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Quantum phase transitions in driven Fock-state lattices with synthetic gauge fields

Jiale Yuan1,*, Jinfeng Deng1, Xiao Wei1, and Da-Wei Wang1,2,3,†

  • 1Zhejiang Key Laboratory of Micro-Nano Quantum Chips and Quantum Control, School of Physics, and State Key Laboratory for Extreme Photonics and Instrumentation, Zhejiang University, Hangzhou 310027, China
  • 2College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China
  • 3Hefei National Laboratory, Hefei 230088, Anhui Province, China

  • *Contact author: jialeyuan@zju.edu.cn
  • †Contact author: dwwang@zju.edu.cn
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Phys. Rev. Research 7, 043191 – Published 20 November, 2025

DOI: https://doi.org/10.1103/4fq1-nb4r

Abstract

Quantum phase transitions (QPTs) typically emerge in the thermodynamic limit, yet a single-atom QPT can arise when it is coupled to a coherently driven cavity, which provides a simple and unique platform to engineer quantum states with quantum criticality. In this driven Jaynes-Cummings (JC) model, the cavity field becomes squeezed near the critical point. However, vanishing energy gaps at the critical points lead to nonadiabaticity, hindering the practical realization of squeezing. In this work, we introduce a spin-dependent cavity drive, which induces a synthetic gauge field in the Fock-state lattice and enriches the phase diagram of the driven JC model. Remarkably, the energy spectrum can remain discrete for all driving strengths, allowing an adiabatic preparation of squeezed states with robust energy gaps. Moreover, we identify a topological phase transition characterized by projected winding numbers in the presence of broken chiral symmetry. Our results unveil topology and QPTs in a quantized light-matter system and offer a robust strategy for realizing squeezed states.

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References (60)

  1. M. Uhlarz, C. Pfleiderer, and S. M. Hayden, Quantum phase transitions in the itinerant ferromagnet ZrZn2, Phys. Rev. Lett. 93, 256404 (2004).
  2. S. Sachdev, Colloquium: Order and quantum phase transitions in the cuprate superconductors, Rev. Mod. Phys. 75, 913 (2003).
  3. Y. K. Wang and F. T. Hioe, Phase transition in the Dicke model of superradiance, Phys. Rev. A 7, 831 (1973).
  4. V. M. Bastidas, C. Emary, B. Regler, and T. Brandes, Nonequilibrium quantum phase transitions in the Dicke model, Phys. Rev. Lett. 108, 043003 (2012).
  5. M. Feng, Y. Zhong, T. Liu, L. Yan, W. Yang, J. Twamley, and H. Wang, Exploring the quantum critical behavior in a driven Tavis–Cummings circuit, Nat. Commun. 6, 7111 (2015).
  6. C. J. Zhu, L. L. Ping, Y. P. Yang, and G. S. Agarwal, Squeezed light induced symmetry breaking superradiant phase transition, Phys. Rev. Lett. 124, 073602 (2020).
  7. M.-J. Hwang and M. B. Plenio, Quantum phase transition in the finite Jaynes-Cummings lattice systems, Phys. Rev. Lett. 117, 123602 (2016).
  8. M.-J. Hwang, R. Puebla, and M. B. Plenio, Quantum phase transition and universal dynamics in the Rabi model, Phys. Rev. Lett. 115, 180404 (2015).
  9. M. Liu, S. Chesi, Z.-J. Ying, X. Chen, H.-G. Luo, and H.-Q. Lin, Universal scaling and critical exponents of the anisotropic quantum Rabi model, Phys. Rev. Lett. 119, 220601 (2017).
  10. M.-L. Cai, Z.-D. Liu, W.-D. Zhao, Y.-K. Wu, Q.-X. Mei, Y. Jiang, L. He, X. Zhang, Z.-C. Zhou, and L.-M. Duan, Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion, Nat. Commun. 12, 1126 (2021).
  11. R.-H. Zheng, W. Ning, Y.-H. Chen, J.-H. Lü, L.-T. Shen, K. Xu, Y.-R. Zhang, D. Xu, H. Li, Y. Xia, F. Wu, Z.-B. Yang, A. Miranowicz, N. Lambert, D. Zheng, H. Fan, F. Nori, and S.-B. Zheng, Observation of a superradiant phase transition with emergent cat states, Phys. Rev. Lett. 131, 113601 (2023).
  12. P. Alsing and H. Carmichael, Spontaneous dressed-state polarization of a coupled atom and cavity mode, Quantum Opt.: J. Eur. Opt. Soc. Part B 3, 13 (1991).
  13. P. Alsing, D.-S. Guo, and H. J. Carmichael, Dynamic Stark effect for the Jaynes-Cummings system, Phys. Rev. A 45, 5135 (1992).
  14. H. J. Carmichael, Breakdown of photon blockade: A dissipative quantum phase transition in zero dimensions, Phys. Rev. X 5, 031028 (2015).
  15. J. M. Fink, A. Dombi, A. Vukics, A. Wallraff, and P. Domokos, Observation of the photon-blockade breakdown phase transition, Phys. Rev. X 7, 011012 (2017).
  16. R. Sett, F. Hassani, D. Phan, S. Barzanjeh, A. Vukics, and J. M. Fink, Emergent macroscopic bistability induced by a single superconducting qubit, PRX Quantum 5, 010327 (2024).
  17. J.-H. Lü, W. Ning, F. Wu, R.-H. Zheng, K. Chen, X. Zhu, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, Critical quantum metrology robust against dissipation and non-adiabaticity, arXiv:2403.04475.
  18. P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, Squeezed-light-enhanced polarization interferometer, Phys. Rev. Lett. 59, 2153 (1987).
  19. M. Xiao, L.-A. Wu, and H. J. Kimble, Precision measurement beyond the shot-noise limit, Phys. Rev. Lett. 59, 278 (1987).
  20. LIGO Scientific Collaboration, A gravitational wave observatory operating beyond the quantum shot-noise limit, Nat. Phys. 7, 962 (2011).
  21. F. Li, T. Li, M. O. Scully, and G. S. Agarwal, Quantum advantage with seeded squeezed light for absorption measurement, Phys. Rev. Appl. 15, 044030 (2021).
  22. T. Li, F. Li, X. Liu, V. V. Yakovlev, and G. S. Agarwal, Quantum-enhanced stimulated Brillouin scattering spectroscopy and imaging, Optica 9, 959 (2022).
  23. J. Qin, Y.-H. Deng, H.-S. Zhong, L.-C. Peng, H. Su, Y.-H. Luo, J.-M. Xu, D. Wu, S.-Q. Gong, H.-L. Liu, H. Wang, M.-C. Chen, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, Unconditional and robust quantum metrological advantage beyond N00N states, Phys. Rev. Lett. 130, 070801 (2023).
  24. T. Gehring, V. Händchen, J. Duhme, F. Furrer, T. Franz, C. Pacher, R. F. Werner, and R. Schnabel, Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks, Nat. Commun. 6, 8795 (2015).
  25. I. Derkach, V. C. Usenko, and R. Filip, Squeezing-enhanced quantum key distribution over atmospheric channels, New J. Phys. 22, 053006 (2020).
  26. O. Thearle, J. Janousek, S. Armstrong, S. Hosseini, M. Schünemann (Mraz), S. Assad, T. Symul, M. R. James, E. Huntington, T. C. Ralph, and P. K. Lam, Violation of Bell’s inequality using continuous variable measurements, Phys. Rev. Lett. 120, 040406 (2018).
  27. Y. Wu, J. Yuan, C. Zhang, Z. Zhu, J. Deng, X. Zhang, P. Zhang, Q. Guo, Z. Wang, J. Huang, C. Song, H. Li, D.-W. Wang, H. Wang, and G. S. Agarwal, Testing the unified bounds of the quantum speed limit, Phys. Rev. A 110, 042215 (2024).
  28. D. Sharma and B. Kumar, Power-law growth of time and strength of squeezing near a quantum critical point, Phys. Rev. A 102, 033702 (2020).
  29. K. Gietka, Squeezing by critical speeding up: Applications in quantum metrology, Phys. Rev. A 105, 042620 (2022).
  30. K. Hayashida, T. Makihara, N. Marquez Peraca, D. Fallas Padilla, H. Pu, J. Kono, and M. Bamba, Perfect intrinsic squeezing at the superradiant phase transition critical point, Sci. Rep. 13, 2526 (2023).
  31. T. Roscilde, F. Caleca, A. Angelone, and F. Mezzacapo, Scalable spin squeezing from critical slowing down in short-range interacting systems, Phys. Rev. Lett. 133, 210401 (2024).
  32. D.-W. Wang, H. Cai, R.-B. Liu, and M. O. Scully, Mesoscopic superposition states generated by synthetic spin-orbit interaction in Fock-state lattices, Phys. Rev. Lett. 116, 220502 (2016).
  33. H. Cai and D. W. Wang, Topological phases of quantized light, Nat. Sci. Rev. 8, nwaa196 (2021).
  34. P. Saugmann and J. Larson, Fock-state-lattice approach to quantum optics, Phys. Rev. A 108, 033721 (2023).
  35. J. Yuan, H. Cai, and D.-W. Wang, Quantum simulation in Fock-state lattices, Adv. Phys. X 9, 2325611 (2024).
  36. J. Yang, Y. Li, Y. Yang, X. Xie, Z. Zhang, J. Yuan, H. Cai, D.-W. Wang, and F. Gao, Realization of all-band-flat photonic lattices, Nat. Commun. 15, 1484 (2024).
  37. M. Peng, Q. Wei, J. Yuan, D.-W. Wang, M. Yan, H. Cai, and G. Chen, Ideal flat and resolved SU(3) Landau levels in three dimensions, Phys. Rev. Lett. 134, 116601 (2025).
  38. J. Deng, H. Dong, C. Zhang, Y. Wu, J. Yuan, X. Zhu, F. Jin, H. Li, Z. Wang, H. Cai, C. Song, H. Wang, J. Q. You, and D.-W. Wang, Observing the quantum topology of light, Science 378, 966 (2022).
  39. Y. Wang, Y.-K. Wu, Y. Jiang, M.-L. Cai, B.-W. Li, Q.-X. Mei, B.-X. Qi, Z.-C. Zhou, and L.-M. Duan, Realizing synthetic dimensions and artificial magnetic flux in a trapped-ion quantum simulator, Phys. Rev. Lett. 132, 130601 (2024).
  40. J. Zhang, W. Huang, J. Chu, J. Qiu, X. Sun, Z. Tao, J. Zhang, L. Zhang, Y. Zhou, Y. Chen, Y. Liu, S. Liu, Y. Zhong, J.-J. Miao, J. Niu, and D. Yu, Synthetic multidimensional Aharonov-Bohm cages in Fock state lattices, Phys. Rev. Lett. 134, 070601 (2025).
  41. J. Yuan, C. Xu, H. Cai, and D. W. Wang, Gap-protected transfer of topological defect states in photonic lattices, APL Photonics 6, 030803 (2021).
  42. J. Yuan, H. Cai, C. Wu, S.-Y. Zhu, R.-B. Liu, and D.-W. Wang, Unification of valley and anomalous Hall effects in a strained lattice, Phys. Rev. B 104, 035410 (2021).
  43. C. Wu, W. Liu, Y. Jia, G. Chen, and F. Chen, Observation of topological pumping of a defect state in a Fock photonic lattice, Phys. Rev. A 107, 033501 (2023).
  44. T. Tian, H. Cai, L. Zhang, Y. Zhang, C.-K. Duan, and J. Zhou, Nonadiabatic topological transfer in a nanomechanical phononic lattice, Phys. Rev. B 109, 125123 (2024).
  45. Q. Wang and N. Hao, Generalized topology in lattice models without chiral symmetry, arXiv:2407.00795.
  46. D.-W. Wang, C. Song, W. Feng, H. Cai, D. Xu, H. Deng, H. Li, D. Zheng, X. Zhu, H. Wang et al., Synthesis of antisymmetric spin exchange interaction and chiral spin clusters in superconducting circuits, Nat. Phys. 15, 382 (2019).
  47. W. Liu, W. Feng, W. Ren, D.-W. Wang, and H. Wang, Synthesizing three-body interaction of spin chirality with superconducting qubits, Appl. Phys. Lett. 116, 114001 (2020).
  48. N. Goldman and J. Dalibard, Periodically driven quantum systems: Effective Hamiltonians and engineered gauge fields, Phys. Rev. X 4, 031027 (2014).
  49. See Supplemental Material at http://link.aps.org/supplemental/10.1103/4fq1-nb4r for model diagonalization, Floquet effective Hamiltonian, quasi-momentum-space description, and steady-state solution.
  50. V. M. Pereira, A. H. Castro Neto, and N. M. R. Peres, Tight-binding approach to uniaxial strain in graphene, Phys. Rev. B 80, 045401 (2009).
  51. Y.-H. Ho, E. V. Castro, and M. A. Cazalilla, Haldane model under nonuniform strain, Phys. Rev. B 96, 155446 (2017).
  52. C.-K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
  53. Y. Tang, Y. Yang, M. An, J. Xie, Y. Wang, F. Wang, and F. Li, Critical properties of quantum Fisher information of SU(1,1)-dynamic systems, Phys. Rev. A 110, 022611 (2024).
  54. Y. Yang, H. Yuan, and F. Li, Quantum multiparameter estimation enhanced by a topological phase transition, Phys. Rev. A 109, 022604 (2024).
  55. C. Hotter, H. Ritsch, and K. Gietka, Combining critical and quantum metrology, Phys. Rev. Lett. 132, 060801 (2024).
  56. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  57. E. J. Meier, F. A. An, and B. Gadway, Observation of the topological soliton state in the Su–Schrieffer–Heeger model, Nat. Commun. 7, 13986 (2016).
  58. K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Dicke quantum phase transition with a superfluid gas in an optical cavity, Nature (London) 464, 1301 (2010).
  59. M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, Realization of the Dicke model using cavity-assisted Raman transitions, Phys. Rev. Lett. 113, 020408 (2014).
  60. J. Yuan, J. Deng, X. Wei, and D.-W. Wang, Quantum phase transitions in driven Fock-state lattices with synthetic gauge fields [Data set], Zenodo (2025), doi: 10.5281/zenodo.16279175.

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Phys. Rev. Research 7, 043191– Published 20 November, 2025
  • Received 21 July 2025
  • Accepted 1 November 2025
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