McDonald, A., Pereg-Barnea, T. & Clerk, A. A. Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain. Phys. Rev. X 8, 041031 (2018).
Wanjura, C. C., Brunelli, M. & Nunnenkamp, A. Topological framework for directional amplification in driven-dissipative cavity arrays. Nat. Commun. 11, 3149 (2020).
Wanjura, C. C. et al. Quadrature nonreciprocity in bosonic networks without breaking time-reversal symmetry. Nat. Phys. 19, 1429–1436 (2023).
Valcárcel, G. J., Patera, G., Treps, N. & Fabre, C. Multimode squeezing of frequency combs. Phys. Rev. A 74, 061801 (2006).
Roslund, J., Araújo, R. M., Jiang, S., Fabre, C. & Treps, N. Wavelength-multiplexed quantum networks with ultrafast frequency combs. Nat. Photon. 8, 109–112 (2014).
Chen, M., Menicucci, N. C. & Pfister, O. Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb. Phys. Rev. Lett. 112, 120505 (2014).
Cai, Y. et al. Multimode entanglement in reconfigurable graph states using optical frequency combs. Nat. Commun. 8, 15645 (2017).
Madsen, L. S. et al. Quantum computational advantage with a programmable photonic processor. Nature 606, 75–81 (2022).
Wan, L.-L. & Lü, X.-Y. Quantum-squeezing-induced point-gap topology and skin effect. Phys. Rev. Lett. 130, 203605 (2023).
Flynn, V. P., Cobanera, E. & Viola, L. Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians. N. J. Phys. 22, 083004 (2020).
Poli, C., Bellec, M., Kuhl, U., Mortessagne, F. & Schomerus, H. Selective enhancement of topologically induced interface states in a dielectric resonator chain. Nat. Commun. 6, 6710 (2015).
Luo, X.-W., Zhang, C. & Du, S. Quantum squeezing and sensing with pseudo-anti-parity-time symmetry. Phys. Rev. Lett. 128, 173602 (2022).
Uddin, S. Z. et al. Noise-immune quantum correlations of intense light. Nat. Photon. 19, 751–757 (2025).
Fabre, C. & Treps, N. Modes and states in quantum optics. Rev. Mod. Phys. 92, 035005 (2020).
Braunstein, S. L. & Loock, P. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005).
Leefmans, C. et al. Topological dissipation in a time-multiplexed photonic resonator network. Nat. Phys. 18, 442–449 (2022).
Wang, Y.-X. & Clerk, A. A. Non-Hermitian dynamics without dissipation in quantum systems. Phys. Rev. A 99, 063834 (2019).
Roy, A., Jahani, S., Langrock, C., Fejer, M. & Marandi, A. Spectral phase transitions in optical parametric oscillators. Nat. Commun. 12, 835 (2021).
Pino, J., Slim, J. J. & Verhagen, E. Non-Hermitian chiral phononics through optomechanically induced squeezing. Nature 606, 82–87 (2022).
Slim, J. J. et al. Optomechanical realization of the bosonic Kitaev chain. Nature 627, 767–771 (2024).
Chembo, Y. K. Quantum dynamics of Kerr optical frequency combs below and above threshold: spontaneous four-wave mixing, entanglement, and squeezed states of light. Phys. Rev. A 93, 033820 (2016).
Yang, Z. et al. A squeezed quantum microcomb on a chip. Nat. Commun. 12, 4781 (2021).
Zhao, Y. et al. Near-degenerate quadrature-squeezed vacuum generation on a silicon-nitride chip. Phys. Rev. Lett. 124, 193601 (2020).
Jahanbozorgi, M. et al. Generation of squeezed quantum microcombs with silicon nitride integrated photonic circuits. Optica 10, 1100–1101 (2023).
Javid, U. A. et al. Chip-scale simulations in a quantum-correlated synthetic space. Nat. Photon. 17, 883–890 (2023).
Del’Haye, P. et al. Optical frequency comb generation from a monolithic microresonator. Nature 450, 1214–1217 (2007).
Herr, T. et al. Temporal solitons in optical microresonators. Nat. Photon. 8, 145–152 (2014).
Cole, D. C., Lamb, E. S., Del’Haye, P., Diddams, S. A. & Papp, S. B. Soliton crystals in Kerr resonators. Nat. Photon. 11, 671–676 (2017).
Reimer, C. et al. Generation of multiphoton entangled quantum states by means of integrated frequency combs. Science 351, 1176–1180 (2016).
Kues, M. et al. On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature 546, 622–626 (2017).
Moille, G., Menyuk, C., Chembo, Y. K., Dutt, A. & Srinivasan, K. Synthetic frequency lattices from an integrated dispersive multi-color soliton. Preprint at https://arxiv.org/abs/2210.09036 (2022).
Englebert, N. et al. Bloch oscillations of coherently driven dissipative solitons in a synthetic dimension. Nat. Phys. 19, 1014–1021 (2023).
Guidry, M. A., Lukin, D. M., Yang, K. Y., Trivedi, R. & Vučković, J. Quantum optics of soliton microcombs. Nat. Photon. 16, 52–58 (2022).
Bensemhoun, A. et al. Multipartite entanglement in bright frequency combs out of microresonators. Phys. Lett. A 493, 129272 (2024).
Guidry, M. A., Lukin, D. M., Yang, K. Y. & Vučković, J. Multimode squeezing in soliton crystal microcombs. Optica 10, 694–701 (2023).
Gouzien, E. et al. Hidden and detectable squeezing from microresonators. Phys. Rev. Res. 5, 023178 (2023).
Rüter, C. E. et al. Observation of parity-time symmetry in optics. Nat. Phys. 6, 192–195 (2010).
Regensburger, A. et al. Parity-time synthetic photonic lattices. Nature 488, 167–171 (2012).
Zeuner, J. M. et al. Observation of a topological transition in the bulk of a non-Hermitian system. Phys. Rev. Lett. 115, 040402 (2015).
Weimann, S. et al. Topologically protected bound states in photonic parity-time-symmetric crystals. Nat. Mater. 16, 433–438 (2017).
Xia, S. et al. Nonlinear tuning of PT symmetry and non-Hermitian topological states. Science 372, 72–76 (2021).
Chembo, Y. K. & Menyuk, C. R. Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators. Phys. Rev. A 87, 053852 (2013).
Coen, S. & Haelterman, M. Continuous-wave ultrahigh-repetition-rate pulse-train generation through modulational instability in a passive fiber cavity. Opt. Lett. 26, 39–41 (2001).
Yuan, L., Shi, Y. & Fan, S. Photonic gauge potential in a system with a synthetic frequency dimension. Opt. Lett. 41, 741–744 (2016).
Ozawa, T., Price, H. M., Goldman, N., Zilberberg, O. & Carusotto, I. Synthetic dimensions in integrated photonics: from optical isolation to four-dimensional quantum Hall physics. Phys. Rev. A 93, 043827 (2016).
Lustig, E. et al. Photonic topological insulator in synthetic dimensions. Nature 567, 356–360 (2019).
Dutt, A. et al. Experimental band structure spectroscopy along a synthetic dimension. Nat. Commun. 10, 3122 (2019).
Wang, K. et al. Generating arbitrary topological windings of a non-Hermitian band. Science 371, 1240–1245 (2021).
Dutt, A. et al. Creating boundaries along a synthetic frequency dimension. Nat. Commun. 13, 3377 (2022).
Herr, T. et al. Universal formation dynamics and noise of Kerr-frequency combs in microresonators. Nat. Photon. 6, 480–487 (2012).
Marino, A. M., Stroud, J., Wong, V., Bennink, R. S. & Boyd, R. W. Bichromatic local oscillator for detection of two-mode squeezed states of light. J. Opt. Soc. Am. B 24, 335–339 (2007).
Wang, Z. et al. Large-scale cluster quantum microcombs. Light Sci. Appl. 14, 164 (2025).
Jia, X. et al. Continuous-variable multipartite entanglement in an integrated microcomb. Nature 639, 329–336 (2025).
Herman, D. I. et al. Squeezed dual-comb spectroscopy. Science 387, 653–658 (2025).
McCuller, L. et al. Frequency-dependent squeezing for advanced LIGO. Phys. Rev. Lett. 124, 171102 (2020).
Leefmans, C. R. et al. Cavity soliton-induced topological edge states. Preprint at https://arxiv.org/abs/2311.04873 (2023).
Flower, C. J. et al. Observation of topological frequency combs. Science 384, 1356–1361 (2024).
Lukin, D. M. et al. 4H-silicon-carbide-on-insulator for integrated quantum and nonlinear photonics. Nat. Photon. 14, 330–334 (2020).
Wang, W. et al. Coherent terahertz radiation with 2.8-octave tunability through chip-scale photomixed microresonator optical parametric oscillation. Nat. Commun. 13, 5123 (2022).
Gouzien, E., Tanzilli, S., D’Auria, V. & Patera, G. Morphing supermodes: a full characterization for enabling multimode quantum optics. Phys. Rev. Lett. 125, 103601 (2020).
Lustig, E., Guidry, M. A., Lukin, D. M., Shanhui, F. & Vučković, J. Quadrature-dependent lattice dynamics of dissipative microcombs data. figshare https://doi.org/10.6084/m9.figshare.29652338 (2025).