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Collective flow of fermionic impurities immersed in a Bose–Einstein condensate

Nature Physics volume20,pages1395–1400 (2024)Cite this article

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Abstract

Interacting mixtures of bosons and fermions are ubiquitous in nature. They form the backbone of the standard model of physics, provide a framework for understanding quantum materials and are of technological importance in helium dilution refrigerators. However, the description of their coupled thermodynamics and collective behaviour is challenging. Bose–Fermi mixtures of ultracold atoms provide a platform to investigate their properties in a highly controllable environment, where the species concentration and interaction strength can be tuned at will. Here we characterize the collective oscillations of spin-polarized fermionic impurities immersed in a Bose–Einstein condensate as a function of the interaction strength and temperature. For strong interactions, the Fermi gas perfectly mimics the superfluid hydrodynamic modes of the condensate, from low-energy quadrupole modes to high-order Faraday excitations. With an increasing number of bosonic thermal excitations, the dynamics of the impurities cross over from the collisionless to the hydrodynamic regime, reminiscent of the emergence of hydrodynamics in two-dimensional electron fluids.

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Fig. 1: Collective oscillations in a Bose–Fermi mixture.
Fig. 2: Evolution of Bose–Fermi collective modes across varying interaction strength.
Fig. 3: Fermionic mode frequencies versus interspecies interaction.
Fig. 4: Temperature dependence of the bosonic and fermionic collective modes ataBF = −400a0.
Fig. 5: Faraday waves in a Bose–Fermi mixture.

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Data availability

The data that support the plots within this paper and other findings of this study are available as source data files. All other data are available from the corresponding author upon reasonable request.

References

  1. Landau, L. D. The movement of electrons in the crystal lattice.Phys. Z. Sowjetunion3,644 (1933).

    Google Scholar

  2. Pekar, S. I. Autolocalization of the electron in an inertially polarizable dielectric medium.Zh. Eksp. Teor. Fiz.16,335 (1946).

    Google Scholar

  3. Ebner, C. & Edwards, D. The low temperature thermodynamic properties of superfluid solutions of3He in4He.Phys. Rep.2,77–154 (1971).

    Article ADS Google Scholar

  4. Schaefer, B.-J. & Wambach, J. The phase diagram of the quark–meson model.Nucl. Phys. A757,479–492 (2005).

    Article ADS Google Scholar

  5. Sidler, M. et al. Fermi polaron-polaritons in charge-tunable atomically thin semiconductors.Nat. Phys.13,255–261 (2017).

    Article Google Scholar

  6. Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiréheterostructure.Nature580,472–477 (2020).

    Article ADS Google Scholar

  7. Schwartz, I. et al. Electrically tunable Feshbach resonances in twisted bilayer semiconductors.Science374,336–340 (2021).

    Article ADS Google Scholar

  8. Hadzibabic, Z. et al. Two-species mixture of quantum degenerate Bose and Fermi gases.Phys. Rev. Lett.88,160401 (2002).

    Article ADS Google Scholar

  9. Stan, C. A., Zwierlein, M. W., Schunck, C. H., Raupach, S. M. F. & Ketterle, W. Observation of Feshbach resonances between two different atomic species.Phys. Rev. Lett.93,143001 (2004).

    Article ADS Google Scholar

  10. Inouye, S. et al. Observation of heteronuclear Feshbach resonances in a mixture of bosons and fermions.Phys. Rev. Lett.93,183201 (2004).

    Article ADS Google Scholar

  11. Silber, C. et al. Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases.Phys. Rev. Lett.95,170408 (2005).

    Article ADS Google Scholar

  12. Ospelkaus, S., Ospelkaus, C., Humbert, L., Sengstock, K. & Bongs, K. Tuning of heteronuclear interactions in a degenerate Fermi–Bose mixture.Phys. Rev. Lett.97,120403 (2006).

    Article ADS Google Scholar

  13. Zaccanti, M. et al. Control of the interaction in a Fermi–Bose mixture.Phys. Rev. A74,041605 (2006).

    Article ADS Google Scholar

  14. Shin, Y.-i, Schirotzek, A., Schunck, C. H. & Ketterle, W. Realization of a strongly interacting Bose–Fermi mixture from a two-component Fermi gas.Phys. Rev. Lett.101,070404 (2008).

    Article ADS Google Scholar

  15. Wu, C.-H., Santiago, I., Park, J. W., Ahmadi, P. & Zwierlein, M. W. Strongly interacting isotopic Bose–Fermi mixture immersed in a Fermi sea.Phys. Rev. A84,011601 (2011).

    Article ADS Google Scholar

  16. Park, J. W. et al. Quantum degenerate Bose–Fermi mixture of chemically different atomic species with widely tunable interactions.Phys. Rev. A85,051602 (2012).

    Article ADS Google Scholar

  17. Vaidya, V. D., Tiamsuphat, J., Rolston, S. L. & Porto, J. V. Degenerate Bose–Fermi mixtures of rubidium and ytterbium.Phys. Rev. A92,043604 (2015).

    Article ADS Google Scholar

  18. Trautmann, A. et al. Dipolar quantum mixtures of erbium and dysprosium atoms.Phys. Rev. Lett.121,213601 (2018).

    Article ADS Google Scholar

  19. Lous, R. S. et al. Probing the interface of a phase-separated state in a repulsive Bose–Fermi mixture.Phys. Rev. Lett.120,243403 (2018).

    Article ADS Google Scholar

  20. DeSalvo, B. J., Patel, K., Cai, G. & Chin, C. Observation of fermion-mediated interactions between bosonic atoms.Nature568,61–64 (2019).

    Article ADS Google Scholar

  21. Patel, K., Cai, G., Ando, H. & Chin, C. Sound propagation in a Bose–Fermi mixture: from weak to strong interactions.Phys. Rev. Lett.131,083003 (2023).

    Article ADS Google Scholar

  22. Viverit, L., Pethick, C. J. & Smith, H. Zero-temperature phase diagram of binary boson–fermion mixtures.Phys. Rev. A61,053605 (2000).

    Article ADS Google Scholar

  23. Büchler, H. P. & Blatter, G. Supersolid versus phase separation in atomic Bose–Fermi mixtures.Phys. Rev. Lett.91,130404 (2003).

    Article ADS Google Scholar

  24. Bertaina, G., Fratini, E., Giorgini, S. & Pieri, P. Quantum Monte Carlo study of a resonant Bose–Fermi mixture.Phys. Rev. Lett.110,115303 (2013).

    Article ADS Google Scholar

  25. Kinnunen, J. J. & Bruun, G. M. Induced interactions in a superfluid Bose–Fermi mixture.Phys. Rev. A91,041605 (2015).

    Article ADS Google Scholar

  26. Ludwig, D., Floerchinger, S., Moroz, S. & Wetterich, C. Quantum phase transition in Bose-Fermi mixtures.Phys. Rev. A84,033629 (2011).

    Article ADS Google Scholar

  27. Ferrier-Barbut, I. et al. A mixture of Bose and Fermi superfluids.Science345,1035–1038 (2014).

    Article ADS Google Scholar

  28. Delehaye, M. et al. Critical velocity and dissipation of an ultracold Bose–Fermi counterflow.Phys. Rev. Lett.115,265303 (2015).

    Article ADS Google Scholar

  29. Yao, X.-C. et al. Observation of coupled vortex lattices in a mass-imbalance Bose and Fermi superfluid mixture.Phys. Rev. Lett.117,145301 (2016).

    Article ADS Google Scholar

  30. Roy, R., Green, A., Bowler, R. & Gupta, S. Two-element mixture of Bose and Fermi superfluids.Phys. Rev. Lett.118,055301 (2017).

    Article ADS Google Scholar

  31. Wu, Y. P. et al. Coupled dipole oscillations of a mass-imbalanced Bose–Fermi superfluid mixture.Phys. Rev. B97,020506 (2018).

    Article ADS Google Scholar

  32. Ospelkaus, C., Ospelkaus, S., Sengstock, K. & Bongs, K. Interaction-driven dynamics of40K–87Rb fermion–boson gas mixtures in the large-particle-number limit.Phys. Rev. Lett.96,020401 (2006).

    Article ADS Google Scholar

  33. Huang, B. et al. Breathing mode of a Bose–Einstein condensate repulsively interacting with a fermionic reservoir.Phys. Rev. A99,041602 (2019).

    Article ADS Google Scholar

  34. Hu, M.-G. et al. Bose polarons in the strongly interacting regime.Phys. Rev. Lett.117,055301 (2016).

    Article ADS Google Scholar

  35. Yan, Z. Z., Ni, Y., Robens, C. & Zwierlein, M. W. Bose polarons near quantum criticality.Science368,190–194 (2020).

    Article ADS MathSciNet Google Scholar

  36. Landau, L. D. Two-fluid model of liquid helium II.J. Phys. USSR5,71–90 (1941).

    Google Scholar

  37. Chevy, F. Counterflow in a doubly superfluid mixture of bosons and fermions.Phys. Rev. A91,063606 (2015).

    Article ADS Google Scholar

  38. Seetharam, K., Shchadilova, Y., Grusdt, F., Zvonarev, M. B. & Demler, E. Dynamical quantum Cherenkov transition of fast impurities in quantum liquids.Phys. Rev. Lett.127,185302 (2021).

  39. Seetharam, K., Shchadilova, Y., Grusdt, F., Zvonarev, M. & Demler, E. Quantum Cherenkov transition of finite momentum Bose polarons. Preprint athttps://arxiv.org/abs/2109.12260(2021).

  40. Miyakawa, T., Suzuki, T. & Yabu, H. Sum-rule approach to collective oscillations of a boson–fermion mixed condensate of alkali-metal atoms.Phys. Rev. A62,063613–063611 (2000).

    Article ADS Google Scholar

  41. Yip, S. K. Collective modes in a dilute Bose–Fermi mixture.Phys. Rev. A64,023609 (2001).

    Article ADS Google Scholar

  42. Sogo, T., Miyakawa, T., Suzuki, T. & Yabu, H. Random-phase approximation study of collective excitations in the Bose–Fermi mixed condensate of alkali-metal gases.Phys. Rev. A66,136181–1361812 (2002).

    Article Google Scholar

  43. Liu, X. J. & Hu, H. Collisionless and hydrodynamic excitations of trapped boson–fermion mixtures.Phys. Rev. A67,023613 (2003).

    Article ADS Google Scholar

  44. Capuzzi, P., Minguzzi, A. & Tosi, M. P. Collisional oscillations of trapped boson–fermion mixtures in the approach to the collapse instability.Phys. Rev. A69,053615 (2004).

    Article ADS Google Scholar

  45. Imambekov, A. & Demler, E. Exactly solvable case of a one-dimensional Bose–Fermi mixture.Phys. Rev. A73,021602 (2006).

    Article ADS Google Scholar

  46. Banerjee, A. Dipole oscillations of a Bose–Fermi mixture: effect of unequal masses of Bose and Fermi particles.J. Phys. B42,235301 (2009).

  47. Van Schaeybroeck, B. & Lazarides, A. Trapped phase-segregated Bose–Fermi mixtures and their collective excitations.Phys. Rev. A79,033618 (2009).

    Article ADS Google Scholar

  48. Maruyama, T., Yamamoto, T., Nishimura, T. & Yabu, H. Deformation dependence of breathing oscillations in Bose–Fermi mixtures at zero temperature.J. Phys. B47,25–34 (2014).

    Article Google Scholar

  49. Asano, Y., Narushima, M., Watabe, S. & Nikuni, T. Collective excitations in Bose–Fermi mixtures.J. Low Temp. Phys.196,133–139 (2019).

    Article ADS Google Scholar

  50. Ono, Y., Hatsuda, R., Shiina, K., Mori, H. & Arahata, E. Three sound modes in a Bose–Fermi superfluid mixture at finite temperatures.J. Phys. Soc. Jpn88,034003 (2019).

    Article ADS Google Scholar

  51. Zhang, J. et al. Anomalous thermal diffusivity in underdoped YBa2Cu3O6+x.Proc. Natl Acad. Sci. USA114,5378–5383 (2017).

    Article ADS Google Scholar

  52. Gooth, J. et al. Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide.Nat. Commun.9,4093 (2018).

    Article ADS Google Scholar

  53. Jin, D. S., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Collective excitations of a Bose–Einstein condensate in a dilute gas.Phys. Rev. Lett.77,420–423 (1996).

    Article ADS Google Scholar

  54. Mewes, M. O. et al. Collective excitations of a Bose–Einstein condensate in a magnetic trap.Phys. Rev. Lett.77,988–991 (1996).

  55. Stamper-Kurn, D. M., Miesner, H. J., Inouye, S., Andrews, M. R. & Ketterle, W. Collisionless and hydrodynamic excitations of a Bose–Einstein condensate.Phys. Rev. Lett.81,500–503 (1998).

    Article ADS Google Scholar

  56. Gensemer, S. D. & Jin, D. S. Transition from collisionless to hydrodynamic behavior in an ultracold Fermi gas.Phys. Rev. Lett.87,173201 (2001).

    Article ADS Google Scholar

  57. O’Hara, K. M., Hemmer, S. L., Gehm, M. E., Granade, S. R. & Thomas, J. E. Observation of a strongly interacting degenerate Fermi gas of atoms.Science298,2179–2182 (2002).

    Article ADS Google Scholar

  58. Regal, C. A. & Jin, D. S. Measurement of positive and negative scattering lengths in a Fermi gas of atoms.Phys. Rev. Lett.90,230404 (2003).

  59. Bourdel, T. et al. Measurement of the interaction energy near a Feshbach resonance in a6Li Fermi gas.Phys. Rev. Lett.91,020402 (2003).

  60. Trenkwalder, A. et al. Hydrodynamic expansion of a strongly interacting Fermi–Fermi mixture.Phys. Rev. Lett.106,115304 (2011).

    Article ADS Google Scholar

  61. Tey, M. K. et al. Collective modes in a unitary Fermi gas across the superfluid phase transition.Phys. Rev. Lett.110,055303 (2013).

    Article ADS Google Scholar

  62. Ravensbergen, C. et al. Resonantly interacting Fermi–Fermi mixture of161Dy and40K.Phys. Rev. Lett.124,203402 (2020).

    Article ADS Google Scholar

  63. Ferlaino, F. et al. Dipolar oscillations in a quantum degenerate Fermi–Bose atomic mixture.J. Opt. B5,S3–S8 (2003).

    Article Google Scholar

  64. Fukuhara, T., Tsujimoto, T. & Takahashi, Y. Quadrupole oscillations in a quantum degenerate Bose–Fermi mixture.Appl. Phys. B96,271–274 (2009).

    Article ADS Google Scholar

  65. Kagan, M. Y. & Bianconi, A. Fermi–Bose mixtures and BCS–BEC crossover in high-Tcsuperconductors.Condens. Matter4,51 (2019).

  66. Stringari, S. Collective excitations of a trapped Bose-condensed gas.Phys. Rev. Lett.77,2360–2363 (1996).

    Article ADS Google Scholar

  67. Pethick, C. & Smith, H.Bose–Einstein Condensation in Dilute Gases(Cambridge Univ. Press, 2008).

  68. Castin, Y. & Dum, R. Bose–Einstein condensates in time dependent traps.Phys. Rev. Lett.77,5315–5319 (1996).

    Article ADS Google Scholar

  69. DeMarco, B., Bohn, J. L., Burke, J. P., Holland, M. & Jin, D. S. Measurement of p-wave threshold law using evaporatively cooled fermionic atoms.Phys. Rev. Lett.82,4208–4211 (1999).

  70. Dolgirev, P. E. et al. Accelerating analysis of Boltzmann equations using Gaussian mixture models: application to quantum Bose–Fermi mixtures. Preprint athttps://arxiv.org/abs/2304.09911(2022).

  71. Menotti, C., Pedri, P. & Stringari, S. Expansion of an interacting Fermi gas.Phys. Rev. Lett.89,250402 (2002).

    Article ADS Google Scholar

  72. Faraday, M. On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces.Phil. Trans. R. Soc. Lond.121,299–340 (1831).

    ADS Google Scholar

  73. Engels, P., Atherton, C. & Hoefer, M. A. Observation of Faraday waves in a Bose–Einstein condensate.Phys. Rev. Lett.98,095301 (2007).

  74. Groot, A.Excitations in Hydrodynamic Ultra-Cold Bose Gases.PhD thesis, Utrecht Univ. (2015).

  75. Nguyen, J. H. et al. Parametric excitation of a Bose–Einstein condensate: from Faraday waves to granulation.Phys. Rev. X9,11052 (2019).

    Google Scholar

  76. Heiselberg, H., Pethick, C. J., Smith, H. & Viverit, L. Influence of induced interactions on the superfluid transition in dilute Fermi gases.Phys. Rev. Lett.85,2418–2421 (2000).

  77. Bijlsma, M. J., Heringa, B. A. & Stoof, H. T. Phonon exchange in dilute Fermi–Bose mixtures: tailoring the Fermi–Fermi interaction.Phys. Rev. A61,053601 (2000).

    Article ADS Google Scholar

  78. Efremov, D. V. & Viverit, L. p-wave Cooper pairing of fermions in mixtures of dilute Fermi and Bose gases.Phys. Rev. B65,134519 (2002).

    Article ADS Google Scholar

  79. Matera, F. Fermion pairing in Bose–Fermi mixtures.Phys. Rev. A68,043624 (2003).

    Article ADS Google Scholar

  80. Kinnunen, J. J., Wu, Z. & Bruun, G. M. Induced p-wave pairing in Bose-Fermi mixtures.Phys. Rev. Lett.121,253402 (2018).

    Article ADS Google Scholar

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Acknowledgements

We acknowledge E. Wolf for helpful discussions. We acknowledge support from NSF, AFOSR through a MURI on Ultracold Molecules, the Vannevar Bush Faculty Fellowship. Z.Z.Y. and A.C. acknowledge support from the NSF GRFP. C.R. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG) Germany research fellowship (421987027). K.S. acknowledges funding from NSF EAGER-QAC-QCH award no. 2037687. P.D. and E.D. were supported by ARO grant number W911NF-20-1-0163, SNSF project 200021-212899. E.D. acknowledges support from the Swiss National Science Foundation under Division II.

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Authors and Affiliations

  1. MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Zoe Z. Yan, Yiqi Ni, Alexander Chuang, Carsten Robens & Martin Zwierlein

  2. Physics Department and James Franck Institute, University of Chicago, Chicago, IL, USA

    Zoe Z. Yan

  3. Department of Physics, Harvard University, Cambridge, MA, USA

    Pavel E. Dolgirev & Kushal Seetharam

  4. Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland

    Pavel E. Dolgirev & Eugene Demler

  5. Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Kushal Seetharam

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  1. Zoe Z. Yan
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Contributions

M.Z. and E.D. conceived of the experiments and supervised the study. Z.Z.Y., Y.N., A.C. and C.R. performed the experiments and the data analysis. Z.Z.Y., C.R. and M.Z. performed the numerical calculations for the Boltzmann equations without collisions and the mean-field scaling ansatz. P.E.D., K.S. and E.D. performed the theoretical and numerical calculations on the high-temperature Boltzmann equations. All authors contributed to the paper and the interpretation of data.

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Correspondence to Martin Zwierlein.

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Nature Physicsthanks Xing-Can Yao and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–8 and Discussion.

Source data

Source Data Fig. 1

Widths versus frequency for non-interacting Bose–Fermi mixture.

Source Data Fig. 2

Widths versus frequency for Bose–Fermi mixture across different interaction strengths, and their error bars.

Source Data Fig. 3

Files for the colour plots of the fermionic response versus frequency and scattering length, and the theoretical curves as described in the figure caption.

Source Data Fig. 4

Bose and Fermi widths versus frequency.

Source Data Fig. 5

Data for the Faraday mode plots.

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Yan, Z.Z., Ni, Y., Chuang, A.et al.Collective flow of fermionic impurities immersed in a Bose–Einstein condensate. Nat. Phys.20,1395–1400 (2024). https://doi.org/10.1038/s41567-024-02541-w

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