.1103\/PhysRevLett.116.103602\" 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=2016PhRvL.116j3602B\" 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=Enhanced%20optical%20cross%20section%20via%20collective%20coupling%20of%20atomic%20dipoles%20in%20a%202D%20array&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.116.103602&amp;volume=116&amp;publication_year=2016&amp;author=Bettles%2CRJ&amp;author=Gardiner%2CSA&amp;author=Adams%2CCS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR26\">Shahmoon, E., Wild, D. S., Lukin, M. D. &amp; Yelin, S. F. Cooperative resonances in light scattering from two-dimensional atomic arrays. Phys. Rev. Lett. 118, 113601 (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.118.113601\" data-track-item_id=\"10.1103\/PhysRevLett.118.113601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.118.113601\" aria-label=\"Article reference 26\" data-doi=\"10.1103\/PhysRevLett.118.113601\" 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.118k3601S\" aria-label=\"ADS reference 26\" 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 26\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Cooperative%20resonances%20in%20light%20scattering%20from%20two-dimensional%20atomic%20arrays&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.118.113601&amp;volume=118&amp;publication_year=2017&amp;author=Shahmoon%2CE&amp;author=Wild%2CDS&amp;author=Lukin%2CMD&amp;author=Yelin%2CSF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR27\">Chui, S.-T., Du, S. &amp; Jo, G.-B. Subwavelength transportation of light with atomic resonances. Phys. Rev. A 92, 053826 (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\/PhysRevA.92.053826\" data-track-item_id=\"10.1103\/PhysRevA.92.053826\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.92.053826\" aria-label=\"Article reference 27\" data-doi=\"10.1103\/PhysRevA.92.053826\" 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=2015PhRvA..92e3826C\" 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=Subwavelength%20transportation%20of%20light%20with%20atomic%20resonances&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.92.053826&amp;volume=92&amp;publication_year=2015&amp;author=Chui%2CS-T&amp;author=Du%2CS&amp;author=Jo%2CG-B\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR28\">Facchinetti, G., Jenkins, S. D. &amp; Ruostekoski, J. Storing light with subradiant correlations in arrays of atoms. Phys. Rev. Lett. 117, 243601 (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\/PhysRevLett.117.243601\" data-track-item_id=\"10.1103\/PhysRevLett.117.243601\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.117.243601\" aria-label=\"Article reference 28\" data-doi=\"10.1103\/PhysRevLett.117.243601\" 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=2016PhRvL.117x3601F\" 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=Storing%20light%20with%20subradiant%20correlations%20in%20arrays%20of%20atoms&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.117.243601&amp;volume=117&amp;publication_year=2016&amp;author=Facchinetti%2CG&amp;author=Jenkins%2CSD&amp;author=Ruostekoski%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR29\">Asenjo-Garcia, A., Moreno-Cardoner, M., Albrecht, A., Kimble, H. &amp; Chang, D. E. Exponential improvement in photon storage fidelities using subradiance and \u2018selective radiance\u2019 in atomic arrays. Phys. Rev. X 7, 031024 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><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=Exponential%20improvement%20in%20photon%20storage%20fidelities%20using%20subradiance%20and%20%E2%80%98selective%20radiance%E2%80%99%20in%20atomic%20arrays&amp;journal=Phys.%20Rev.%20X&amp;volume=7&amp;publication_year=2017&amp;author=Asenjo-Garcia%2CA&amp;author=Moreno-Cardoner%2CM&amp;author=Albrecht%2CA&amp;author=Kimble%2CH&amp;author=Chang%2CDE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR30\">Manzoni, M. et al. Optimization of photon storage fidelity in ordered atomic arrays. New J. Phys. 20, 083048 (2018).<\/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\/aadb74\" data-track-item_id=\"10.1088\/1367-2630\/aadb74\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1367-2630%2Faadb74\" aria-label=\"Article reference 30\" data-doi=\"10.1088\/1367-2630\/aadb74\" 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=2018NJPh...20h3048M\" 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=Optimization%20of%20photon%20storage%20fidelity%20in%20ordered%20atomic%20arrays&amp;journal=New%20J.%20Phys.&amp;doi=10.1088%2F1367-2630%2Faadb74&amp;volume=20&amp;publication_year=2018&amp;author=Manzoni%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR31\">Needham, J. A., Lesanovsky, I. &amp; Olmos, B. Subradiance-protected excitation transport. New J. Phys. 21, 073061 (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\/ab31e8\" data-track-item_id=\"10.1088\/1367-2630\/ab31e8\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F1367-2630%2Fab31e8\" aria-label=\"Article reference 31\" data-doi=\"10.1088\/1367-2630\/ab31e8\" 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=2019NJPh...21g3061N\" 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=Subradiance-protected%20excitation%20transport&amp;journal=New%20J.%20Phys.&amp;doi=10.1088%2F1367-2630%2Fab31e8&amp;volume=21&amp;publication_year=2019&amp;author=Needham%2CJA&amp;author=Lesanovsky%2CI&amp;author=Olmos%2CB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR32\">Bekenstein, R. et al. Quantum metasurfaces with atom arrays. Nat. Phys. 16, 676\u2013681 (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\/s41567-020-0845-5\" data-track-item_id=\"10.1038\/s41567-020-0845-5\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-020-0845-5\" aria-label=\"Article reference 32\" data-doi=\"10.1038\/s41567-020-0845-5\" 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 32\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20metasurfaces%20with%20atom%20arrays&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-020-0845-5&amp;volume=16&amp;pages=676-681&amp;publication_year=2020&amp;author=Bekenstein%2CR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR33\">Masson, S. J. &amp; Asenjo-Garcia, A. Atomic-waveguide quantum electrodynamics. Phys. Rev. Res. 2, 043213 (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\/PhysRevResearch.2.043213\" data-track-item_id=\"10.1103\/PhysRevResearch.2.043213\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevResearch.2.043213\" aria-label=\"Article reference 33\" data-doi=\"10.1103\/PhysRevResearch.2.043213\" 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 33\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Atomic-waveguide%20quantum%20electrodynamics&amp;journal=Phys.%20Rev.%20Res.&amp;doi=10.1103%2FPhysRevResearch.2.043213&amp;volume=2&amp;publication_year=2020&amp;author=Masson%2CSJ&amp;author=Asenjo-Garcia%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR34\">Patti, T. L., Wild, D. S., Shahmoon, E., Lukin, M. D. &amp; Yelin, S. F. Controlling interactions between quantum emitters using atom arrays. Phys. Rev. Lett. 126, 223602 (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.126.223602\" data-track-item_id=\"10.1103\/PhysRevLett.126.223602\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.126.223602\" aria-label=\"Article reference 34\" data-doi=\"10.1103\/PhysRevLett.126.223602\" 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.126v3602P\" 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=Controlling%20interactions%20between%20quantum%20emitters%20using%20atom%20arrays&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.126.223602&amp;volume=126&amp;publication_year=2021&amp;author=Patti%2CTL&amp;author=Wild%2CDS&amp;author=Shahmoon%2CE&amp;author=Lukin%2CMD&amp;author=Yelin%2CSF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR35\">Castells-Graells, D., Malz, D., Rusconi, C. C. &amp; Cirac, J. I. Atomic waveguide QED with atomic dimers. Phys. Rev. A 104, 063707 (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\/PhysRevA.104.063707\" data-track-item_id=\"10.1103\/PhysRevA.104.063707\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.104.063707\" aria-label=\"Article reference 35\" data-doi=\"10.1103\/PhysRevA.104.063707\" 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=2021PhRvA.104f3707C\" aria-label=\"ADS reference 35\" 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=4361706\" aria-label=\"MathSciNet reference 35\" 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 35\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Atomic%20waveguide%20QED%20with%20atomic%20dimers&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.104.063707&amp;volume=104&amp;publication_year=2021&amp;author=Castells-Graells%2CD&amp;author=Malz%2CD&amp;author=Rusconi%2CCC&amp;author=Cirac%2CJI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR36\">Mekhov, I. B., Maschler, C. &amp; Ritsch, H. Cavity-enhanced light scattering in optical lattices to probe atomic quantum statistics. Phys. Rev. Lett. 98, 100402 (2007).<\/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.98.100402\" data-track-item_id=\"10.1103\/PhysRevLett.98.100402\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.98.100402\" aria-label=\"Article reference 36\" data-doi=\"10.1103\/PhysRevLett.98.100402\" 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=2007PhRvL..98j0402M\" 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-enhanced%20light%20scattering%20in%20optical%20lattices%20to%20probe%20atomic%20quantum%20statistics&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.98.100402&amp;volume=98&amp;publication_year=2007&amp;author=Mekhov%2CIB&amp;author=Maschler%2CC&amp;author=Ritsch%2CH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR37\">Mekhov, I. B., Maschler, C. &amp; Ritsch, H. Light scattering from ultracold atoms in optical lattices as an optical probe of quantum statistics. Phys. Rev. A 76, 053618 (2007).<\/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.76.053618\" data-track-item_id=\"10.1103\/PhysRevA.76.053618\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.76.053618\" aria-label=\"Article reference 37\" data-doi=\"10.1103\/PhysRevA.76.053618\" 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=2007PhRvA..76e3618M\" aria-label=\"ADS reference 37\" 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 37\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Light%20scattering%20from%20ultracold%20atoms%20in%20optical%20lattices%20as%20an%20optical%20probe%20of%20quantum%20statistics&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.76.053618&amp;volume=76&amp;publication_year=2007&amp;author=Mekhov%2CIB&amp;author=Maschler%2CC&amp;author=Ritsch%2CH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR38\">Ruostekoski, J., Foot, C. J. &amp; Deb, A. B. Light scattering for thermometry of fermionic atoms in an optical lattice. Phys. Rev. Lett. 103, 170404 (2009).<\/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.103.170404\" data-track-item_id=\"10.1103\/PhysRevLett.103.170404\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.103.170404\" aria-label=\"Article reference 38\" data-doi=\"10.1103\/PhysRevLett.103.170404\" 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=2009PhRvL.103q0404R\" aria-label=\"ADS reference 38\" 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 38\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Light%20scattering%20for%20thermometry%20of%20fermionic%20atoms%20in%20an%20optical%20lattice&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.103.170404&amp;volume=103&amp;publication_year=2009&amp;author=Ruostekoski%2CJ&amp;author=Foot%2CCJ&amp;author=Deb%2CAB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR39\">Rist, S., Menotti, C. &amp; Morigi, G. Light scattering by ultracold atoms in an optical lattice. Phys. Rev. A 81, 013404 (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.81.013404\" data-track-item_id=\"10.1103\/PhysRevA.81.013404\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.81.013404\" aria-label=\"Article reference 39\" data-doi=\"10.1103\/PhysRevA.81.013404\" 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..81a3404R\" 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=Light%20scattering%20by%20ultracold%20atoms%20in%20an%20optical%20lattice&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.81.013404&amp;volume=81&amp;publication_year=2010&amp;author=Rist%2CS&amp;author=Menotti%2CC&amp;author=Morigi%2CG\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR40\">Kozlowski, W., Caballero-Benitez, S. F. &amp; Mekhov, I. B. Probing matter-field and atom-number correlations in optical lattices by global nondestructive addressing. Phys. Rev. A 92, 013613 (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\/PhysRevA.92.013613\" data-track-item_id=\"10.1103\/PhysRevA.92.013613\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.92.013613\" aria-label=\"Article reference 40\" data-doi=\"10.1103\/PhysRevA.92.013613\" 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=2015PhRvA..92a3613K\" 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=Probing%20matter-field%20and%20atom-number%20correlations%20in%20optical%20lattices%20by%20global%20nondestructive%20addressing&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.92.013613&amp;volume=92&amp;publication_year=2015&amp;author=Kozlowski%2CW&amp;author=Caballero-Benitez%2CSF&amp;author=Mekhov%2CIB\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR41\">Corcovilos, T. A., Baur, S. K., Hitchcock, J. M., Mueller, E. J. &amp; Hulet, R. G. Detecting antiferromagnetism of atoms in an optical lattice via optical bragg scattering. Phys. Rev. A 81, 013415 (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.81.013415\" data-track-item_id=\"10.1103\/PhysRevA.81.013415\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.81.013415\" aria-label=\"Article reference 41\" data-doi=\"10.1103\/PhysRevA.81.013415\" 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..81a3415C\" 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=Detecting%20antiferromagnetism%20of%20atoms%20in%20an%20optical%20lattice%20via%20optical%20bragg%20scattering&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.81.013415&amp;volume=81&amp;publication_year=2010&amp;author=Corcovilos%2CTA&amp;author=Baur%2CSK&amp;author=Hitchcock%2CJM&amp;author=Mueller%2CEJ&amp;author=Hulet%2CRG\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR42\">Douglas, J. S. &amp; Burnett, K. Light scattering from ultracold atomic gases in optical lattices at finite temperature. Phys. Rev. A 84, 033637 (2011).<\/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.84.033637\" data-track-item_id=\"10.1103\/PhysRevA.84.033637\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevA.84.033637\" aria-label=\"Article reference 42\" data-doi=\"10.1103\/PhysRevA.84.033637\" 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=2011PhRvA..84c3637D\" aria-label=\"ADS reference 42\" 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 42\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Light%20scattering%20from%20ultracold%20atomic%20gases%20in%20optical%20lattices%20at%20finite%20temperature&amp;journal=Phys.%20Rev.%20A&amp;doi=10.1103%2FPhysRevA.84.033637&amp;volume=84&amp;publication_year=2011&amp;author=Douglas%2CJS&amp;author=Burnett%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR43\">Fedoseev, V. et al. Coherent and incoherent light scattering by single-atom wavepackets. Phys. Rev. Lett. 135, 043601 (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\/zwhd-1k2t\" data-track-item_id=\"10.1103\/zwhd-1k2t\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2Fzwhd-1k2t\" aria-label=\"Article reference 43\" data-doi=\"10.1103\/zwhd-1k2t\" 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=2025PhRvL.135d3601F\" aria-label=\"ADS reference 43\" 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 43\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Coherent%20and%20incoherent%20light%20scattering%20by%20single-atom%20wavepackets&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2Fzwhd-1k2t&amp;volume=135&amp;publication_year=2025&amp;author=Fedoseev%2CV\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR44\">Kibble, T. W. Topology of cosmic domains and strings. J. Phys. A: Math. Gen. 9, 1387\u20131398 (1976).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1088\/0305-4470\/9\/8\/029\" data-track-item_id=\"10.1088\/0305-4470\/9\/8\/029\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1088%2F0305-4470%2F9%2F8%2F029\" aria-label=\"Article reference 44\" data-doi=\"10.1088\/0305-4470\/9\/8\/029\" 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=1976JPhA....9.1387K\" aria-label=\"ADS reference 44\" 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 44\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topology%20of%20cosmic%20domains%20and%20strings&amp;journal=J.%20Phys.%20A%3A%20Math.%20Gen.&amp;doi=10.1088%2F0305-4470%2F9%2F8%2F029&amp;volume=9&amp;pages=1387-1398&amp;publication_year=1976&amp;author=Kibble%2CTW\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR45\">Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505\u2013508 (1985).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1038\/317505a0\" data-track-item_id=\"10.1038\/317505a0\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2F317505a0\" aria-label=\"Article reference 45\" data-doi=\"10.1038\/317505a0\" 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=1985Natur.317..505Z\" 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=Cosmological%20experiments%20in%20superfluid%20helium%3F&amp;journal=Nature&amp;doi=10.1038%2F317505a0&amp;volume=317&amp;pages=505-508&amp;publication_year=1985&amp;author=Zurek%2CWH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR46\">Del Campo, A. &amp; Zurek, W. H. Universality of phase transition dynamics: topological defects from symmetry breaking. Int. J. Mod. Phys. A 29, 1430018 (2014).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1142\/S0217751X1430018X\" data-track-item_id=\"10.1142\/S0217751X1430018X\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1142%2FS0217751X1430018X\" aria-label=\"Article reference 46\" data-doi=\"10.1142\/S0217751X1430018X\" 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 46\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Universality%20of%20phase%20transition%20dynamics%3A%20topological%20defects%20from%20symmetry%20breaking&amp;journal=Int.%20J.%20Mod.%20Phys.%20A&amp;doi=10.1142%2FS0217751X1430018X&amp;volume=29&amp;publication_year=2014&amp;author=Campo%2CA&amp;author=Zurek%2CWH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR47\">Guerin, W., Rouabah, M. &amp; Kaiser, R. Light interacting with atomic ensembles: collective, cooperative and mesoscopic effects. J. Mod. Opt. 64, 895\u2013907 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1080\/09500340.2016.1215564\" data-track-item_id=\"10.1080\/09500340.2016.1215564\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1080%2F09500340.2016.1215564\" aria-label=\"Article reference 47\" data-doi=\"10.1080\/09500340.2016.1215564\" 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=2017JMOp...64..895G\" 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=Light%20interacting%20with%20atomic%20ensembles%3A%20collective%2C%20cooperative%20and%20mesoscopic%20effects&amp;journal=J.%20Mod.%20Opt.&amp;doi=10.1080%2F09500340.2016.1215564&amp;volume=64&amp;pages=895-907&amp;publication_year=2017&amp;author=Guerin%2CW&amp;author=Rouabah%2CM&amp;author=Kaiser%2CR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR48\">Cohen-Tannoudji, C., Dupont-Roc, J. &amp; Grynberg, G. Atom-Photon Interactions: Basic Processes and Applications (Wiley, 2024).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR49\">Wolf, S., Wechs, J., von Zanthier, J. &amp; Schmidt-Kaler, F. Visibility of young\u2019s interference fringes: scattered light from small ion crystals. Phys. Rev. Lett. 116, 183002 (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\/PhysRevLett.116.183002\" data-track-item_id=\"10.1103\/PhysRevLett.116.183002\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.116.183002\" aria-label=\"Article reference 49\" data-doi=\"10.1103\/PhysRevLett.116.183002\" 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=2016PhRvL.116r3002W\" 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=Visibility%20of%20young%E2%80%99s%20interference%20fringes%3A%20scattered%20light%20from%20small%20ion%20crystals&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.116.183002&amp;volume=116&amp;publication_year=2016&amp;author=Wolf%2CS&amp;author=Wechs%2CJ&amp;author=Zanthier%2CJ&amp;author=Schmidt-Kaler%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR50\">Sachdev, S. Quantum Phase Transitions 2nd edn (Cambridge Univ. Press, 2011).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR51\">Capogrosso-Sansone, B., Prokof\u2019ev, N. V. &amp; Svistunov, B. V. Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model. Phys. Rev. B 75, 134302 (2007).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.75.134302\" data-track-item_id=\"10.1103\/PhysRevB.75.134302\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.75.134302\" aria-label=\"Article reference 51\" data-doi=\"10.1103\/PhysRevB.75.134302\" 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=2007PhRvB..75m4302C\" aria-label=\"ADS reference 51\" 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 51\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Phase%20diagram%20and%20thermodynamics%20of%20the%20three-dimensional%20Bose-Hubbard%20model&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.75.134302&amp;volume=75&amp;publication_year=2007&amp;author=Capogrosso-Sansone%2CB&amp;author=Prokof%E2%80%99ev%2CNV&amp;author=Svistunov%2CBV\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR52\">Jones, K. M., Tiesinga, E., Lett, P. D. &amp; Julienne, P. S. Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering. Rev. Mod. Phys. 78, 483\u2013535 (2006).<\/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.78.483\" data-track-item_id=\"10.1103\/RevModPhys.78.483\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FRevModPhys.78.483\" aria-label=\"Article reference 52\" data-doi=\"10.1103\/RevModPhys.78.483\" 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=2006RvMP...78..483J\" aria-label=\"ADS reference 52\" 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 52\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Ultracold%20photoassociation%20spectroscopy%3A%20long-range%20molecules%20and%20atomic%20scattering&amp;journal=Rev.%20Mod.%20Phys.&amp;doi=10.1103%2FRevModPhys.78.483&amp;volume=78&amp;pages=483-535&amp;publication_year=2006&amp;author=Jones%2CKM&amp;author=Tiesinga%2CE&amp;author=Lett%2CPD&amp;author=Julienne%2CPS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR53\">Polkovnikov, A. Universal adiabatic dynamics in the vicinity of a quantum critical point. Phys. Rev. B 72, 161201 (2005).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.72.161201\" data-track-item_id=\"10.1103\/PhysRevB.72.161201\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.72.161201\" aria-label=\"Article reference 53\" data-doi=\"10.1103\/PhysRevB.72.161201\" 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=2005PhRvB..72p1201P\" aria-label=\"ADS reference 53\" 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 53\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Universal%20adiabatic%20dynamics%20in%20the%20vicinity%20of%20a%20quantum%20critical%20point&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.72.161201&amp;volume=72&amp;publication_year=2005&amp;author=Polkovnikov%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR54\">Pekker, D. et al. Signatures of the superfluid to Mott insulator transition in equilibrium and in dynamical ramps. Phys. Rev. B 86, 144527 (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"10.1103\/PhysRevB.86.144527\" data-track-item_id=\"10.1103\/PhysRevB.86.144527\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevB.86.144527\" aria-label=\"Article reference 54\" data-doi=\"10.1103\/PhysRevB.86.144527\" 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=2012PhRvB..86n4527P\" 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=Signatures%20of%20the%20superfluid%20to%20Mott%20insulator%20transition%20in%20equilibrium%20and%20in%20dynamical%20ramps&amp;journal=Phys.%20Rev.%20B&amp;doi=10.1103%2FPhysRevB.86.144527&amp;volume=86&amp;publication_year=2012&amp;author=Pekker%2CD\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR55\">Scully, M. O. Single photon subradiance: quantum control of spontaneous emission and ultrafast readout. Phys. Rev. Lett. 115, 243602 (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\/PhysRevLett.115.243602\" data-track-item_id=\"10.1103\/PhysRevLett.115.243602\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.115.243602\" aria-label=\"Article reference 55\" data-doi=\"10.1103\/PhysRevLett.115.243602\" 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=2015PhRvL.115x3602S\" 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=Single%20photon%20subradiance%3A%20quantum%20control%20of%20spontaneous%20emission%20and%20ultrafast%20readout&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.115.243602&amp;volume=115&amp;publication_year=2015&amp;author=Scully%2CMO\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR56\">He, Y. et al. Geometric control of collective spontaneous emission. Phys. Rev. Lett. 125, 213602 (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\/PhysRevLett.125.213602\" data-track-item_id=\"10.1103\/PhysRevLett.125.213602\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevLett.125.213602\" aria-label=\"Article reference 56\" data-doi=\"10.1103\/PhysRevLett.125.213602\" 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=2020PhRvL.125u3602H\" 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=Geometric%20control%20of%20collective%20spontaneous%20emission&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2FPhysRevLett.125.213602&amp;volume=125&amp;publication_year=2020&amp;author=He%2CY\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR57\">Gross, C. &amp; Bakr, W. S. Quantum gas microscopy for single atom and spin detection. Nat. Phys. 17, 1316\u20131323 (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\/s41567-021-01370-5\" data-track-item_id=\"10.1038\/s41567-021-01370-5\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41567-021-01370-5\" aria-label=\"Article reference 57\" data-doi=\"10.1038\/s41567-021-01370-5\" 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 57\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20gas%20microscopy%20for%20single%20atom%20and%20spin%20detection&amp;journal=Nat.%20Phys.&amp;doi=10.1038%2Fs41567-021-01370-5&amp;volume=17&amp;pages=1316-1323&amp;publication_year=2021&amp;author=Gross%2CC&amp;author=Bakr%2CWS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR58\">Jepsen, P. N. et al. Spin transport in a tunable heisenberg model realized with ultracold atoms. Nature 588, 403\u2013407 (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\/s41586-020-3033-y\" data-track-item_id=\"10.1038\/s41586-020-3033-y\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1038%2Fs41586-020-3033-y\" aria-label=\"Article reference 58\" data-doi=\"10.1038\/s41586-020-3033-y\" 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..403J\" aria-label=\"ADS reference 58\" 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 58\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Spin%20transport%20in%20a%20tunable%20heisenberg%20model%20realized%20with%20ultracold%20atoms&amp;journal=Nature&amp;doi=10.1038%2Fs41586-020-3033-y&amp;volume=588&amp;pages=403-407&amp;publication_year=2020&amp;author=Jepsen%2CPN\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR59\">Jepsen, P. N. et al. Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms. Physical Review X 11, 041054 (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\/PhysRevX.11.041054\" data-track-item_id=\"10.1103\/PhysRevX.11.041054\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2FPhysRevX.11.041054\" aria-label=\"Article reference 59\" data-doi=\"10.1103\/PhysRevX.11.041054\" 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=2021PhRvX..11d1054J\" 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=Transverse%20spin%20dynamics%20in%20the%20anisotropic%20Heisenberg%20model%20realized%20with%20ultracold%20atoms&amp;journal=Physical%20Review%20X&amp;doi=10.1103%2FPhysRevX.11.041054&amp;volume=11&amp;publication_year=2021&amp;author=Jepsen%2CPN\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR60\">Lee, Y. K. et al. Observation of spin squeezing with contact interactions in one-and three-dimensional easy-plane magnets. Phys. Rev. Lett. 135, 023402 (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\/jqvz-kpwg\" data-track-item_id=\"10.1103\/jqvz-kpwg\" data-track-value=\"article reference\" data-track-action=\"article reference\" href=\"https:\/\/doi.org\/10.1103%2Fjqvz-kpwg\" aria-label=\"Article reference 60\" data-doi=\"10.1103\/jqvz-kpwg\" 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=2025PhRvL.135b3402L\" 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=Observation%20of%20spin%20squeezing%20with%20contact%20interactions%20in%20one-and%20three-dimensional%20easy-plane%20magnets&amp;journal=Phys.%20Rev.%20Lett.&amp;doi=10.1103%2Fjqvz-kpwg&amp;volume=135&amp;publication_year=2025&amp;author=Lee%2CYK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR61\">Lu, Y.-K. Data for figures in \u2018Suppression of coherent light scattering in a three-dimensional atomic array\u2019 (arXiv:2508.10966). Zenodo <a href=\"https:\/\/doi.org\/10.5281\/zenodo.19422912\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.5281\/zenodo.19422912\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.19422912<\/a> (2026).<\/p>\n","protected":false},"excerpt":{"rendered":"Dicke, R. H. Coherence in spontaneous radiation processes. Phys. Rev. 93, 99\u2013110 (1954). Article\u00a0 ADS\u00a0 Google Scholar\u00a0 Lehmberg,&hellip;\n","protected":false},"author":2,"featured_media":618560,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[4491,10242,4490,4495,4494,3250,4489,4492,4493,2302,4682,90,4488,56,54,55],"class_list":["post-618559","post","type-post","status-publish","format-standard","has-post-thumbnail","category-physics","tag-atomic","tag-atomic-and-molecular-interactions-with-photons","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-mechanics","tag-science","tag-theoretical","tag-uk","tag-united-kingdom","tag-unitedkingdom"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts\/618559","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/comments?post=618559"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts\/618559\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/media\/618560"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/media?parent=618559"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/categories?post=618559"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/tags?post=618559"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}