Collective oscillations of an interacting trapped Fermi gas

TL;DR

This paper investigates how two-body interactions influence low-frequency collective oscillations in a trapped Fermi gas, analyzing the transition from collisionless to hydrodynamic regimes and the damping of spin dipole modes.

Contribution

It provides a mean field calculation of collective frequencies in the collisionless regime and discusses the damping of spin dipole modes during the transition to hydrodynamics.

Findings

Mean field effects modify collective oscillation frequencies.

Spin dipole mode becomes overdamped in the hydrodynamic regime.

Relaxation time varies with temperature and Fermi statistics.

Abstract

We calculate the effects of two-body interactions on the low frequency oscillations of a normal Fermi gas confined in a harmonic trap. The mean field contribution to the collective frequencies is evaluated in the collisionless regime using a sum rule approach. We also discuss the transition between the collisionless and hydrodynamic regime with special emphasis to the spin dipole mode in which two atomic clouds occupying different spin states oscillate in opposite phase. The spin dipole mode is predicted to be overdamped in the hydrodynamic regime. The relaxation time is calculated as a function of temperature and the effects of Fermi statistics are explicitly pointed out.