Collective modes of trapped Fermi gases with in-medium interaction

TL;DR

This paper investigates how in-medium interactions, affected by Pauli blocking, influence the collective oscillation modes of trapped Fermi gases, providing improved theoretical explanations for experimental observations near Feshbach resonances.

Contribution

It introduces a calculation of the in-medium $T$ matrix in ladder approximation and applies it to explain collective mode behaviors in trapped Fermi gases.

Findings

In-medium interactions cause an upward shift in quadrupole mode frequency.

Including mean field effects improves agreement with experimental data.

In-medium cross section use worsens the match with observed damping rates.

Abstract

Due to Pauli blocking of intermediate states, the scattering matrix (or $T$ matrix) of two fermionic atoms in a Fermi gas becomes different from that of two atoms in free space. This effect becomes particularly important near a Feshbach resonance, where the interaction in free space is very strong but becomes effectively suppressed in the medium. We calculate the in-medium $T$ matrix in ladder approximation and study its effects on the properties of collective modes of a trapped gas in the normal-fluid phase. We introduce the in-medium interaction on both sides of the Boltzmann equation, namely in the calculation of the mean field and in the calculation of the collision rate. This allows us to explain the observed upward shift of the frequency of the quadrupole mode in the collisionless regime. By including the mean field, we also improve considerably the agreement with the measured temperature dependence of frequency and damping rate of the scissors mode, whereas the use of the in-medium cross section deteriorates the description, in agreement with previous work.