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  • Open Access

Understanding Floquet Resonances in Ultracold Quantum Gas Scattering

Christoph Dauer, Axel Pelster, and Sebastian Eggert*

  • *Contact author: seggert@rptu.de

Phys. Rev. Lett. 135, 033402 – Published 17 July, 2025

DOI: https://doi.org/10.1103/47xs-223h

Abstract

It is demonstrated that the effective scattering length can be highly manipulated via time-periodic driving of a short-range interparticle potential. By developing a Floquet-scattering theory we show that sharp Floquet resonances occur at which the effective interaction can be tuned to very large attractive or repulsive values. The resulting s-wave scattering length can be obtained in analytic form and the shape of these resonances is given by a simple formula describing how resonance position and width can be altered by the driving strength. Our approach allows the identification of the underlying physical mechanism of the scattering resonances as Floquet bound states with positive energies, which are dynamically created by the drive. This insight is valuable for a detailed analysis and uncovers a general resource for enhanced or reduced scattering in Floquet systems, as was recently confirmed experimentally.

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References (74)

  1. U. Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124, 1866 (1961).
  2. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Fano resonances in nanoscale structures, Rev. Mod. Phys. 82, 2257 (2010).
  3. S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, Observation of Feshbach resonances in a Bose-Einstein condensate, Nature (London) 392, 151 (1998).
  4. E. Timmermans, P. Tommasini, M. Hussein, and A. Kerman, Feshbach resonances in atomic Bose-Einstein condensates, Phys. Rep. 315, 199 (1999).
  5. V. Vuletić, A. J. Kerman, C. Chin, and S. Chu, Observation of low-field Feshbach resonances in collisions of Cesium atoms, Phys. Rev. Lett. 82, 1406 (1999).
  6. C. Chin, V. Vuletić, A. J. Kerman, and S. Chu, High resolution Feshbach spectroscopy of Cesium, Phys. Rev. Lett. 85, 2717 (2000).
  7. C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2010).
  8. R. A. Duine and H. T. C. Stoof, Atom–molecule coherence in Bose gases, Phys. Rep. 396, 115 (2004).
  9. P. O. Fedichev, Y. Kagan, G. V. Shlyapnikov, and J. T. M. Walraven, Influence of nearly resonant light on the scattering length in low-temperature atomic gases, Phys. Rev. Lett. 77, 2913 (1996).
  10. M. Theis, G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J. Hecker Denschlag, Tuning the scattering length with an optically induced Feshbach resonance, Phys. Rev. Lett. 93, 123001 (2004).
  11. G. Thalhammer, M. Theis, K. Winkler, R. Grimm, and J. Hecker Denschlag, Inducing an optical Feshbach resonance via stimulated Raman coupling, Phys. Rev. A 71, 033403 (2005).
  12. T. L. Nicholson, S. Blatt, B. J. Bloom, J. R. Williams, J. W. Thomsen, J. Ye, and P. S. Julienne, Optical Feshbach resonances: Field-dressed theory and comparison with experiments, Phys. Rev. A 92, 022709 (2015).
  13. O. Thomas, C. Lippe, T. Eichert, and H. Ott, Experimental realization of a Rydberg optical Feshbach resonance in a quantum many-body system, Nat. Commun. 9, 2238 (2018).
  14. A. M. Kaufman, R. P. Anderson, T. M. Hanna, E. Tiesinga, P. S. Julienne, and D. S. Hall, Radio-frequency dressing of multiple Feshbach resonances, Phys. Rev. A 80, 050701(R) (2009).
  15. P. Zhang, P. Naidon, and M. Ueda, Independent control of scattering lengths in multicomponent quantum gases, Phys. Rev. Lett. 103, 133202 (2009).
  16. T. V. Tscherbul, T. Calarco, I. Lesanovsky, R. V. Krems, A. Dalgarno, and J. Schmiedmayer, Rf-field-induced Feshbach resonances, Phys. Rev. A 81, 050701(R) (2010).
  17. T. M. Hanna, E. Tiesinga, and P. S. Julienne, Creation and manipulation of Feshbach resonances with radiofrequency radiation, New J. Phys. 12, 083031 (2010).
  18. D. J. Papoular, G. V. Shlyapnikov, and J. Dalibard, Microwave-induced Fano-Feshbach resonances, Phys. Rev. A 81, 041603(R) (2010).
  19. D. J. Owens, T. Xie, and J. M. Hutson, Creating Feshbach resonances for ultracold molecule formation with radio-frequency fields, Phys. Rev. A 94, 023619 (2016).
  20. A. Guthmann, F. Lang, L. M. Kienesberger, S. Barbosa, and A. Widera, Floquet-engineering of Feshbach resonances in ultracold gases, arXiv:2503.05454.
  21. D. H. Smith, Inducing resonant interactions in ultracold atoms with a modulated magnetic field, Phys. Rev. Lett. 115, 193002 (2015).
  22. A. G. Sykes, H. Landa, and D. S. Petrov, Two- and three-body problem with Floquet-driven zero-range interactions, Phys. Rev. A 95, 062705 (2017).
  23. J. H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time, Phys. Rev. 138, B979 (1965).
  24. H. Sambe, Steady states and quasienergies of a quantum-mechanical system in an oscillating field, Phys. Rev. A 7, 2203 (1973).
  25. M. Grifoni and P. Hänggi, Driven quantum tunneling, Phys. Rep. 304, 229 (1998).
  26. M. Holthaus, Floquet engineering with quasienergy bands of periodically driven optical lattices, J. Phys. B 49, 013001 (2016).
  27. A. Eckardt, Colloquium: Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys. 89, 1 (2017).
  28. D. H. Dunlap and V. M. Kenkre, Dynamic localization of a charged particle moving under the influence of an electric field, Phys. Rev. B 34, 3625 (1986).
  29. A. Eckardt, C. Weiss, and M. Holthaus, Superfluid-insulator transition in a periodically driven optical lattice, Phys. Rev. Lett. 95, 260404 (2005).
  30. H. Lignier, C. Sias, D. Ciampini, Y. Singh, A. Zenesini, O. Morsch, and E. Arimondo, Dynamical control of matter-wave tunneling in periodic potentials, Phys. Rev. Lett. 99, 220403 (2007).
  31. C. Sias, H. Lignier, Y. P. Singh, A. Zenesini, D. Ciampini, O. Morsch, and E. Arimondo, Observation of photon-assisted tunneling in optical lattices, Phys. Rev. Lett. 100, 040404 (2008).
  32. A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimondo, Coherent control of dressed matter waves, Phys. Rev. Lett. 102, 100403 (2009).
  33. T. Salger, S. Kling, T. Hecking, C. Geckeler, L. Morales-Molina, and M. Weitz, Directed transport of atoms in a Hamiltonian quantum ratchet, Science 326, 1241 (2009).
  34. T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Topological characterization of periodically driven quantum systems, Phys. Rev. B 82, 235114 (2010).
  35. S. E. Pollack, D. Dries, R. G. Hulet, K. M. F. Magalhães, E. A. L. Henn, E. R. F. Ramos, M. A. Caracanhas, and V. S. Bagnato, Collective excitation of a Bose-Einstein condensate by modulation of the atomic scattering length, Phys. Rev. A 81, 053627 (2010).
  36. J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Colloquium: Artificial gauge potentials for neutral atoms, Rev. Mod. Phys. 83, 1523 (2011).
  37. I. Vidanović, A. Balaž, H. Al-Jibbouri, and A. Pelster, Nonlinear Bose-Einstein-condensate dynamics induced by a harmonic modulation of the s-wave scattering length, Phys. Rev. A 84, 013618 (2011).
  38. 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).
  39. P. Hauke, O. Tieleman, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, and A. Eckardt, Non-Abelian gauge fields and topological insulators in shaken optical lattices, Phys. Rev. Lett. 109, 145301 (2012).
  40. M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices, Phys. Rev. Lett. 111, 185301 (2013).
  41. M. S. Rudner, N. H. Lindner, E. Berg, and M. Levin, Anomalous edge states and the bulk-edge correspondence for periodically driven two-dimensional systems, Phys. Rev. X 3, 031005 (2013).
  42. T. Wang, X.-F. Zhang, F. E. A. dos Santos, S. Eggert, and A. Pelster, Tuning the quantum phase transition of bosons in optical lattices via periodic modulation of the s-wave scattering length, Phys. Rev. A 90, 013633 (2014).
  43. N. Goldman and J. Dalibard, Periodically driven quantum systems: Effective Hamiltonians and engineered gauge fields, Phys. Rev. X 4, 1 (2014).
  44. 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).
  45. W. Cairncross and A. Pelster, Parametric resonance in Bose-Einstein condensates with periodic modulation of attractive interaction, Europhys. J. D 68, 106 (2014).
  46. N. Fläschner, D. Vogel, M. Tarnowski, B. S. Rem, D. S. Lühmann, M. Heyl, J. C. Budich, L. Mathey, K. Sengstock, and C. Weitenberg, Observation of dynamical vortices after quenches in a system with topology, Nat. Phys. 14, 1 (2017).
  47. L. W. Clark, A. Gaj, L. Feng, and C. Chin, Collective emission of matter-wave jets from driven Bose–Einstein condensates, Nature (London) 551, 356 (2017).
  48. N. Mann, M. Reza Bakhtiari, F. Massel, A. Pelster, and M. Thorwart, Driven Bose-Hubbard model with a parametrically modulated harmonic trap, Phys. Rev. A 95, 043604 (2017).
  49. B. Wang, F. N. Ünal, and A. Eckardt, Floquet engineering of optical solenoids and quantized charge pumping along tailored paths in two-dimensional Chern insulators, Phys. Rev. Lett. 120, 243602 (2018).
  50. A. J. E. Kreil, H. Y. Musiienko-Shmarova, S. Eggert, A. A. Serga, B. Hillebrands, D. A. Bozhko, A. Pomyalov, and V. S. L’vov, Tunable space-time crystal in room-temperature magnetodielectrics, Phys. Rev. B 100, 020406(R) (2019).
  51. J. H. V. Nguyen, M. C. Tsatsos, D. Luo, A. U. J. Lode, G. D. Telles, V. S. Bagnato, and R. G. Hulet, Parametric excitation of a Bose-Einstein condensate: From Faraday waves to granulation, Phys. Rev. X 9, 011052 (2019).
  52. Z. Fedorova (Cherpakova), C. Jörg, C. Dauer, F. Letscher, M. Fleischhauer, S. Eggert, S. Linden, and G. von Freymann, Limits of topological protection under local periodic driving, Light Sci. Appl. 8, 63 (2019).
  53. T. Wang, S. Hu, S. Eggert, M. Fleischhauer, A. Pelster, and X.-F. Zhang, Floquet-induced superfluidity with periodically modulated interactions of two-species hardcore bosons in a one-dimensional optical lattice, Phys. Rev. Res. 2, 013275 (2020).
  54. S. Fazzini, P. Chudzinski, C. Dauer, I. Schneider, and S. Eggert, Nonequilibrium Floquet steady states of time-periodic driven Luttinger liquids, Phys. Rev. Lett. 126, 243401 (2021).
  55. Simon B. Jäger, Jan Mathis Giesen, Imke Schneider, and Sebastian Eggert, Dissipative dicke time crystals: An atom’s point of view, Phys. Rev. A 110, L010202 (2024).
  56. Z. Fedorova, C. Dauer, A. Sidorenko, S. Eggert, J. Kroha, and S. Linden, Dissipation engineered directional filter for quantum ratchets, Phys. Rev. Res. 3, 013260 (2021).
  57. E. Wamba, A. Pelster, and J. R. Anglin, Mapping as a probe for heating suppression in periodically driven quantum many-body systems, arXiv:2108.07171.
  58. D. Thuberg, S. A. Reyes, and S. Eggert, Quantum resonance catastrophe for conductance through a periodically driven barrier, Phys. Rev. B 93, 180301(R) (2016).
  59. S. A. Reyes, D. Thuberg, D. Pérez, C. Dauer, and S. Eggert, Transport through an AC-driven impurity: Fano interference and bound states in the continuum, New J. Phys. 19, 043029 (2017).
  60. D. Thuberg, E. Muñoz, S. Eggert, and S. A. Reyes, Perfect spin filter by periodic drive of a ferromagnetic quantum barrier, Phys. Rev. Lett. 119, 267701 (2017).
  61. F. Hübner, C. Dauer, S. Eggert, C. Kollath, and A. Sheikhan, Floquet-engineered pair and single particle filter in the Fermi Hubbard model, Phys. Rev. A 106, 043303 (2022).
  62. F. Hübner, C. Dauer, S. Eggert, C. Kollath, and A. Sheikhan, Momentum-resolved Floquet-engineered pair and single-particle filter in the Fermi-Hubbard model, Phys. Rev. A 108, 023307 (2023).
  63. K. Huang and C. N. Yang, Quantum-mechanical many-body problem with hard-sphere interaction, Phys. Rev. 105, 767 (1957).
  64. R. Stock, A. Silberfarb, E. L. Bolda, and I. H. Deutsch, Generalized pseudopotentials for higher partial wave scattering, Phys. Rev. Lett. 94, 023202 (2005).
  65. H. Friedrich, Scattering Theory (Springer, Berlin, 2015).
  66. C. Brezinski, History of Continnued Fractions and Padé Approximations (Springer, Berlin, 1991).
  67. C. Simmendinger, A. Wunderlin, and A. Pelster, Analytical approach for the Floquet theory of delay differential equations, Phys. Rev. E 59, 5344 (1999).
  68. D. Martinez, Floquet theory and continued fractions for harmonically driven systems, Ph.D. thesis, The University of Texas, Austin, 2003, http://hdl.handle.net/2152/756.
  69. H. Friedrich and D. Wintgen, Physical realization of bound states in the continuum, Phys. Rev. A 31, 3964 (1985).
  70. H. Friedrich and D. Wintgen, Interfering resonances and bound states in the continuum, Phys. Rev. A 32, 3231 (1985).
  71. For the scalar product time averaging and space integration are used, so different Fourier components n≠n′ are orthogonal.

  72. Christoph Dauer, Resonances in interacting Floquet systems and dynamic transport phenomena, Doctoral thesis, University of Kaiserslautern, 2022, 10.26204/KLUEDO/8782.
  73. A. M. Ishkhanyan, Exact solution of the Schrödinger equation for the inverse square root potential v0/x, Europhys. Lett. 112, 10006 (2015).
  74. G. Zürn, T. Lompe, A. N. Wenz, S. Jochim, P. S. Julienne, and J. M. Hutson, Precise characterization of Li6 Feshbach resonances using trap-sideband-resolved rf spectroscopy of weakly bound molecules, Phys. Rev. Lett. 110, 135301 (2013).

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