Collective modes of three- and two-dimensional trapped Fermi gases in the normal phase

M Urban,T Enss,D Davesne,S Chiacchiera,P-A Pantel

doi:10.1088/1742-6596/497/1/012028

Abstract

We study the transition from the hydrodynamic to the collisionless regime in collective modes of three- and two-dimensional Fermi gases by using the semiclassical Boltzmann equation. We use direct numerical simulations as well as the method of phase-space moments to solve the Boltzmann equation and show that the restriction to second-order moments is not accurate enough. By including higher-order moments, we can successfully describe the hydrodynamic to collisionless transition observed in the quadrupole mode in three-dimensional Fermi gases and the frequency shift and damping of the sloshing mode due to the anharmonic shape of the experimental trap potential. In the case of two-dimensional Fermi gases, however, the strong damping of the quadrupole mode observed in a recent experiment remains unexplained.

Highlights

By studying collective motion in ultracold atoms, one can address some questions that cannot be answered from the measurement of static quantities alone
In the anisotropic expansion of normal-fluid Fermi gases in the unitary limit it was observed that the viscosity of these systems is surprisingly low [4]
Summary We have studied various aspects of collective modes of trapped Fermi gases in the normalfluid phase

Summary

Introduction

Concentrating here on the case of unpolarized Fermi gases, let us mention the superfluid-normal phase transition, which can be seen most convincingly by looking at vortices in rotating traps [1]. It shows up, somewhat less impressively, in the radial quadrupole mode [2, 3]. While in the usual three-dimensional traps the axial breathing mode behaves always hydrodynamically because of its low frequency, the frequency and damping rate of the radial breathing mode are sensitive to the transition from the hydrodynamic to the collisionless regime. The damping is maximal in the intermediate regime between the two limits

Formalism

Importance of higher-order moments