Low-Lying Excitation Modes of Trapped Dipolar Fermi Gases: From Collisionless to Hydrodynamic Regime

TL;DR

This paper models the low-lying excitation modes of trapped dipolar Fermi gases across different regimes using kinetic equations, providing insights into their dynamical behavior relevant for current experiments.

Contribution

It introduces an approximate solution to the Boltzmann-Vlasov equation for dipolar Fermi gases, bridging collisionless and hydrodynamic regimes with a focus on excitation modes.

Findings

Determines frequencies and damping rates of excitation modes.

Provides a theoretical framework applicable to current experiments.

Analyzes the transition from collisionless to hydrodynamic behavior.

Abstract

By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time approximation for the collision integral. Then, we proceed by linearizing the equations of motion around the equilibrium in order to study both the frequencies and the damping of the low-lying excitation modes all the way from the collisionless to the hydrodynamic regime. Our theoretical results are expected to be relevant for understanding current experiments with trapped dipolar Fermi gases.