- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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
  • Editors' Suggestion
  • Open Access

Imaginary Gauge Potentials in a Non-Hermitian Spin-Orbit Coupled Quantum Gas

J. Tao1,2,*, E. D. Mercado-Gutierrez1,*, M. Zhao1, and I. B. Spielman1,†

  • *These authors contributed equally to this work.
  • †Contact author: ian.spielman@nist.gov
PDF

Phys. Rev. Lett. 136, 113401 – Published 17 March, 2026

DOI: https://doi.org/10.1103/tpfc-n3bq

Abstract

In 1996, Hatano and Nelson proposed a non-Hermitian lattice model containing an imaginary Peierls phase [Phys. Rev. Lett. 77, 570 (1996)], which subsequent analyses revealed to be an instance of a new class of topological systems. Here, we experimentally realize a continuum analog to this model containing an imaginary gauge potential using a homogeneous spin-orbit coupled Bose-Einstein condensate (BEC). Non-Hermiticity is introduced by adding tunable spin-dependent loss via microwave coupling to a subspace with spontaneous emission. We demonstrate that the resulting Heisenberg equations of motion for position and momentum depend explicitly on the system’s phase-space distribution. First, we observe collective nonreciprocal transport in real space, with a “self-acceleration” that decreases with the BEC’s spatial extent, consistent with non-Hermitian Gross-Pitaevskii simulations. We then examine localized edge states: the relatively strong interactions in our BEC suppress the formation of topological edge states, yielding instead highly excited states localized by an interplay between self-acceleration and wave function spreading. Finally, we confirm that our non-Hermitian description remains valid at all times by comparing it to a multilevel master equation treatment.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (47)

  1. W. Happer, Optical pumping, Rev. Mod. Phys. 44, 169 (1972).
  2. H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, Measurement-based quantum computation, Nat. Phys. 5, 19 (2009).
  3. B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87, 307 (2015).
  4. M.-A. Miri and A. Alu, Exceptional points in optics and photonics, Science 363, eaar7709 (2019).
  5. Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys. 69, 249 (2020).
  6. E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys. 93, 015005 (2021).
  7. Z. Ren, D. Liu, E. Zhao, C. He, K. K. Pak, J. Li, and G.-B. Jo, Chiral control of quantum states in non-Hermitian spin–orbit-coupled fermions, Nat. Phys. 18, 385 (2022).
  8. Y.-J. Liu, K. K. Pak, P. Ren, M. Guo, E. Zhao, C. He, and G.-B. Jo, Third-order exceptional point in non-Hermitian spin-orbit-coupled cold atoms, Phys. Rev. A 112, 023305 (2025).
  9. K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Symmetry and topology in non-Hermitian physics, Phys. Rev. X 9, 041015 (2019).
  10. K. Wang, A. Dutt, C. C. Wojcik, and S. Fan, Topological complex-energy braiding of non-Hermitian bands, Nature (London) 598, 59 (2021).
  11. N. Hatano and D. R. Nelson, Localization transitions in non-Hermitian quantum mechanics, Phys. Rev. Lett. 77, 570 (1996).
  12. N. Hatano and D. R. Nelson, Vortex pinning and non-Hermitian quantum mechanics, Phys. Rev. B 56, 8651 (1997).
  13. K. Zhang, Z. Yang, and C. Fang, Correspondence between winding numbers and skin modes in non-Hermitian systems, Phys. Rev. Lett. 125, 126402 (2020).
  14. S. Yao and Z. Wang, Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett. 121, 086803 (2018).
  15. F. Song, S. Yao, and Z. Wang, Non-Hermitian skin effect and chiral damping in open quantum systems, Phys. Rev. Lett. 123, 170401 (2019).
  16. Q. Liang, D. Xie, Z. Dong, H. Li, H. Li, B. Gadway, W. Yi, and B. Yan, Dynamic signatures of non-Hermitian skin effect and topology in ultracold atoms, Phys. Rev. Lett. 129, 070401 (2022).
  17. X. Zhang, Y. Tian, J.-H. Jiang, M.-H. Lu, and Y.-F. Chen, Observation of higher-order non-Hermitian skin effect, Nat. Commun. 12, 5377 (2021).
  18. L. Xiao, T. Deng, K. Wang, G. Zhu, Z. Wang, W. Yi, and P. Xue, Non-Hermitian bulk–boundary correspondence in quantum dynamics, Nat. Phys. 16, 761 (2020).
  19. S. Weidemann, M. Kremer, T. Helbig, T. Hofmann, A. Stegmaier, M. Greiter, R. Thomale, and A. Szameit, Topological funneling of light, Science 368, 311 (2020).
  20. E. Zhao, Z. Wang, C. He, T. F. J. Poon, K. K. Pak, Y.-J. Liu, P. Ren, X.-J. Liu, and G.-B. Jo, Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas, Nature (London) 637, 565 (2025).
  21. T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L. Molenkamp, C. Lee, A. Szameit, M. Greiter, and R. Thomale, Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits, Nat. Phys. 16, 747 (2020).
  22. C. Lv, R. Zhang, Z. Zhai, and Q. Zhou, Curving the space by non-Hermiticity, Nat. Commun. 13, 2184 (2022).
  23. C. Lv and Q. Zhou, Complexity geometry in Hermitian and non-Hermitian quantum dynamics, Phys. Rev. D 110, 084039 (2024).
  24. Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, Spin–orbit-coupled Bose–Einstein condensates, Nature (London) 471, 83 (2011).
  25. Y.-J. Lin, R. L. Compton, A. R. Perry, W. D. Phillips, J. V. Porto, and I. B. Spielman, Bose-Einstein condensate in a uniform light-induced vector potential, Phys. Rev. Lett. 102, 130401 (2009).
  26. Y.-J. Lin, R. L. Compton, K. Jimenez-Garcia, W. D. Phillips, J. V. Porto, and I. B. Spielman, A synthetic electric force acting on neutral atoms, Nat. Phys. 7, 531 (2011).

  27. Here we use the saturation intensity suitable for the transition under consideration.

  28. C. Wang, N. Li, J. Xie, C. Ding, Z. Ji, L. Xiao, S. Jia, B. Yan, Y. Hu, and Y. Zhao, Exceptional nexus in Bose-Einstein condensates with collective dissipation, Phys. Rev. Lett. 132, 253401 (2024).
  29. L. Pan, X. Chen, Y. Chen, and H. Zhai, Non-Hermitian linear response theory, Nat. Phys. 16, 767 (2020).
  30. A. Ramanathan, S. R. Muniz, K. C. Wright, R. P. Anderson, W. D. Phillips, K. Helmerson, and G. K. Campbell, Partial-transfer absorption imaging: A versatile technique for optimal imaging of ultracold gases, Rev. Sci. Instrum. 83, 083119 (2012).

  31. An equivalent sign change follows from swapping the frequencies of two Raman laser beams since B∝p0.

  32. We note, however, that this antiunitary gauge transformation is incompatible with periodic boundary conditions.

  33. In this gauge, the interaction coefficient becomes spatially dependent, g(x)=gexp(2Bx/ℏ), leading to a position-dependent healing length ξ that slightly shifts ⟨x⟩ toward the edge with larger g.

  34. D.-W. Zhang, Y.-L. Chen, G.-Q. Zhang, L.-J. Lang, Z. Li, and S.-L. Zhu, Skin superfluid, topological Mott insulators, and asymmetric dynamics in an interacting non-Hermitian Aubry-André-Harper model, Phys. Rev. B 101, 235150 (2020).
  35. K. Kawabata, K. Shiozaki, and S. Ryu, Many-body topology of non-Hermitian systems, Phys. Rev. B 105, 165137 (2022).
  36. M. Zheng, Y. Qiao, Y. Wang, J. Cao, and S. Chen, Exact solution of the Bose-Hubbard model with unidirectional hopping, Phys. Rev. Lett. 132, 086502 (2024).
  37. M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction, Phys. Rev. Lett. 95, 010402 (2005).

  38. For these data, set the bias field to B0=670  μT.

  39. W. M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Quantum Zeno effect, Phys. Rev. A 41, 2295 (1990).
  40. Q. Zhou and W. Xu (private communication).
  41. L. M. Farrell, C. J. Howls, and D. H. J. O’Dell, Logarithmic catastrophes and Stokes’s phenomenon in waves at horizons, J. Phys. A 56, 044001 (2023).
  42. Y. Huang and B. Shklovskii, Anderson transition in three-dimensional systems with non-Hermitian disorder, Phys. Rev. B 101, 014204 (2020).
  43. A. Tzortzakakis, K. Makris, and E. Economou, Non-Hermitian disorder in two-dimensional optical lattices, Phys. Rev. B 101, 014202 (2020).
  44. L. Mao, Y. Hao, and L. Pan, Non-Hermitian skin effect in a one-dimensional interacting Bose gas, Phys. Rev. A 107, 043315 (2023).
  45. R. Hamazaki, K. Kawabata, and M. Ueda, Non-Hermitian many-body localization, Phys. Rev. Lett. 123, 090603 (2019).
  46. J. Tao, E. D. Mercado-Gutierrez, M. Zhao, and I. B. Spielman, Data for imaginary gauge potentials in a non-Hermitian spin-orbit coupled quantum gas, Zenodo, 2026, 10.5281/zenodo.18650354.
  47. See Supplemental Material at http://link.aps.org/supplemental/10.1103/tpfc-n3bq for experimental and data analysis methods, derivations of the imaginary gauge potential and the non-Hermitian equations of motion.

Outline

Information

Phys. Rev. Lett. 136, 113401– Published 17 March, 2026
  • Received 25 May 2025
  • Revised 4 January 2026
  • Accepted 13 February 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