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

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 at aBF = −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.

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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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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 Physics thanks 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. (2024). https://doi.org/10.1038/s41567-024-02541-w

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