- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Floquet solutions in a parity-time-symmetric Rabi model

M. Baradaran1,*, D. Braak2,†, L. M. Nieto3,‡, and S. Zarrinkamar3,4,§

  • *Contact author: marzieh.baradaran@uhk.cz
  • †Contact author: daniel.braak@uni-a.de
  • ‡Contact author: luismiguel.nieto.calzada@uva.es
  • §Contact author: saber.zarrinkamar@uva.es
PDF

Phys. Rev. Research 8, 013097 – Published 28 January, 2026

DOI: https://doi.org/10.1103/2h1h-svtx

Abstract

It is shown that a semiclassical Rabi model with parity-time (PT) symmetry possesses quasiexact solutions, which can be found using the Lie-algebraic approach. These solutions are located precisely at the exceptional points of the spectrum, the boundaries of the PT-symmetric phase. The corresponding constraints on the model parameters can be interpreted as a resonance relationship between the constant and periodic driving terms. For sufficiently large resonance ratio and judiciously chosen parameters, we find that the time evolution of the complete qubit can be described exactly.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. C. M. Bender and S. Boettcher, Real spectra in non-Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett. 80, 5243 (1998).
  2. C. M. Bender and D. W. Hook, PT-symmetric quantum mechanics, Rev. Mod. Phys. 96, 045002 (2024).
  3. C. E. Rüter, et al., Observation of parity–time symmetry in optic, Nat. Phys. 6, 192 (2010).
  4. V. V. Konotop, J. Yang, and D. A. Zezyulin, Nonlinear waves in PT-symmetric systems, Rev. Mod. Phys. 88, 035002 (2016).
  5. L. Chang, et al., Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators, Nat. Photon 8, 524 (2014).
  6. B. Peng, et al., Parity–time-symmetric whispering-gallery microcavities, Nat. Phys. 10, 394 (2014).
  7. Y. Ashida, S. Furukawa, and M. Ueda, Parity-time-symmetric quantum critical phenomena, Nat. Commun. 8, 15791 (2017).
  8. S. Assawaworrarit, X. Yu, and Sh Fan, Robust wireless power transfer using a nonlinear parity–time-symmetric circuit, Nature (London) 546, 387 (2017).
  9. L. Xiao, et al., Observation of topological edge states in parity–time-symmetric quantum walks, Nat. Phys. 13, 1117 (2017).
  10. S. Weimann, et al., Topologically protected bound states in photonic parity–time-symmetric crystals, Nat. Mater. 16, 433 (2017).
  11. P.-Y. Chen, et al., Generalized parity–time symmetry condition for enhanced sensor telemetry, Nat. Electron. 1, (2018) 297.
  12. S. Assawaworrarit and Sh Fan, Robust and efficient wireless power transfer using a switch-mode implementation of a nonlinear parity–time symmetric circuit, Nat. Electron. 3, 273 (2020).
  13. W. Cao, et al., Fully integrated parity–time-symmetric electronics, Nat. Nanotechnol. 17, 262 (2022).
  14. W. Liu, et al., Floquet parity-time symmetry in integrated photonics, Nat. Commun. 15, 946 (2024).
  15. A. Fritzsche, et al., Parity–time-symmetric photonic topological insulator, Nat. Mater. 23, 377 (2024).
  16. I. I. Rabi, Space quantization in a gyrating magnetic field, Phys. Rev. 51, 652 (1937).
  17. Q. Xie, et al., The quantum Rabi model: Solution and dynamics, J. Phys. A: Math. Theor. 50, 113001 (2017).
  18. T. E. Lee and Y. N. Joglekar, PT-symmetric Rabi model: Perturbation theory, Phys. Rev. A 92, 042103 (2015).
  19. J. Gong and Q. H. Wang, Stabilizing non-Hermitian systems by periodic driving, Phys. Rev. A 91, 042135 (2015).
  20. J. Li, et al., Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms, Nat. Commun. 10, 855 (2019).
  21. Y. Liu, L. Mao, and Y. Zhang, Floquet analysis of extended Rabi models based on high-frequency expansion, Phys. Rev. A 105, 053717 (2022).
  22. X. Lu, H. Li, J. K. Shi, L. B. Fan, V. Mangazeev, Z. M. Li, and M. T. Batchelor, PT-symmetric quantum Rabi model, Phys. Rev. A 108, 053712 (2023).
  23. L. Guo, M. Marthaler, and G. Schön, Phase space crystals: A new way to create a quasienergy band structure, Phys. Rev. Lett. 111, 205303 (2013).
  24. S. Mundhada, et al., Encoding a qubit in an oscillator, Phys. Rev. Appl. 12, 054051 (2019).
  25. C. W. S. Chang, C. Sabin, P. Forn Díaz, F. Quijandria, A. M. Vadiraj, I. Nsanzineza, G. Johansson, and C. M. Wilson, Observation of three-photon spontaneous parametric down-conversion in a superconducting parametric cavity, Phys. Rev. X 10, 011011 (2020).
  26. Q. Xie, Sh Rong, and X. Liu, Exceptional points in a time-periodic parity-time-symmetric Rabi model, Phys. Rev. A 98, 052122 (2018).
  27. A. Turbiner, Quasi-exactly-solvable problems and sl(2) algebra, Commun. Math. Phys. 118, 467 (1988).
  28. A. V. TurbinerOne-dimensional quasi-exactly solvable Schrödinger equations, Phys. Rep. 642, 1 (2016).
  29. A. Gonzalez-Lopez, N. Kamran, and P. J. Olver, Quasi-exact solvability, Contemp. Math. 160, 113 (1994).
  30. J. H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time, Phys. Rev. 138, B979 (1965).
  31. H. Sambe, Steady states and quasienergies of a quantum-mechanical system in an oscillating field, Phys. Rev. A 7, 2203 (1973).
  32. B. Höckendorf, A. Alvermann, and H. Fehske, Topological origin of quantized transport in non-Hermitian Floquet chains, Phys. Rev. Res. 2, 023235 (2020).
  33. R. Tat, Semiclassical Floquet-Markov master equation for Monte Carlo spin integration, Phys. Rev. A 112, 013113 (2025).
  34. Heun's Differential Equations, edited by A. Ronveaux (Oxford University Press, New York, 1995).
  35. S. Y. Slavyanov and W. Lay, Special Functions: A Unified Theory Based on Singularities (Oxford University Press, New York, 2000).
  36. A. M. Ishkhanyan, T. A. Shahverdyan, and T. A. Ishkhanyan, Thirty five classes of solutions of the quantum time-dependent two-state problem in terms of the general Heun functions, Eur. Phys. J. D 69, 10 (2015).
  37. A. Khare and B. Mandal, A PT-invariant potential with complex QES eigenvalues, Phys. Lett. A 272, 53 (2000).

Outline

Information

Phys. Rev. Research 8, 013097– Published 28 January, 2026
  • Received 25 February 2025
  • Accepted 10 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation