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Quantized Hall Drift in a Frequency-Encoded Photonic Chern Insulator

A. Chénier1, B. d’Aligny2,3, F. Pellerin1, P.-É. Blanchard1, T. Ozawa4, I. Carusotto2, and P. St-Jean1,5

Phys. Rev. X 16, 011020 – Published 5 February, 2026

DOI: https://doi.org/10.1103/2dyh-yhrb

Abstract

The quantization of transport and its resilience to backscattering are key features for leveraging topological matter in applications that demand stringent noise mitigation, such as metrology and quantum information processing. Because of the bosonic nature of light, engineering such robust, “one-way” channels in synthetic photonic systems imposes the implementation of topological models with broken time-reversal symmetry; this is challenging, since photons possess neither an electric charge nor a magnetic moment. Here, we propose and demonstrate an approach to realizing photonic Chern insulators—topological insulators with broken time-reversal symmetry—by encoding a Haldane-like model in the synthetic frequency dimension of an optical fiber loop platform. The bands’ topology is assessed by reconstructing the Bloch state geometry across the Brillouin zone. We further highlight its consequences by measuring a driven-dissipative analog of the quantized transverse Hall conductivity. Our results open avenues for harnessing topologically protected light propagation in frequency-multiplexed photonic systems, with applications ranging from precision metrology to photonic quantum processors.

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References (83)

  1. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  2. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  3. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982).
  4. The Quantum Hall Effect, edited by R. E. Prange and S. M. Girvin, 2nd ed., Graduate Texts in Contemporary Physics (Springer-Verlag, New York, 1990).
  5. K. von Klitzing, Essay: Quantum Hall effect and the new international system of units, Phys. Rev. Lett. 122, 200001 (2019).
  6. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  7. F. Zangeneh-Nejad, D. L. Sounas, A. Alù, and R. Fleury, Analogue computing with metamaterials, Nat. Rev. Mater. 6, 207 (2021).
  8. S. Raghu and F. D. M. Haldane, Analogs of quantum-Hall-effect edge states in photonic crystals, Phys. Rev. A 78, 033834 (2008).
  9. T. Ozawa and H. M. Price, Topological quantum matter in synthetic dimensions, Nat. Rev. Phys. 1, 349 (2019).
  10. H. Price et al., Roadmap on topological photonics, J. Phys. 4, 032501 (2022).
  11. B. Bahari, A. Ndao, F. Vallini, A. El Amili, Y. Fainman, and B. Kanté, Nonreciprocal lasing in topological cavities of arbitrary geometries, Science 358, 636 (2017).
  12. S. Klembt, T. H. Harder, O. A. Egorov, K. Winkler, R. Ge, M. A. Bandres, M. Emmerling, L. Worschech, T. C. H. Liew, M. Segev, C. Schneider, and S. Höfling, Exciton-polariton topological insulator, Nature (London) 562, 552 (2018).
  13. Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, Topological states and adiabatic pumping in quasicrystals, Phys. Rev. Lett. 109, 106402 (2012).
  14. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Photonic Floquet topological insulators, Nature (London) 496, 196 (2013).
  15. M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, Imaging topological edge states in silicon photonics, Nat. Photonics 7, 1001 (2013).
  16. L.-H. Wu and X. Hu, Scheme for achieving a topological photonic crystal by using dielectric material, Phys. Rev. Lett. 114, 223901 (2015).
  17. T. Ma and G. Shvets, All-Si valley-Hall photonic topological insulator, New J. Phys. 18, 025012 (2016).
  18. J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, Observation of photonic topological valley Hall edge states, Phys. Rev. Lett. 120, 063902 (2018).
  19. C. A. Rosiek, G. Arregui, A. Vladimirova, M. Albrechtsen, B. Vosoughi Lahijani, R. E. Christiansen, and S. Stobbe, Observation of strong backscattering in valley-Hall photonic topological interface modes, Nat. Photonics 17, 386 (2023).
  20. L. Lu, J. D. Joannopoulos, and M. Soljačić, Topological states in photonic systems, Nat. Phys. 12, 626 (2016).
  21. A. D’Errico, F. Cardano, M. Maffei, A. Dauphin, R. Barboza, C. Esposito, B. Piccirillo, M. Lewenstein, P. Massignan, and L. Marrucci, Two-dimensional topological quantum walks in the momentum space of structured light, Optica 7, 108 (2020).
  22. T. Ozawa and I. Carusotto, Anomalous and quantum Hall effects in lossy photonic lattices, Phys. Rev. Lett. 112, 133902 (2014).
  23. F. D. M. Haldane, Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly,” Phys. Rev. Lett. 61, 2015 (1988).
  24. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermions, Nature (London) 515, 237 (2014).
  25. N. Fläschner, D. Vogel, M. Tarnowski, B. S. Rem, D.-S. Lühmann, M. Heyl, J. C. Budich, L. Mathey, K. Sengstock, and C. Weitenberg, Observation of dynamical vortices after quenches in a system with topology, Nat. Phys. 14, 265 (2018).
  26. S. Mitra, A. Jiménez-Galán, M. Aulich, M. Neuhaus, R. E. F. Silva, V. Pervak, M. F. Kling, and S. Biswas, Light-wave-controlled Haldane model in monolayer hexagonal boron nitride, Nature (London) 628, 752 (2024).
  27. W. Zhao, K. Kang, Y. Zhang, P. Knüppel, Z. Tao, L. Li, C. L. Tschirhart, E. Redekop, K. Watanabe, T. Taniguchi, A. F. Young, J. Shan, and K. F. Mak, Realization of the Haldane Chern insulator in a moiré lattice, Nat. Phys. 20, 275 (2024).
  28. J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, Y. Ran, T. Cao, L. Fu, D. Xiao, W. Yao, and X. Xu, Signatures of fractional quantum anomalous Hall states in twisted MoTe2, Nature (London) 622, 63 (2023).
  29. L. He, Z. Addison, J. Jin, E. J. Mele, S. G. Johnson, and B. Zhen, Floquet Chern insulators of light, Nat. Commun. 10, 4194 (2019).
  30. Y. G. N. Liu, P. S. Jung, M. Parto, D. N. Christodoulides, and M. Khajavikhan, Gain-induced topological response via tailored long-range interactions, Nat. Phys. 17, 704 (2021).
  31. S. K. Sridhar, S. Ghosh, D. Srinivasan, A. R. Miller, and A. Dutt, Quantized topological pumping in Floquet synthetic dimensions with a driven dissipative photonic molecule, Nat. Phys. 20, 843 (2024).
  32. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
  33. L. Yuan, Q. Lin, M. Xiao, and S. Fan, Synthetic dimension in photonics, Optica 5, 1396 (2018).
  34. A. Parriaux, K. Hammani, and G. Millot, Electro-optic frequency combs, Adv. Opt. Photonics 12, 223 (2020).
  35. T. Ozawa, H. M. Price, N. Goldman, O. Zilberberg, and I. Carusotto, Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics, Phys. Rev. A 93, 043827 (2016).
  36. A. Dutt, M. Minkov, Q. Lin, L. Yuan, D. A. B. Miller, and S. Fan, Experimental band structure spectroscopy along a synthetic dimension, Nat. Commun. 10, 3122 (2019).
  37. S. Sriram, S. K. Sridhar, and A. Dutt, Quantized topological phases beyond square lattices in Floquet synthetic dimensions [Invited], Opt. Mater. Express 15, 272 (2025).
  38. D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
  39. A. Dutt, Q. Lin, L. Yuan, M. Minkov, M. Xiao, and S. Fan, A single photonic cavity with two independent physical synthetic dimensions, Science 367, 59 (2020).
  40. L. Yuan, M. Xiao, Q. Lin, and S. Fan, Synthetic space with arbitrary dimensions in a few rings undergoing dynamic modulation, Phys. Rev. B 97, 104105 (2018).
  41. A. Senanian, L. G. Wright, P. F. Wade, H. K. Doyle, and P. L. McMahon, Programmable large-scale simulation of bosonic transport in optical synthetic frequency lattices, Nat. Phys. 19, 1333 (2023).
  42. D. Cheng, E. Lustig, K. Wang, and S. Fan, Multi-dimensional band structure spectroscopy in the synthetic frequency dimension, Light Sci. Appl. 12, 158 (2023).
  43. See Supplemental Material at http://link.aps.org/supplemental/10.1103/2dyh-yhrb for details on the derivations of the effective Hamiltonian, time-resolved signals, Chern number extraction, and numerical simulations of the anomalous transverse displacement, including Ref. [44].
  44. L. Yuan and S. Fan, Three-dimensional dynamic localization of light from a time-dependent effective gauge field for photons, Phys. Rev. Lett. 114, 243901 (2015).
  45. S. Mittal, V. V. Orre, D. Leykam, Y. D. Chong, and M. Hafezi, Photonic anomalous quantum Hall effect, Phys. Rev. Lett. 123, 043201 (2019).
  46. F. Pellerin, R. Houvenaghel, W. A. Coish, I. Carusotto, and P. St-Jean, Wave-function tomography of topological dimer chains with long-range couplings, Phys. Rev. Lett. 132, 183802 (2024).
  47. A. Gianfrate, O. Bleu, L. Dominici, V. Ardizzone, M. De Giorgi, D. Ballarini, G. Lerario, K. W. West, L. N. Pfeiffer, D. D. Solnyshkov, D. Sanvitto, and G. Malpuech, Measurement of the quantum geometric tensor and of the anomalous Hall drift, Nature (London) 578, 381 (2020).
  48. T. Fukui, Y. Hatsugai, and H. Suzuki, Chern numbers in discretized brillouin zone: Efficient method of computing (spin) Hall conductances, J. Phys. Soc. Jpn. 74, 1674 (2005).
  49. C.-Z. Chang, C.-X. Liu, and A. H. MacDonald, Colloquium: Quantum anomalous Hall effect, Rev. Mod. Phys. 95, 011002 (2023).
  50. G. Li, Y. Zheng, A. Dutt, D. Yu, Q. Shan, S. Liu, L. Yuan, S. Fan, and X. Chen, Dynamic band structure measurement in the synthetic space, Sci. Adv. 7, eabe4335 (2021).
  51. C. Oliver, A. Smith, T. Easton, G. Salerno, V. Guarrera, N. Goldman, G. Barontini, and H. M. Price, Bloch oscillations along a synthetic dimension of atomic trap states, Phys. Rev. Res. 5, 033001 (2023).
  52. T. Ozawa, Steady-state Hall response and quantum geometry of driven-dissipative lattices, Phys. Rev. B 97, 041108(R) (2018).
  53. M. Wimmer, H. M. Price, I. Carusotto, and U. Peschel, Experimental measurement of the Berry curvature from anomalous transport, Nat. Phys. 13, 545 (2017).
  54. I. T. Rosen, S. Muschinske, C. N. Barrett, A. Chatterjee, M. Hays, M. A. DeMarco, A. H. Karamlou, D. A. Rower, R. Das, D. K. Kim, B. M. Niedzielski, M. Schuldt, K. Serniak, M. E. Schwartz, J. L. Yoder, J. A. Grover, and W. D. Oliver, A synthetic magnetic vector potential in a 2D superconducting qubit array, Nat. Phys. 20, 1881 (2024).
  55. D. Cheng, K. Wang, C. Roques-Carmes, E. Lustig, O. Y. Long, H. Wang, and S. Fan, Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions, Nature (London) 637, 52 (2025).
  56. M. Bello, G. Platero, J. I. Cirac, and A. González-Tudela, Unconventional quantum optics in topological waveguide QED, Sci. Adv. 5, eaaw0297 (2019).
  57. J. C. Owens, M. G. Panetta, B. Saxberg, G. Roberts, S. Chakram, R. Ma, A. Vrajitoarea, J. Simon, and D. I. Schuster, Chiral cavity quantum electrodynamics, Nat. Phys. 18, 1048 (2022).
  58. D. De Bernardis, F. S. Piccioli, P. Rabl, and I. Carusotto, Chiral quantum optics in the bulk of photonic quantum Hall systems, PRX Quantum 4, 030306 (2023).
  59. A. Dutt, L. Yuan, K. Y. Yang, K. Wang, S. Buddhiraju, J. Vučković, and S. Fan, Creating boundaries along a synthetic frequency dimension, Nat. Commun. 13, 3377 (2022).
  60. D. G. Reid, C. Oliver, P. Regan, A. Smith, T. Easton, G. Salerno, G. Barontini, N. Goldman, and H. M. Price, Topological chiral edge states in a synthetic dimension of atomic trap states, Phys. Rev. A 111, 033301 (2025).
  61. Z. Zhu, M. Gächter, A.-S. Walter, K. Viebahn, and T. Esslinger, Reversal of quantized Hall drifts at noninteracting and interacting topological boundaries, Science 384, 317 (2024).
  62. C.-K. Chiu, Jeffrey C. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
  63. I. Carusotto, A. A. Houck, A. J. Kollár, P. Roushan, D. I. Schuster, and J. Simon, Photonic materials in circuit quantum electrodynamics, Nat. Phys. 16, 268 (2020).
  64. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, Observation of unidirectional backscattering-immune topological electromagnetic states, Nature (London) 461, 772 (2009).
  65. G. Villa, I. Carusotto, and T. Ozawa, Mean-chiral displacement in coherently driven photonic lattices and its application to synthetic frequency dimensions, Commun. Phys. 7, 246 (2024).
  66. S. K. Sridhar, R. Srikanth, A. R. Miller, F. J. McComb, and A. Dutt, Measuring Z2 invariants in dimer models and cross-coupled ladders with a programmable photonic molecule, arXiv:2505.04151.
  67. H. X. Dinh, A. Balčytis, T. Ozawa, Y. Ota, G. Ren, T. Baba, S. Iwamoto, A. Mitchell, and T. G. Nguyen, Reconfigurable synthetic dimension frequency lattices in an integrated lithium niobate ring cavity, Commun. Phys. 7, 185 (2024).
  68. C. R. Leefmans, M. Parto, J. Williams, G. H. Y. Li, A. Dutt, F. Nori, and A. Marandi, Topological temporally mode-locked laser, Nat. Phys. 20, 852 (2024).
  69. Z. Yang, E. Lustig, G. Harari, Y. Plotnik, Y. Lumer, M. A. Bandres, and M. Segev, Mode-locked topological insulator laser utilizing synthetic dimensions, Phys. Rev. X 10, 011059 (2020).
  70. S. Mittal, G. Moille, K. Srinivasan, Y. K. Chembo, and M. Hafezi, Topological frequency combs and nested temporal solitons, Nat. Phys. 17, 1169 (2021).
  71. Y. Hu, C. Reimer, A. Shams-Ansari, M. Zhang, and M. Loncar, Realization of high-dimensional frequency crystals in electro-optic microcombs, Optica 7, 1189 (2020).
  72. M. Zhang, B. Buscaino, C. Wang, A. Shams-Ansari, C. Reimer, R. Zhu, J. M. Kahn, and M. Lončar, Broadband electro-optic frequency comb generation in a lithium niobate microring resonator, Nature (London) 568, 373 (2019).
  73. S. Buddhiraju, A. Dutt, M. Minkov, I. A. D. Williamson, and S. Fan, Arbitrary linear transformations for photons in the frequency synthetic dimension, Nat. Commun. 12, 2401 (2021).
  74. J. C. Budich and E. J. Bergholtz, Non-Hermitian topological sensors, Phys. Rev. Lett. 125, 180403 (2020).
  75. A. McDonald and A. A. Clerk, Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics, Nat. Commun. 11, 5382 (2020).
  76. E. Lustig, Y. Sharabi, and M. Segev, Topological aspects of photonic time crystals, Optica 5, 1390 (2018).
  77. N. I. Zheludev, Time crystals for photonics and timetronics, Nat. Photonics 18, 1123 (2024).
  78. L. Fan, K. Wang, H. Wang, A. Dutt, and S. Fan, Experimental realization of convolution processing in photonic synthetic frequency dimensions, Sci. Adv. 9, eadi4956 (2023).
  79. C. C. Wanjura and F. Marquardt, Fully nonlinear neuromorphic computing with linear wave scattering, Nat. Phys. 20, 1434 (2024).
  80. U. A. Javid, R. Lopez-Rios, J. Ling, A. Graf, J. Staffa, and Q. Lin, Chip-scale simulations in a quantum-correlated synthetic space, Nat. Photonics 17, 883 (2023).
  81. B. Bartlett, O. Y. Long, A. Dutt, and S. Fan, Programmable photonic system for quantum simulation in arbitrary topologies, APL Quantum 1, 016102 (2024).
  82. J. Argüello-Luengo, U. Bhattacharya, A. Celi, R. W. Chhajlany, T. Grass, M. Płodzień, D. Rakshit, T. Salamon, P. Stornati, L. Tarruell, and M. Lewenstein, Synthetic dimensions for topological and quantum phases, Commun. Phys. 7, 1 (2024).
  83. A. Chénier, B. d’Aligny, F. Pellerin, P.-É. Blanchard, T. Ozawa, I. Carusotto, and P. St-Jean, Data for the article “Quantized Hall drift in a frequency-encoded Chern insulator”, 10.17605/OSF.IO/ATRNV.

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