Virial expansion for a strongly correlated Fermi gas

TL;DR

This paper uses a high temperature virial expansion to study the thermodynamics of strongly correlated Fermi gases near the BEC-BCS crossover, providing new methods to determine expansion coefficients and calculating the third order coefficient at finite temperatures.

Contribution

It introduces a practical approach to determine virial expansion coefficients for trapped and homogeneous Fermi gases and calculates the third order coefficient at finite temperatures.

Findings

Third order coefficient at resonance is approximately -0.291 in free space.

Results agree with recent experiments on $^{6}$Li atoms.

Comparison with Monte Carlo simulations validates the approach.

Abstract

Using a high temperature virial expansion, we present a controllable study of the thermodynamics of strongly correlated Fermi gases near the BEC-BCS crossover region. We propose a practical way to determine the expansion coefficients for both harmonically trapped and homogeneous cases, and calculate the third order coefficient $b_{3}(T)$ at finite temperatures $T$. At resonance, a $T$-independent coefficient $b_{3,\infty}^{\hom}\approx-0.29095295$ is determined in free space. These results are compared with a recent thermodynamic measurement of $^{6}$Li atoms, at temperatures below the degeneracy temperature, and with Monte Carlo simulations.