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Chinese Physics Letters

Dipole Oscillation in a Bose–Fermi Superfluid Mixture of 41 K and 6 Li

Ren Zhang

Published Apr 1, 2018• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/35/4/046701

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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.
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 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 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.
Abstract Motivated by the first experimental realization by the Ecole Normale Supérieure (ENS) group of a mixture of a Bose–Einstein condensate with a Fermi superfluid continuously changing from a Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC) (Ferrier-Barbut et al 2014 Science 345 1035 ), we analytically study the dipole modes of the superfluid Bose–Fermi mixture in the BCS-BEC crossover. The analytical approach can explicitly reveal relationships between the frequencies of the dipole modes and the microscopic properties of the novel system. We start from coupled hydrodynamic equations, where the equation of state for the Fermi superfluid in the crossover is an analytical fitting formula based on experimental data, and by using a scaling approach we analytically study eigenfrequencies of the dipole modes for the coupled system in the ENS experimental parameters. Without the boson–fermion interaction in the equilibrium density profiles, our theoretical results can be reduced to the mean-field model and is consistent with the experimental data. However, by further taking into account the boson–fermion interaction numerically and analytically, we find that the results disagree with the experiment, especially in the parameter regime where the boson interaction is smaller than the boson–fermion interaction.
This thesis theoretically deals with collective modes in the normal phase of a Bose-Fermi mixture composed of single-species bosons and single-species fermions.The mixture is experimentally established as an ultracold atomic gas.While the community studies the mixture including a superfluid phase, relevant to Bose-Einstein condensation of bosons and Cooper paring of fermions, dynamical behaviors in the normal phase have been not fully understood so that we are interested in.We consider the mixture in both spatially uniform and harmonically trapped systems with the Boltzmann equation at finite temperatures.We perform the analysis under the assumption that the physical quantities are near to equilibrium.After the linerization, we apply the moment method to the equation, obtaining a closed set of coupled equations to describe sound or oscillation.The collisional property of the system characterizes the collective modes in the sense of the hydrodynamic regime, collisionless regime, and transition between these regimes.In the uniform system, we investigate sound mode and the dynamic density structure factor.With decreasing temperature, we find that the sound velocity deviates from that of the hydrodynamic mode.Even at a temperature much lower than the Fermi temperature, the sound velocity does not reach the collisionless limit analogous to the zero sound in a Fermi system.However, we show the existence of a long-lived sound at a low temperature as distinct from the first and zero sounds.Nature of the long-lived sound seems to be originated by Pauli blocking of fermions; this statistical effect makes the interspecies collision suppress in the Bose-Fermi mixture.In the trapped system, we mainly study dipole oscillation.We consistently define the relaxation time originated by the interspecies scattering.We find that two oscillating modes in the collisionless regime have distinct fates in the hydrodynamic regime; one collisionless mode shows a crossover to a hydrodynamic in-phase mode, and the other collisionless mode shows a transition to two purely-damped modes.We show the time evolution of the three types of hydrodynamic modes with suitable initial conditions.We discuss temperature dependence of the dipole modes.We observe that the relaxation time dominates the dependence compared to the mean-field contribution.We also observe the nonmonotonic behavior of the relaxation time when Pauli blocking of fermions is not negligible.i List of Figures 1.1 Two schematic images of collisions with a period of oscillation . . . . . . . . . . . . . . . . 1 1.2 Measurement of the zero sound in pure liquid 3 He . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Transition between the first sound and the zero sound in a two-component Fermi gas . . . 3 1.4 Dipole oscillations of the two-component gas of 40 K . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Frequencies of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . . . 4 1.6 Damping times of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . 5 1.7 Dipole oscillations of the mixture of 87 Rb and 40 K in the hydrodynamic regime . . . . . . .6 1.8 Dipole oscillations of the mixture of 87 Rb and 40 K in the deeper hydrodynamic regime . . .6 1.9 Dipole oscillations of the mixture of 87 Rb and 40 K in the collisionless regime . . . . . . . .7 2.1 Results obtained by solving the coupled moment equations for sound mode . . . . . . . . .26 3.1 Time evolution of the center-of-mass positions and velocity fields . . . . . . . . . . . . . .39 3.2 Dipole modes as a function of the relaxation time with N B = N F . . . . . . . . . . . . . . .40 3.3 Dipole modes as a function of the relaxation time with N B /N F = 0.2 . . . . . . . . . . . . .41 3.4 Ratio of the displacement of the center of mass to the velocity field as a function of the relaxation time . . . . . . . . . . . . . . . . . . .
Collective oscillations of superfluid mixtures of ultracold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation models and ordinary differential equation models for the dynamics. An application to the recent experiment with fermionic 6Li^{6}\mathrm{Li}6Li and bosonic 7Li^{7}\mathrm{Li}7Li atoms, which approximately have the same masses, is discussed.