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Observation of Non-Hermitian Topology in Cold Rydberg Quantum Gases

Jun Zhang*, Ya-Jun Wang*, Shi-Yao Shao*, Bang Liu, Li-Hua Zhang, Zheng-Yuan Zhang, Xin Liu, Chao Yu, Qing Li et al.

Han-Chao Chen, Yu Ma, Tian-Yu Han, Qi-Feng Wang, Jia-Dou Nan, Yi-Ming Yin, Dong-Yang Zhu, Qiao-Qiao Fang, Dong-Sheng Ding†, and Bao-Sen Shi

  • *J. Z, Y.-J. W, and S.-Y. S contributed equally to this work.
  • †Contact author: dds@ustc.edu.cn
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PRX Quantum 7, 033004 – Published 6 July, 2026

DOI: https://doi.org/10.1103/rrrm-s1xn

Abstract

The pursuit of topological phenomena in non-Hermitian systems has unveiled new physics beyond the conventional Hermitian paradigm, yet their realization in interacting many-body platforms remains a critical challenge. Exploring this interplay is essential to understand how strong interactions and dissipation collectively shape topological phases in open quantum systems. Here, we experimentally demonstrate dynamical spectral topology in a dissipative Rydberg atomic gas and characterize parameter-dependent winding numbers, which quantify a geometric winding of the spectral topology. By increasing the interaction strength, the system evolves from Hermitian to non-Hermitian regime, accompanying emergence of trajectory loop in the complex energy plane. As the scanning time is varied, the spectral topology becomes twisted in the complex energy plane, forming enclosed sub-loops characterized by opposite winding numbers. Furthermore, by changing the scanning direction, we observe the differentiated spectral loops, revealing a signature of scan-direction-dependent nonreciprocity. This work establishes cold Rydberg gases as a versatile platform for exploring the rich interplay between non-Hermitian topology, strong interactions, and dissipative quantum dynamics.

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Popular Summary

Exploring topological phenomena in open, non-Hermitian systems has revealed new physics beyond the conventional Hermitian paradigm. However, observing and controlling these behaviors within interacting many-body platforms remains a critical challenge. Investigating the interplay between many-body interactions and dissipation is essential to understand how they collectively shape topological phases in open quantum systems. In this work, we experimentally demonstrate dynamic spectral topology within a dissipative Rydberg atomic gas. As interactions strengthen, the system transitions into a non-Hermitian regime, resulting in the emergence of distinct trajectory loops in the complex energy plane. Varying the scan time, we observe that the spectral loops become dynamically twisted. Moreover, changing the scan direction produces a distinct asymmetric spectral topology, revealing a scan-direction-dependent nonreciprocity. By revealing these topological features, our work establishes cold Rydberg gases as an ideal platform for exploring the complex interplay between non-Hermitian physics, strong many-body interactions, and dissipative quantum dynamics.

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References (79)

  1. S.-Y. Xu, Y. Xia, L. Wray, S. Jia, F. Meier, J. Dil, J. Osterwalder, B. Slomski, A. Bansil, H. Lin et al., Topological phase transition and texture inversion in a tunable topological insulator, Science 332, 560 (2011).
  2. M. Caraglio, C. Micheletti, and E. Orlandini, Stretching response of knotted and unknotted polymer chains, Phys. Rev. Lett. 115, 188301 (2015).
  3. K. Kawabata, S. Higashikawa, Z. Gong, Y. Ashida, and M. Ueda, Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics, Nat. Commun. 10, 297 (2019).
  4. K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Symmetry and topology in non-Hermitian physics, Phys. Rev. X 9, 041015 (2019).
  5. W. Ji and X.-G. Wen, Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions, Phy. Rev. Res. 2, 033417 (2020).
  6. S. Xia, D. Kaltsas, D. Song, I. Komis, J. Xu, A. Szameit, H. Buljan, K. G. Makris, and Z. Chen, Nonlinear tuning of pt symmetry and non-Hermitian topological states, Science 372, 72 (2021).
  7. H. Qin, Z. Zhang, J. Wang, and R. Fleury, Topological hysteretic winding for temporal anti-lasing, Nat. Commun. 16, 6189 (2025).
  8. S.-Y. Xu, C. Liu, N. Alidoust, M. Neupane, D. Qian, I. Belopolski, J. Denlinger, Y. Wang, H. Lin, L. a. Wray et al., Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe, Nat. Commun. 3, 1192 (2012).
  9. C. Heide, Y. Kobayashi, D. R. Baykusheva, D. Jain, J. A. Sobota, M. Hashimoto, P. S. Kirchmann, S. Oh, T. F. Heinz, D. A. Reis et al., Probing topological phase transitions using high-harmonic generation, Nat. Photonics 16, 620 (2022).
  10. K. Ding, C. Fang, and G. Ma, Non-Hermitian topology and exceptional-point geometries, Nat. Rev. Phys. 4, 745 (2022).
  11. Z. Lin, L. Zhang, X. Long, Y.-A. Fan, Y. Li, K. Tang, J. Li, X. Nie, T. Xin, X.-J. Liu et al., Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic schrödinger equation, npj Quantum Inf. 8, 77 (2022).
  12. S.-L. Zhu, Z.-D. Wang, Y.-H. Chan, and L.-M. Duan, Topological bose-mott insulators in a one-dimensional optical superlattice, Phy. Rev. Lett. 110, 075303 (2013).
  13. S. Mittal, S. Ganeshan, J. Fan, A. Vaezi, and M. Hafezi, Measurement of topological invariants in a 2D photonic system, Nat. Photonics 10, 180 (2016).
  14. J. Y. Lee, J. Ahn, H. Zhou, and A. Vishwanath, Topological correspondence between Hermitian and non-Hermitian systems: Anomalous dynamics, Phys. Rev. Lett. 123, 206404 (2019).
  15. K. Wang, T. Li, L. Xiao, Y. Han, W. Yi, and P. Xue, Detecting non-bloch topological invariants in quantum dynamics, Phy. Rev. Lett. 127, 270602 (2021).
  16. G. Li, L. Wang, R. Ye, Y. Zheng, D.-W. Wang, X.-J. Liu, A. Dutt, L. Yuan, and X. Chen, Direct extraction of topological Zak phase with the synthetic dimension, Light: Sci. Appl. 12, 81 (2023).
  17. X. Liu, J. Wang, R. Mao, H. Hu, S.-Y. Zhu, X. Xu, H. Cai, and D.-W. Wang, Zak phase induced topological nonreciprocity, Phys. Rev. Lett. 134, 193602 (2025).
  18. L. Xiao, X. Zhan, Z. Bian, K. Wang, X. Zhang, X. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami et al., Observation of topological edge states in parity–time-symmetric quantum walks, Nat. Phys. 13, 1117 (2017).
  19. S. de Léséleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. Büchler, T. Lahaye, and A. Browaeys, Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms, Science 365, 775 (2019).
  20. H. Cai and D.-W. Wang, Topological phases of quantized light, Nat. Sci. Rev. 8, nwaa196 (2021).
  21. M. Yang, H.-Q. Zhang, Y.-W. Liao, Z.-H. Liu, Z.-W. Zhou, X.-X. Zhou, J.-S. Xu, Y.-J. Han, C.-F. Li, and G.-C. Guo, Topological band structure via twisted photons in a degenerate cavity, Nat. Commun. 13, 2040 (2022).
  22. D. Hao, L. Wang, X. Lu, X. Cao, S. Jia, Y. Hu, and Y. Xiao, Topological atomic spin wave lattices by dissipative couplings, Phys. Rev. Lett. 130, 153602 (2023).
  23. M. Yang, Y.-W. Liao, H.-Q. Zhang, Y. Li, Z.-H. Hao, Z.-W. Zhou, X.-W. Luo, J.-S. Xu, C.-F. Li, and G.-C. Guo, Observing half-integer topological winding numbers in non-Hermitian synthetic lattices, Light Sci. Appl. 14, 225 (2025).
  24. Z. Yue, Y.-F. Mao, X. Liang, Z.-X. Hua, P. Ge, Y.-X. Chao, K. Li, C. Jia, M. K. Tey, Y. Xu, and L. You, Observation of average topological phase in disordered Rydberg atom array, arXiv:2505.06286.
  25. T. Insulator, Topological phase transition and texture inversion in a tunable, Science 1201607, 332 (2011).
  26. J. Zhang, C.-Z. Chang, P. Tang, Z. Zhang, X. Feng, K. Li, L.-l.. Wang, X. Chen, C. Liu, W. Duan et al., Topology-driven magnetic quantum phase transition in topological insulators, Science 339, 1582 (2013).
  27. Q. Lin, T. Li, L. Xiao, K. Wang, W. Yi, and P. Xue, Observation of non-Hermitian topological Anderson insulator in quantum dynamics, Nat. Commun. 13, 3229 (2022).
  28. G. Zhang et al., Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures, Phys. Rev. Lett 105, 10 (2013).
  29. P. Zhang, K. Yaji, T. Hashimoto, Y. Ota, T. Kondo, K. Okazaki, Z. Wang, J. Wen, G. D. Gu, H. Ding et al., Observation of topological superconductivity on the surface of an iron-based superconductor, Science 360, 182 (2018).
  30. S. Vajna and Bázs Dóra, Topological classification of dynamical phase transitions, Phys. Rev. B. 91, 155127 (2015).
  31. M. Heyl and J. C. Budich, Dynamical topological quantum phase transitions for mixed states, Phys. Rev. B. 96, 180304 (2017).
  32. Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Topological phases of non-Hermitian systems, Phys. Rev. X. 8, 031079 (2018).
  33. S. Longhi, Topological phase transition in non-Hermitian quasicrystals, Phys. Rev. Lett. 122, 237601 (2019).
  34. Q. Lin, T. Li, L. Xiao, K. Wang, W. Yi, and P. Xue, Topological phase transitions and mobility edges in non-Hermitian quasicrystals, Phy. Rev. Lett. 129, 113601 (2022).
  35. T. Dai, Y. Ao, J. Mao, Y. Yang, Y. Zheng, C. Zhai, Y. Li, J. Yuan, B. Tang, Z. Li et al., Non-Hermitian topological phase transitions controlled by nonlinearity, Nat. Phys. 20, 101 (2024).
  36. Z. Li, L.-W. Wang, X. Wang, Z.-K. Lin, G. Ma, and J.-H. Jiang, Observation of dynamic non-Hermitian skin effects, Nat. Commun. 15, 6544 (2024).
  37. 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).
  38. M. Heyl, Dynamical quantum phase transitions: A review, Rep. Prog. Phys. 81, 054001 (2018).
  39. R. J. Valencia-Tortora, N. Pancotti, M. Fleischhauer, H. Bernien, and J. Marino, Rydberg platform for nonergodic chiral quantum dynamics, Phys. Rev. Lett. 132, 223201 (2024).
  40. H.-X. Xiao, W. Jiang, P. Qian, H. Li, Z. Li, H. Shen, and B. Chen, Dynamical topological quantum phase transitions in high-order topological systems, Phys. Rev. B. 110, 064306 (2024).
  41. M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with Rydberg atoms, Rev. Mod. Phys. 82, 2313 (2010).
  42. C. S. Adams, J. D. Pritchard, and J. P. Shaffer, Rydberg atom quantum technologies, J. Phys. B 53, 012002 (2019).
  43. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
  44. R. Samajdar, W. W. Ho, H. Pichler, M. D. Lukin, and S. Sachdev, Quantum phases of Rydberg atoms on a kagome lattice, Proc. Natl. Acad. Sci. U.S.A. 118, e2015785118 (2021).
  45. X. Li and S. D. Sarma, Exotic topological density waves in cold atomic Rydberg-dressed fermions, Nat. Commun. 6, 7137 (2015).
  46. K. Li, J.-H. Wang, Y.-B. Yang, and Y. Xu, Symmetry-protected topological phases in a Rydberg glass, Phys. Rev. Lett. 127, 263004 (2021).
  47. R. Verresen, M. D. Lukin, and A. Vishwanath, Prediction of toric code topological order from Rydberg blockade, Phys. Rev. X. 11, 031005 (2021).
  48. S. K. Kanungo, J. D. Whalen, Y. Lu, M. Yuan, S. Dasgupta, F. B. Dunning, K. R. A. Hazzard, and T. C. Killian, Realizing topological edge states with Rydberg-atom synthetic dimensions, Nat. Commun. 13, 972 (2022).
  49. T. E. Lee, H. Häffner, and M. C. Cross, Collective quantum jumps of Rydberg atoms, Phys. Rev. Lett. 108, 023602 (2012).
  50. C. Carr, R. Ritter, C. Wade, C. S. Adams, and K. J. Weatherill, Nonequilibrium phase transition in a dilute Rydberg ensemble, Phys. Rev. Lett. 111, 113901 (2013).
  51. H. Schempp, G. Günter, M. Robert-de Saint-Vincent, C. S. Hofmann, D. Breyel, A. Komnik, D. W. Schönleber, M. Gärttner, J. Evers, S. Whitlock, and M. Weidemüller, Full counting statistics of laser excited Rydberg aggregates in a one-dimensional geometry, Phys. Rev. Lett. 112, 013002 (2014).
  52. M. Marcuzzi, E. Levi, S. Diehl, J. P. Garrahan, and I. Lesanovsky, Universal nonequilibrium properties of dissipative Rydberg gases, Phys. Rev. Lett. 113, 210401 (2014).
  53. I. Lesanovsky and J. P. Garrahan, Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation, Phys. Rev. A 90, 011603 (2014).
  54. A. Urvoy, F. Ripka, I. Lesanovsky, D. Booth, J. P. Shaffer, T. Pfau, and R. Löw, Strongly correlated growth of Rydberg aggregates in a vapor cell, Phys. Rev. Lett. 114, 203002 (2015).
  55. F. M. Gambetta, F. Carollo, M. Marcuzzi, J. P. Garrahan, and I. Lesanovsky, Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems, Phys. Rev. Lett. 122, 015701 (2019).
  56. D.-S. Ding, Z.-K. Liu, B.-S. Shi, G.-C. Guo, K. Mølmer, and C. S. Adams, Enhanced metrology at the critical point of a many-body Rydberg atomic system, Nat. Phys. 18, 1447 (2022).
  57. S. Helmrich, A. Arias, G. Lochead, T. M. Wintermantel, M. Buchhold, S. Diehl, and S. Whitlock, Signatures of self-organized criticality in an ultracold atomic gas, Nature (London) 577, 481 (2020).
  58. D.-S. Ding, H. Busche, B.-S. Shi, G.-C. Guo, and C. S. Adams, Phase diagram of non-equilibrium phase transition in a strongly-interacting Rydberg atom vapour, Phys. Rev. X 10, 021023 (2020).
  59. T. M. Wintermantel, Y. Wang, G. Lochead, S. Shevate, G. K. Brennen, and S. Whitlock, Unitary and nonunitary quantum cellular automata with Rydberg arrays, Phys. Rev. Lett. 124, 070503 (2020).
  60. K. Klocke, T. Wintermantel, G. Lochead, S. Whitlock, and M. Buchhold, Hydrodynamic stabilization of self-organized criticality in a driven Rydberg gas, Phys. Rev. Lett. 126, 123401 (2021).
  61. K. Wadenpfuhl and C. S. Adams, Emergence of synchronization in a driven-dissipative hot Rydberg vapor, Phys. Rev. Lett. 131, 143002 (2023).
  62. D. Ding, Z. Bai, Z. Liu, B. Shi, G. Guo, W. Li, and C. S. Adams, Ergodicity breaking from Rydberg clusters in a driven-dissipative many-body system, Sci. Adv. 10, eadl5893 (2024).
  63. X. Wu, Z. Wang, F. Yang, R. Gao, C. Liang, M. K. Tey, X. Li, T. Pohl, and L. You, Dissipative time crystal in a strongly interacting Rydberg gas, Nat. Phys. 20, 1389 (2024).
  64. B. Liu, L.-H. Zhang, Q.-F. Wang, Y. Ma, T.-Y. Han, J. Zhang, Z.-Y. Zhang, S.-Y. Shao, Q. Li, H.-C. Chen et al., Higher-order and fractional discrete time crystals in floquet-driven Rydberg atoms, Nat. Commun. 15, 9730 (2024).
  65. B. Liu, L.-H. Zhang, Y. Ma, T.-Y. Han, Q.-F. Wang, J. Zhang, Z.-Y. Zhang, S.-Y. Shao, Q. Li, H.-C. Chen et al., Quantum synchronization at the critical point of floquet driven Rydberg atoms, arXiv:2404.12180.
  66. B. Liu, L.-H. Zhang, Y. Ma, Q.-F. Wang, T.-Y. Han, J. Zhang, Z.-Y. Zhang, S.-Y. Shao, Q. Li, H.-C. Chen, G.-C. Guo, D.-S. Ding, and B.-S. Shi, Bifurcation of time crystals in driven and dissipative Rydberg atomic gas, Nat. Commun. 16, 1419 (2025).
  67. P. Delplace, T. Yoshida, and Y. Hatsugai, Symmetry-protected multifold exceptional points and their topological characterization, Phys. Rev. Lett. 127, 186602 (2021).
  68. J. Zhang, E.-Z. Li, Y.-J. Wang, B. Liu, L.-H. Zhang, Z.-Y. Zhang, S.-Y. Shao, Q. Li, H.-C. Chen, Y. Ma et al., Exceptional point and hysteresis trajectories in cold Rydberg atomic gases, Nat. Commun. 16, 3511 (2025).
  69. J. C. Budich and E. J. Bergholtz, Non-Hermitian topological sensors, Phys. Rev. Lett. 125, 180403 (2020).
  70. K. Wang, A. Dutt, K. Y. Yang, C. C. Wojcik, J. Vučković, and S. Fan, Generating arbitrary topological windings of a non-Hermitian band, Science 371, 1240 (2021).
  71. R. W. Boyd, A. L. Gaeta, and E. Giese, Nonlinear optics, in Springer Handbook of Atomic, Molecular, and Optical Physics (Springer, Cham, 2008), pp. 1097–1110, https://link.springer.com/chapter/10.1007/978-3-030-73893-8_76.
  72. K. Sun and W. Yi, Encircling the Liouvillian exceptional points: A brief review, AAPPS Bull. 34, 22 (2024).
  73. F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spectral theory of Liouvillians for dissipative phase transitions, Phys. Rev. A 98, 042118 (2018).
  74. T. Yoshida and Y. Hatsugai, Fate of exceptional points under interactions: Reduction of topological classifications, Phys. Rev. B 107, 075118 (2023).
  75. M. Kato and T. Yoshida, Interaction-enabled two-and three-fold exceptional points, arXiv:2602.14056.
  76. S.-B. Zhang, M. M. Denner, Táš Bzdušek, M. A. Sentef, and T. Neupert, Symmetry breaking and spectral structure of the interacting Hatano-Nelson model, Phys. Rev. B 106, L121102 (2022).
  77. K. Kawabata, K. Shiozaki, and S. Ryu, Many-body topology of non-Hermitian systems, Phys. Rev. B 105, 165137 (2022).
  78. 10.5281/zenodo.19677052.10.5281/zenodo.19677052
  79. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Electromagnetically induced transparency: Optics in coherent media, Rev. Mod. Phys. 77, 633 (2005).

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PRX Quantum 7, 033004– Published 6 July, 2026
  • Received 27 January 2026
  • Accepted 27 May 2026
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