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arXiv:1502.02116 · Physical Review A

Landau damping in a mixture of Bose and Fermi superfluids

Huitao Shen, Wei Zheng

Published Sep 21, 2015• 11 citations
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Abstract

We study Landau damping in a Bose-Fermi superfluid mixture at finite temperatures. We find that at low temperatures, the Landau damping rate will be exponentially suppressed on both the BCS side and the BEC side of the Fermi superfluid. The momentum dependence of the damping rate is obtained, and it is quite different from the BCS side to the BEC side since the dominated low-energy excitations are different on the two sides. The relation between our result and the collective mode experiment in the recently realized Bose-Fermi superfluid mixture is also discussed.

DOI
10.1103/physreva.92.033620

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We study Landau damping in a Bose-Fermi superfluid mixture at finite temperatures. We find that at low temperatures, the Landau damping rate will be exponentially suppressed on both the BCS side and the BEC side of the Fermi superfluid. The momentum dependence of the damping rate is obtained, and it is quite different from the BCS side to the BEC side since the dominated low-energy excitations are different on the two sides. The relation between our result and the collective mode experiment in the recently realized Bose-Fermi superfluid mixture is also discussed.
In this Letter, we study the effect of quasiparticle interactions in a Bose-Fermi superfluid mixture. We consider the lifetime of a quasiparticle of the Bose superfluid due to its interaction with quasiparticles in the Fermi superfluid. We find that this damping rate, i.e., the inverse of the lifetime, has quite a different threshold behavior at the BCS and the BEC side of the Fermi superfluid. The damping rate is a constant near the threshold momentum in the BCS side, while it increases rapidly in the BEC side. This is because, in the BCS side, the decay process is restricted by the constraint that the fermion quasiparticle is located near the Fermi surface, while such a restriction does not exist in the BEC side where the damping process is dominated by bosonic quasiparticles of the Fermi superfluid. Our results are related to the collective mode experiment in the recently realized Bose-Fermi superfluid mixture.
By using a mean-field approximation which describes the coupled oscillations of condensate and noncondensate atoms in the collisionless regime, Landau damping in a dilute dipolar Bose–Fermi mixture in the BEC limit where Fermi superfluid is treated as tightly bounded molecules, is investigated. In the case of a uniform quasi-two-dimensional (2D) case, the results for the Landau damping due to the Bose–Fermi interaction are obtained at low and high temperatures. It is shown that at low temperatures, the Landau damping rate is exponentially suppressed. By increasing the strength of dipolar interaction, and the energy of boson quasiparticles, Landau damping is suppressed over a broader temperature range.
A mechanism is proposed to explain the puzzling damping of collective excitations, which was recently observed in the experiments of strongly interacting Fermi gases below the superfluid critical temperature on the fermionic (BCS) side of Feshbach resonance. Sound velocity, superfluid density, and damping rate are calculated with effective field theory. We find that a dominant damping process is due to the interaction between superfluid phonons and thermally excited fermionic quasiparticles, in contrast to the previously proposed pair-breaking mechanism. Results from our effective model are compared quantitatively with recent experimental findings, showing a good agreement.
We analyze a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC crossover. Using a quasiparticle random-phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC, respectively, we show that the single-particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, we can use these prominent effects to systematically probe the strongly interacting Fermi gas.
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.
Using the effective action formalism, we investigate collective excitations of a dilute mixture of a Bose gas and a two component Fermi gas when both bosons and fermions have undergone superfluid transitions. We show that there is a repulsion between Bogoliubov and Anderson modes, which has important implications including disappearance of boson superfluidity. We derive an analytic expression for the long-wavelength dispersion relation of the mixture at zero temperature and give a condition for the instability. We also numerically calculate the damping rate due to boson-fermion interaction at finite temperatures and show that the two modes are stable at sufficiently low temperatures.