Collective excitations of a trapped degenerate Fermi gas

TL;DR

This paper analyzes the small-amplitude collective excitations of a trapped degenerate Fermi gas, deriving dispersion relations in different regimes and geometries, and comparing Fermi and Bose vapour oscillation modes.

Contribution

It provides a new analytical dispersion law for Fermi gas excitations in a harmonic trap and explores both collisional and collisionless regimes with variational methods.

Findings

Derived dispersion law for collisional regime in spherical traps

Analyzed low-energy excitations in axially symmetric traps

Compared oscillation modes of Fermi and Bose vapours

Abstract

We evaluate the small-amplitude excitations of a spin-polarized vapour of Fermi atoms confined inside a harmonic trap. The dispersion law $\omega=\omega_{f}[l+4n(n+l+2)/3]^{1/2}$ is obtained for the vapour in the collisional regime inside a spherical trap of frequency $\omega_{f}$, with $n$ the number of radial nodes and $l$ the orbital angular momentum. The low-energy excitations are also treated in the case of an axially symmetric harmonic confinement. The collisionless regime is discussed with main reference to a Landau-Boltzmann equation for the Wigner distribution function: this equation is solved within a variational approach allowing an account for non-linearities. A comparative discussion of the eigenmodes of oscillation for confined Fermi and Bose vapours is presented in an Appendix.