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arXiv:1705.04496 · Physical review. B./Physical review. B

Coupled dipole oscillations of a mass-imbalanced Bose-Fermi superfluid mixture

Yu-Ping Wu, Xing-Can Yao, Xiangpei Liu, Xiaoqiong Wang, Yu‐Xuan Wang, Hao-Ze Chen, Youjin Deng, Yu-Ao Chen, Jian-Wei Pan

Published Jan 22, 2018• 30 citations
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Abstract

Recent experimental realizations of superfluid mixtures of Bose and Fermi quantum gases provide a unique platform for exploring diverse superfluid phenomena. We study dipole oscillations of a double superfluid in a cigar-shaped optical dipole trap, consisting of $^{41}\mathrm{K}$ and $^{6}\mathrm{Li}$ atoms with a large mass imbalance, where the oscillations of the bosonic and fermionic components are coupled via the Bose-Fermi interaction. In our high-precision measurements, the frequencies of both components are observed to be shifted from the single-species ones, and exhibit unusual features. The frequency shifts of the $^{41}\mathrm{K}$ component are upward (downward) in the radial (axial) direction, whereas the $^{6}\mathrm{Li}$ component has downshifted frequencies in both directions. Most strikingly, as the interaction strength is varied, the frequency shifts display a resonantlike behavior in both directions, for both species, and around a similar location at the BCS side of the fermionic superfluid. These rich phenomena challenge the theoretical understanding of superfluids.

DOI
10.1103/physrevb.97.020506

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Recent experimental realizations of superfluid mixtures of Bose and Fermi quantum gases provide a unique platform for exploring diverse superfluid phenomena. We study dipole oscillations of a double superfluid in a cigar-shaped optical dipole trap, consisting of 41K^{41}\mathrm{K}41K and 6Li^{6}\mathrm{Li}6Li atoms with a large mass imbalance, where the oscillations of the bosonic and fermionic components are coupled via the Bose-Fermi interaction. In our high-precision measurements, the frequencies of both components are observed to be shifted from the single-species ones, and exhibit unusual features. The frequency shifts of the 41K^{41}\mathrm{K}41K component are upward (downward) in the radial (axial) direction, whereas the 6Li^{6}\mathrm{Li}6Li component has downshifted frequencies in both directions. Most strikingly, as the interaction strength is varied, the frequency shifts display a resonantlike behavior in both directions, for both species, and around a similar location at the BCS side of the fermionic superfluid. These rich phenomena challenge the theoretical understanding of superfluids.
We present a study for the collective dipole oscillations of a mixture of Bose and Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in the ENS experimental setup (Ferrier-Barbut et al 2014 Science 345 1035). The dynamics of the double superfluidity is described by coupled time-dependent order-parameter equations, which are Gross–Pitaevskii equations for the Bose superfluid, coupled to the order-parameter equation including the equation of state fitting from the experimental data for the Fermi superfluid in the BCS–BEC crossover. The numerical simulations show that due to the boson–fermion interaction, the frequencies of the dipole oscillations of the Bose and Fermi superfluids are both downshifted and the frequency shifts increase monotonically from the BCS side to BEC side, which are in agreement with the experiment. We further study the dependencies of the frequency shifts on the oscillation amplitudes and the nonlinear effects, in which the Bose and Fermi superfliuds show different features. The frequency shifts of the Bose superfluid increase linearly as the oscillation amplitudes increase, while the frequency shifts of the Fermi superfluid show a quadratical increase. It is found that the intrinsic dipole oscillations of the Bose (Fermi) superfluid can be triggered by only boosting the Fermi (Bose) superfluid.
Quantized vortices play an essential role in diverse superfluid phenomena. In a Bose-Fermi superfluid mixture, especially of two mass-imbalance species, such macroscopic quantum phenomena are particularly rich due to the interplay between the Bose and Fermi superfluidity. However, generating a Bose-Fermi two-species superfluid, producing coupled vortex lattices within, and further probing interspecies interaction effects remain challenging. Here, we experimentally realize a two-species superfluid with dilute gases of lithium-6 and potassium-41, having a mass ratio of about seven. By rotating the superfluid mixture, we simultaneously produce coupled vortex lattices of the two species and thus present a definitive visual evidence for the double superfluidity. Moreover, we report several unconventional behaviors, due to the Bose-Fermi interaction, on the formation and decay of two-species vortices.
We study the relation between the bosonic frequency shift of a dipole oscillation and the fermionic compressibility in a Bose–Fermi superfluid mixture. Our results show that the Λ transition occurs in such a system, which interprets the perplexing phenomenon observed in the recent experiment [arXiv:1705.04496]. In that experiment, the frequency shift of the bosonic gas was measured with different fermion-fermion s-wave scattering lengths a f . The most striking feature of their measurement is that the frequency shift shows a puzzling non-monotonic behavior around 1/ k F a f ≃ −0.2 with k F being the Fermi momentum. In the present work, the relation between the bosonic frequency shift and the compressibility of the Fermi gas is revealed by means of the equation of state of the superfluid mixture. Making use of the relation, we find that the compressibility of Fermi gas shows a Λ-like shape around 1/ k F a f ≃ −0.2. We would like to stress that no free parameter is used in our calculation and our results can be further testified in a future experiment.
Superconductivity and superfluidity of fermionic and bosonic systems are remarkable many-body quantum phenomena. In liquid helium and dilute gases, Bose and Fermi superfluidity has been observed separately, but producing a mixture in which both the fermionic and the bosonic components are superfluid is challenging. Here we report on the observation of such a mixture with dilute gases of two lithium isotopes, lithium-6 and lithium-7. We probe the collective dynamics of this system by exciting center-of-mass oscillations that exhibit extremely low damping below a certain critical velocity. Using high-precision spectroscopy of these modes, we observe coherent energy exchange and measure the coupling between the two superfluids. Our observations can be captured theoretically using a sum-rule approach that we interpret in terms of two coupled oscillators.
We report on the production of a stable mixture of bosonic and fermionic superfluids composed of the elements ^{174}Yb and ^{6}Li which feature a strong mismatch in mass and distinct electronic properties. We demonstrate elastic coupling between the superfluids by observing the shift in dipole oscillation frequency of the bosonic component due to the presence of the fermions. The measured magnitude of the shift is consistent with a mean-field model and its direction determines the previously unknown sign of the interspecies scattering length to be positive. We also observe the exchange of angular momentum between the superfluids from the excitation of a scissors mode in the bosonic component through interspecies interactions. We explain this observation using an analytical model based on superfluid hydrodynamics.
We investigate the homogeneous superfluid mixtures of a Bardeen-Cooper-Schrieffer (BCS) superfluid originating from pairing two-species fermionic atoms and superfluidity stemming from condensation of bosonic atoms. By integrating out the freedoms associated with the BCS superfluid, we derive the fermion-mediated interactions between bosons, which is attractive and can be tuned from long range in the BCS region to short range in the region of Bose-Einstein condensation of molecular dimers. By analyzing the Bogoliubov spectrum and the damping rate of bosonic superfluid, we map out the phase diagram spanned by the boson-fermion mass ratio and the boson-fermion coupling strength, which consists of a phase separation region and two phase-mixing regions with and without Landau damping. The three different phases can coexist at a tricritical point, which moves toward a low boson-fermion mass ratio and a high boson-fermion scattering length as the fermion-fermion interaction strength is tuned up on the BCS side.