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Floquet polaron and molecule in a highly polarized Fermi gas with periodically modulated interactions

Ming-Yue Yang, An-Chun Ji*, and Qing Sun†

  • *Contact author: andrewjee@sina.com
  • †Contact author: sunqing@cnu.edu.cn
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Phys. Rev. Research 8, 013108 – Published 30 January, 2026

DOI: https://doi.org/10.1103/gkw6-sb9q

Abstract

We investigate the impurity problem of a highly polarized Fermi gas with periodically modulated atom-atom interactions. We find that generalized time-periodic Floquet polaron and molecule emerge as quasistationary quasiparticle states of the system, which exhibit peculiar features distinct from those in a static system. Even in the high-frequency limit, the periodic driving can renormalize the scattering length of the static (effective) Hamiltonian and thus modify the polaron-to-molecule transition. Remarkably, due to the folding of the quasienergy of the Floquet states in the Floquet Brillouin zone, unusual energy-level crossings beyond the conventional polaron-to-molecule transition occur. In particular, when the driving frequency is in resonance with the quasienergy difference, both branches of the Floquet polaron can intersect with the molecular state or even themselves under weak driving. The unique physics of these Floquet impurity states is further characterized and elucidated by the experimentally measurable spectral functions and the radio-frequency spectra. Our results pave a way to explore the intriguing nonequililbrium impurity physics beyond a static system via “Floquet engineering.”

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References (99)

  1. L. D. Landau and S. I. Pekar, Effective mass of a polaron, Zh. Eksp. Teor. Fiz. 18, 419 (1948).
  2. H. Fröhlich, Electrons in lattice fields, Adv. Phys. 3, 325 (1954).
  3. P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006).
  4. K. B. Gubbels and H. T. C. Stoof, Imbalanced Fermi gases at unitarity, Phys. Rep. 525, 255 (2013).
  5. C. H. Greene, P. Giannakeas, and J. Pérez-Ríos, Universal few-body physics and cluster formation, Rev. Mod. Phys. 89, 035006 (2017).
  6. A. S. Alexandrov and J. T. Devreese, Advances in Polaron Physics, Springer Series in Solid-State Sciences, Vol. 159 (Springer, Berlin, 2010).
  7. C. Franchini, M. Reticcioli, M. Steven, and U. Diebold, Polarons in materials, Nat. Rev. Mater. 6, 560 (2021).
  8. I. Bloch, J. Dalibard, and S. Nascimbène, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012).
  9. C. Baroni, G. Lamporesi, and M. Zaccanti, Quantum mixtures of ultracold gases of neutral atoms, Nat. Rev. Phys. 6, 736 (2024).
  10. F. Chevy and C. Mora, Ultra-cold polarized Fermi gases, Rep. Prog. Phys. 73, 112401 (2010).
  11. P. Massignan, M. Zaccanti, and G. M. Bruun, Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases, Rep. Prog. Phys. 77, 034401 (2014).
  12. F. Scazza, M. Zaccanti, P. Massignan, M. M. Parish, and J. Levinsen, Repulsive Fermi and Bose polarons in quantum gases, Atoms 10, 55 (2022).
  13. M. M. Parish and J. Levinsen, Fermi polarons and beyond, arXiv:2306.01215.
  14. F. Chevy, Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations, Phys. Rev. A 74, 063628 (2006).
  15. R. Combescot, A. Recati, C. Lobo, and F. Chevy, Normal state of highly polarized Fermi gases: Simple many-body approaches, Phys. Rev. Lett. 98, 180402 (2007).
  16. S. Nascimbéne, N. Navon, K. J. Jiang, L. Tarruell, M. Teichmann, J. McKeever, F. Chevy, and C. Salomon, Collective oscillations of an imbalanced Fermi gas: Axial compression modes and polaron effective mass, Phys. Rev. Lett. 103, 170402 (2009).
  17. M. Punk, P. T. Dumitrescu, and W. Zwerger, Polaron-to-molecule transition in a strongly imbalanced Fermi gas, Phys. Rev. A 80, 053605 (2009).
  18. X. Cui and H. Zhai, Stability of a fully magnetized ferromagnetic state in repulsively interacting ultracold Fermi gases, Phys. Rev. A 81, 041602(R) (2010).
  19. S. Pilati, G. Bertaina, S. Giorgini, and M. Troyer, Itinerant ferromagnetism of a repulsive atomic Fermi gas: A quantum Monte Carlo study, Phys. Rev. Lett. 105, 030405 (2010).
  20. P. Massignan and G. M. Bruun, Repulsive polarons and itinerant ferromagnetism in strongly polarized Fermi gases, Eur. Phys. J. D 65, 83 (2011).
  21. J. Vlietinck, J. Ryckebusch, and K. Van Houcke, Quasiparticle properties of an impurity in a Fermi gas, Phys. Rev. B 87, 115133 (2013).
  22. A. Schirotzek, C.-H. Wu, A. Sommer, and M. W. Zwierlein, Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms, Phys. Rev. Lett. 102, 230402 (2009).
  23. C. Kohstall, M. Zaccanti, M. Jag, A. Trenkwalder, P. Massignan, G. M. Bruun, F. Schreck, and R. Grimm, Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture, Nature (London) 485, 615 (2012).
  24. M. Koschorreck, D. Pertot, E. Vogt, B. Fröhlich, M. Feld, and M. Köhl, Attractive and repulsive Fermi polarons in two dimensions, Nature (London) 485, 619 (2012).
  25. M. Cetina, et al., Ultrafast many-body interferometry of impurities coupled to a Fermi sea, Science 354, 96 (2016).
  26. F. Scazza, G. Valtolina, P. Massignan, A. Recati, A. Amico, A. Burchianti, C. Fort, M. Inguscio, M. Zaccanti, and G. Roati, Repulsive Fermi polarons in a resonant mixture of ultracold Li6 atoms, Phys. Rev. Lett. 118, 083602 (2017).
  27. G. Ness, C. Shkedrov, Y. Florshaim, O. K. Diessel, J. von Milczewski, R. Schmidt, and Y. Sagi, Observation of a smooth polaron-molecule transition in a degenerate Fermi gas, Phys. Rev. X 10, 041019 (2020).
  28. C. Baroni, Mediated interactions between Fermi polarons and the role of impurity quantum statistics, Nat. Phys. 20, 68 (2024).
  29. M.-G. Hu, M. J. Van de Graaff, D. Kedar, J. P. Corson, E. A. Cornell, and D. S. Jin, Bose polarons in the strongly interacting regime, Phys. Rev. Lett. 117, 055301 (2016).
  30. N. B. Jørgensen, L. Wacker, K. T. Skalmstang, M. M. Parish, J. Levinsen, R. S. Christensen, G. M. Bruun, and J. J. Arlt, Observation of attractive and repulsive polarons in a Bose-Einstein condensate, Phys. Rev. Lett. 117, 055302 (2016).
  31. Z. Z. Yan, Y. Ni, C. Robens, and M. W. Zwierlein, Bose polarons near quantum criticality, Science 368, 190 (2020).
  32. F. M. Cucchietti and E. Timmermans, Strong-coupling polarons in dilute gas Bose-Einstein condensates, Phys. Rev. Lett. 96, 210401 (2006).
  33. Y. E. Shchadilova, R. Schmidt, F. Grusdt, and E. Demler, Quantum dynamics of ultracold Bose polarons, Phys. Rev. Lett. 117, 113002 (2016).
  34. N.-E. Guenther, P. Massignan, M. Lewenstein, and G. M. Bruun, Bose polarons at finite temperature and strong coupling, Phys. Rev. Lett. 120, 050405 (2018).
  35. P. Massignan, N. Yegovtsev, and V. Gurarie, Universal aspects of a strongly interacting impurity in a dilute Bose condensate, Phys. Rev. Lett. 126, 123403 (2021).
  36. F. Grusdt, N. Mostaan, E. Demler, and L. A. P. Ardila, Impurities and polarons in bosonic quantum gases: A review on recent progress, Rep. Prog. Phys. 88, 066401 (2025).
  37. G. M. Bruun and P. Massignan, Decay of polarons and molecules in a strongly polarized Fermi gas, Phys. Rev. Lett. 105, 020403 (2010).
  38. R. Schmidt and T. Enss, Excitation spectra and rf response near the polaron-to-molecule transition from the functional renormalization group, Phys. Rev. A 83, 063620 (2011).
  39. S. Zöllner, G. M. Bruun, and C. J. Pethick, Polarons and molecules in a two-dimensional Fermi gas, Phys. Rev. A 83, 021603(R) (2011).
  40. X. Cui, Fermi polaron revisited: Polaron-molecule transition and coexistence, Phys. Rev. A 102, 061301(R) (2020).
  41. C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2010).
  42. J. H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time, Phys. Rev. 138, B979 (1965).
  43. H. Sambe, Steady states and quasienergies of a quantum-mechanical system in an oscillating field, Phys. Rev. A 7, 2203 (1973).
  44. N. Goldman and J. Dalibard, Periodically driven quantum systems: Effective Hamiltonians and engineered gauge fields, Phys. Rev. X 4, 031027 (2014).
  45. A. Eckardt and E. Anisimovas, High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective, New J. Phys. 17, 093039 (2015).
  46. M. Bukov, L. D’Alessio, and A. Polkovnikov, Universal high-frequency behavior of periodically driven systems: From dynamical stabilization to Floquet engineering, Adv. Phys. 64, 139 (2015).
  47. A. Eckardt, Colloquium: Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys. 89, 011004 (2017).
  48. T. Oka and S. Kitamura, Floquet engineering of quantum materials, Annu. Rev. Condens. Matter Phys. 10, 387 (2019).
  49. C. Weitenberg, Tailoring quantum gases by Floquet engineering, Nat. Phys. 17, 1342 (2021).
  50. Á. Rapp, X. Deng, and L. Santos, Ultracold lattice gases with periodically modulated interactions, Phys. Rev. Lett. 109, 203005 (2012).
  51. F. Meinert, M. J. Mark, K. Lauber, A. J. Daley, and H.-C. Nägerl, Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms, Phys. Rev. Lett. 116, 205301 (2016).
  52. J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, Tunable gauge potential for neutral and spinless particles in driven optical lattices, Phys. Rev. Lett. 108, 225304 (2012).
  53. B. M. Anderson, I. B. Spielman, and G. Juzeliūnas, Magnetically generated spin-orbit coupling for ultracold atoms, Phys. Rev. Lett. 111, 125301 (2013).
  54. S. Greschner, G. Sun, D. Poletti, and L. Santos, Density-dependent synthetic gauge fields using periodically modulated interactions, Phys. Rev. Lett. 113, 215303 (2014).
  55. K. Jiménez-García, L. J. LeBlanc, R. A. Williams, M. C. Beeler, C. Qu, M. Gong, C. Zhang, and I. B. Spielman, Tunable spin-orbit coupling via strong driving in ultracold-atom systems, Phys. Rev. Lett. 114, 125301 (2015).
  56. L. W. Clark, B. M. Anderson, L. Feng, A. Gaj, K. Levin, and C. Chin, Observation of density-dependent gauge fields in a Bose-Einstein condensate based on micromotion control in a shaken two-dimensional lattice, Phys. Rev. Lett. 121, 030402 (2018).
  57. P. Xu, T. -S. Deng, W. Zheng, and H. Zhai, Density-dependent spin-orbit coupling in degenerate quantum gases, Phys. Rev. A 103, L061302 (2021).
  58. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermions, Nature (London) 515, 237 (2014).
  59. W. Zheng and H. Zhai, Floquet topological states in shaking optical lattices, Phys. Rev. A 89, 061603(R) (2014).
  60. M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimbène, N. R. Cooper, I. Bloch, and N. Goldman, Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms, Nat. Phys. 11, 162 (2015).
  61. N. R. Cooper, J. Dalibard, and I. B. Spielman, Topological bands for ultracold atoms, Rev. Mod. Phys. 91, 015005 (2019).
  62. K. Wintersperger, C. Braun, F. N. Ünal, A. Eckardt, M. D. Liberto, N. Goldman, I. Bloch, and M. Aidelsburger, Realization of an anomalous Floquet topological system with ultracold atoms, Nat. Phys. 16, 1058 (2020).
  63. L. Zhang, L. Zhang, and X.-J. Liu, Unified theory to characterize Floquet topological phases by quench dynamics, Phys. Rev. Lett. 125, 183001 (2020).
  64. J.-Y. Zhang, C.-R. Yi, L. Zhang, R.-H. Jiao, K.-Y. Shi, H. Yuan, W. Zhang, X.-J. Liu, S. Chen, and J.-W. Pan, Tuning anomalous Floquet topological bands with ultracold atoms, Phys. Rev. Lett. 130, 043201 (2023).
  65. D. V. Else, B. Bauer, and C. Nayak, Floquet time crystals, Phys. Rev. Lett. 117, 090402 (2016).
  66. N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath, Discrete time crystals: Rigidity, criticality, and realizations, Phys. Rev. Lett. 118, 030401 (2017).
  67. J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I.-D. Potirniche, A. C. Potter, A. Vishwanath, N. Y. Yao, and C. Monroe, Observation of a discrete time crystal, Nature (London) 543, 217 (2017).
  68. S. Choi, et al., Observation of discrete time-crystalline order in a disordered dipolar many-body system, Nature (London) 543, 221 (2017).
  69. B. Huang, Y.-H. Wu, and W. V. Liu, Clean Floquet time crystals: Models and realizations in cold atoms, Phys. Rev. Lett. 120, 110603 (2018).
  70. J. Rovny, R. L. Blum, and S. E. Barrett, Observation of discrete-time-crystal signatures in an ordered dipolar many-body system, Phys. Rev. Lett. 120, 180603 (2018).
  71. M. Randeria, Bose-Einstein Condensation (Cambridge University Press, Cambridge, 1995), Vol. 355.
  72. C. Langmack, D. H. Smith, and E. Braaten, Association of atoms into universal dimers using an oscillating magnetic field, Phys. Rev. Lett. 114, 103002 (2015).
  73. D. H. Smith, Inducing resonant interactions in ultracold atoms with a modulated magnetic field, Phys. Rev. Lett. 115, 193002 (2015).
  74. See Supplemental Material at http://link.aps.org/supplemental/10.1103/gkw6-sb9q for the derivations of the Floquet polaron and molecule and their spectral functions, as well as the numerical details.
  75. C. Dauer, A. Pelster, and S. Eggert, Understanding Floquet resonances in ultracold quantum gas scattering, Phys. Rev. Lett. 135, 033402 (2025).
  76. C. J. M. Mathy, M. M. Parish, and D. A. Huse, Trimers, molecules, and polarons in mass-imbalanced atomic Fermi gases, Phys. Rev. Lett. 106, 166404 (2011).
  77. M. M. Parish and J. Levinsen, Highly polarized Fermi gases in two dimensions, Phys. Rev. A 87, 033616 (2013).
  78. X. Qiu, X. Cui, and W. Yi, Universal trimers emerging from a spin-orbit-coupled Fermi sea, Phys. Rev. A 94, 051604(R) (2016).
  79. P. Naidon and S. Endo, Efimov physics: A review, Rep. Prog. Phys. 80, 056001 (2017).
  80. C. Shkedrov, M. Menashes, G. Ness, A. Vainbaum, E. Altman, and Y. Sagi, Absence of heating in a uniform Fermi gas created by periodic driving, Phys. Rev. X 12, 011041 (2022).
  81. A. Kell, M. Breyer, D. Eberz, and M. Köhl, Exciting the Higgs mode in a strongly interacting Fermi gas by interaction modulation, Phys. Rev. Lett. 133, 150403 (2024).
  82. D. Eberz, A. Kell, M. Breyer, and M. Köhl, Cooling a strongly interacting quantum gas by interaction modulation, Phys. Rev. A 112, L021302 (2025).
  83. H. Hu and X.-J. Liu, Fermi polarons at finite temperature: Spectral function and rf spectroscopy, Phys. Rev. A 105, 043303 (2022).
  84. T. Qin and W. Hofstetter, Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study, Phys. Rev. B 96, 075134 (2017).
  85. G. S. Uhrig, M. H. Kalthoff, and J. K. Freericks, Positivity of the spectral densities of retarded Floquet Green functions, Phys. Rev. Lett. 122, 130604 (2019).
  86. N. Tsuji, T. Oka, and H. Aoki, Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism, Phys. Rev. B 78, 235124 (2008).
  87. T. Bilitewski and N. R. Cooper, Scattering theory for Floquet-Bloch states, Phys. Rev. A 91, 033601 (2015).
  88. E. Kandelaki and M. S. Rudner, Many-body dynamics and gap opening in interacting periodically driven systems, Phys. Rev. Lett. 121, 036801 (2018).
  89. M. S. Rudner and N. H. Lindner, The Floquet engineer's handbook, arXiv:2003.08252.
  90. A. Altland and B. Simons, Condensed Matter Field Theory, 2nd ed. (Cambridge University Press, Cambridge, 2010), p. 786.
  91. A. Lazarides, A. Das, and R. Moessner, Equilibrium states of generic quantum systems subject to periodic driving, Phys. Rev. E 90, 012110 (2014).
  92. L. D’Alessio and M. Rigol, Long-time behavior of isolated periodically driven interacting lattice systems, Phys. Rev. X 4, 041048 (2014).
  93. C. Chin, M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, J. H. Denschlag, and R. Grimm, Observation of the pairing gap in a strongly interacting Fermi gas, Science 305, 1128 (2004).
  94. C. Chin and P. S. Julienne, Radio-frequency transitions on weakly bound ultracold molecules, Phys. Rev. A 71, 012713 (2005).
  95. M. M. Parish and J. Levinsen, Quantum dynamics of impurities coupled to a Fermi sea, Phys. Rev. B 94, 184303 (2016).
  96. R. Schmidt, M. Knap, D. A. Ivanov, J.-S. You, M. Cetina, and E. Demler, Universal many-body response of heavy impurities coupled to a Fermi sea: A review of recent progress, Rep. Prog. Phys. 81, 024401 (2018).
  97. W. E. Lilu, J. Levinsen, and M. M. Parish, Variational approach for impurity dynamics at finite temperature, Phys. Rev. Lett. 122, 205301 (2019).
  98. F. Yang and R. Qi, Non-equilibrium dynamics of Fermi polarons driven by time-dependent interaction, arXiv:2501.08444.
  99. Q. Chen, Z. Wang, R. Boyack, S. Yang, and K. Levin, When superconductivity crosses over: From BCS to BEC, Rev. Mod. Phys. 96, 025002 (2024).

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Phys. Rev. Research 8, 013108– Published 30 January, 2026
  • Received 25 March 2025
  • Accepted 2 January 2026
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