Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Time-resolved detection of spin-spatial-coupling-induced dynamical phase transitions

J. O. Austin-Harris*, Z. N. Hardesty-Shaw, C. Binegar, P. Sigdel, N. Rago, T. Bilitewski, and Y. Liu

  • *Contact author: jared.o.austin@okstate.edu
  • Contact author: yingmei.liu@okstate.edu

Phys. Rev. A 114, 023326 – Published 28 August, 2026

DOI: https://doi.org/10.1103/bl8c-sdhy

Abstract

We demonstrate the time-resolved detection of dynamical phase transitions (DPTs) in lattice-confined spinor gases subject to a priori unknown time-variant interactions, via the temporal behaviors of both the system energy and spinor phases extracted from the observed spin dynamics. Using this technique, we describe the observed nonequilibrium spin dynamics, governed by intricate spin-spatial couplings, across a range of conditions. This work also introduces a diagnostic tool that can quickly identify DPTs without requiring observations over at least a full period of the spin dynamics. Our approach can naturally extend to other complex systems subject to time-dependent parameters, such as Floquet systems under driven magnetic fields, driven interactions, or spin-flopping fields, with potential applications in the study of DPTs in nonintegrable models.

Physics Subject Headings (PhySH)

Article Text

References (40)

  1. D. M. Stamper-Kurn and M. Ueda, Spinor Bose gases: Symmetries, magnetism, and quantum dynamics, Rev. Mod. Phys. 85, 1191 (2013).
  2. Y. Kawaguchi and M. Ueda, Spinor Bose–Einstein condensates, Phys. Rep. 520, 253 (2012).
  3. W. Zhang, D. L. Zhou, M.-S. Chang, M. S. Chapman, and L. You, Coherent spin mixing dynamics in a spin-1 atomic condensate, Phys. Rev. A 72, 013602 (2005).
  4. M.-S. Chang, Q. Qin, W. Zhang, L. You, and M. S. Chapman, Coherent spinor dynamics in a spin-1 Bose condensate, Nat. Phys. 1, 111 (2005).
  5. J. O. Austin-Harris, Z. N. Hardesty-Shaw, Q. Guan, C. Binegar, D. Blume, R. J. Lewis-Swan, and Y. Liu, Engineering dynamical phase diagrams with driven lattices in spinor gases, Phys. Rev. A 109, 043309 (2024).
  6. Z. N. Hardesty-Shaw, Q. Guan, J. O. Austin, D. Blume, R. J. Lewis-Swan, and Y. Liu, Quench-induced nonequilibrium dynamics of spinor gases in a moving lattice, Phys. Rev. A 107, 053311 (2023).
  7. Z. Chen, T. Tang, J. Austin, Z. Shaw, L. Zhao, and Y. Liu, Quantum quench and nonequilibrium dynamics in lattice-confined spinor condensates, Phys. Rev. Lett. 123, 113002 (2019).
  8. J. O. Austin, Z. Chen, Z. N. Shaw, K. W. Mahmud, and Y. Liu, Quantum critical dynamics in a spinor Hubbard model quantum simulator, Commun. Phys. 4, 61 (2021).
  9. J. O. Austin, Z. N. Shaw, Z. Chen, K. W. Mahmud, and Y. Liu, Manipulating atom-number distributions and detecting spatial distributions in lattice-confined spinor gases, Phys. Rev. A 104, L041304 (2021).
  10. Q. Guan, D. Blume, and R. J. Lewis-Swan, Controlling the dynamical phase diagram of a spinor Bose-Einstein condensate using time-dependent potentials, Phys. Rev. A 112, 023306 (2025).
  11. H.-X. Yang, T. Tian, Y.-B. Yang, L.-Y. Qiu, H.-Y. Liang, A.-J. Chu, C. B. Dağ, Y. Xu, Y. Liu, and L.-M. Duan, Observation of dynamical quantum phase transitions in a spinor condensate, Phys. Rev. A 100, 013622 (2019).
  12. Q. Guan and R. J. Lewis-Swan, Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing, Phys. Rev. Res. 3, 033199 (2021).
  13. J. Marino, M. Eckstein, M. S. Foster, and A. M. Rey, Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: Theory and experiments, Rep. Prog. Phys. 85, 116001 (2022).
  14. L. Zhou, J. Kong, Z. Lan, and W. Zhang, Dynamical quantum phase transitions in a spinor Bose-Einstein condensate and criticality enhanced quantum sensing, Phys. Rev. Res. 5, 013087 (2023).
  15. P. Feldmann, C. Klempt, A. Smerzi, L. Santos, and M. Gessner, Interferometric order parameter for excited-state quantum phase transitions in Bose-Einstein condensates, Phys. Rev. Lett. 126, 230602 (2021).
  16. W. Zhang, D. L. Zhou, M.-S. Chang, M. S. Chapman, and L. You, Dynamical instability and domain formation in a spin-1 Bose-Einstein condensate, Phys. Rev. Lett. 95, 180403 (2005).
  17. A. T. Black, E. Gomez, L. D. Turner, S. Jung, and P. D. Lett, Spinor dynamics in an antiferromagnetic spin-1 condensate, Phys. Rev. Lett. 99, 070403 (2007).
  18. Y. Liu, S. Jung, S. E. Maxwell, L. D. Turner, E. Tiesinga, and P. D. Lett, Quantum phase transitions and continuous observation of spinor dynamics in an antiferromagnetic condensate, Phys. Rev. Lett. 102, 125301 (2009).
  19. Y. Liu, E. Gomez, S. E. Maxwell, L. D. Turner, E. Tiesinga, and P. D. Lett, Number fluctuations and energy dissipation in sodium spinor condensates, Phys. Rev. Lett. 102, 225301 (2009).
  20. H. K. Pechkis, J. P. Wrubel, A. Schwettmann, P. F. Griffin, R. Barnett, E. Tiesinga, and P. D. Lett, Spinor dynamics in an antiferromagnetic spin-1 thermal Bose gas, Phys. Rev. Lett. 111, 025301 (2013).
  21. L. Zhao, J. Jiang, T. Tang, M. Webb, and Y. Liu, Dynamics in spinor condensates tuned by a microwave dressing field, Phys. Rev. A 89, 023608 (2014).
  22. L. Zhao, J. Jiang, T. Tang, M. Webb, and Y. Liu, Antiferromagnetic spinor condensates in a two-dimensional optical lattice, Phys. Rev. Lett. 114, 225302 (2015).
  23. J. O. Austin-Harris, P. Sigdel, C. Binegar, S. E. Begg, T. Bilitewski, and Y. Liu, Control of dynamical phase transitions and nonergodic relaxation via spinor phases Phys. Rev. A 113, 063302 (2026).
  24. J. Kronjäger, C. Becker, P. Navez, K. Bongs, and K. Sengstock, Magnetically tuned spin dynamics resonance, Phys. Rev. Lett. 97, 110404 (2006).
  25. J. Jiang, L. Zhao, M. Webb, and Y. Liu, Mapping the phase diagram of spinor condensates via adiabatic quantum phase transitions, Phys. Rev. A 90, 023610 (2014).
  26. J. O. Austin-Harris, I. Rana, S. E. Begg, C. Binegar, T. Bilitewski, and Y. Liu, Observation of ergodicity breaking and quantum many-body scars in spinor gases, Phys. Rev. Lett. 134, 113401 (2025).
  27. C. Binegar, J. O. Austin-Harris, S. E. Begg, P. Sigdel, T. Bilitewski, and Y. Liu, Lattice-enabled detection of spin-dependent three-body interactions, Phys. Rev. A 113, 043304 (2026).
  28. R. J. Lewis-Swan, S. R. Muleady, D. Barberena, J. J. Bollinger, and A. M. Rey, Characterizing the dynamical phase diagram of the Dicke model via classical and quantum probes, Phys. Rev. Res. 3, L022020 (2021).
  29. C. B. Dağ, S.-T. Wang, and L.-M. Duan, Classification of quench-dynamical behaviors in spinor condensates, Phys. Rev. A 97, 023603 (2018).
  30. R. Shimano and N. Tsuji, Higgs mode in superconductors, Annu. Rev. Condens. Matter Phys. 11, 103 (2020).
  31. R. Matsunaga, Y. I. Hamada, K. Makise, Y. Uzawa, H. Terai, Z. Wang, and R. Shimano, Higgs amplitude mode in the BCS superconductors Nb1xTixN induced by terahertz pulse excitation, Phys. Rev. Lett. 111, 057002 (2013).
  32. N. Fläschner, D. Vogel, M. Tarnowski, B. Rem, D.-S. Lühmann, M. Heyl, J. Budich, L. Mathey, K. Sengstock, and C. Weitenberg, Observation of dynamical vortices after quenches in a system with topology, Nat. Phys. 14, 265 (2018).
  33. P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, and C. F. Roos, Direct observation of dynamical quantum phase transitions in an interacting many-body system, Phys. Rev. Lett. 119, 080501 (2017).
  34. J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, Nature (London) 551, 601 (2017).
  35. B. Evrard, A. Pizzi, S. I. Mistakidis, and C. B. Dag, Quantum scars and regular eigenstates in a chaotic spinor condensate, Phys. Rev. Lett. 132, 020401 (2024).
  36. K. Fujimoto and S. Uchino, Floquet spinor Bose gases, Phys. Rev. Res. 1, 033132 (2019).
  37. B. Evrard, A. Qu, K. Jiménez-García, J. Dalibard, and F. Gerbier, Relaxation and hysteresis near Shapiro resonances in a driven spinor condensate, Phys. Rev. A 100, 023604 (2019).
  38. Z.-C. Li, Q.-H. Jiang, Z. Lan, W. Zhang, and L. Zhou, Nonlinear Floquet dynamics of spinor condensates in an optical cavity: Cavity-amplified parametric resonance, Phys. Rev. A 100, 033617 (2019).
  39. C.-J. Liu, Y.-C. Meng, J.-L. Qin, and L. Zhou, Classical and quantum chaos in a spin-1 atomic Bose–Einstein condensate via Floquet driving, Results Phys. 43, 106091 (2022).
  40. Z. N. Hardesty-Shaw, Q. Guan, J. O. Austin-Harris, D. Blume, R. J. Lewis-Swan, and Y. Liu, Nonlinear multistate tunneling dynamics in a spinor Bose-Einstein condensate, Phys. Rev. A 108, 053307 (2023).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation