Thermodynamics of the two-component Fermi gas with unequal masses at unitarity

TL;DR

This paper investigates the thermodynamics of mass-imbalanced two-component Fermi gases at unitarity, revealing how mass ratio influences virial coefficients, polarization, and stability in trapped and homogeneous systems.

Contribution

It provides the first detailed analysis of high-temperature thermodynamics and polarization effects in mass-imbalanced Fermi gases at unitarity using virial expansion up to third order.

Findings

The third-order virial coefficient for two light and one heavy atom is negative.

The virial coefficient for two heavy and one light atom changes sign with mass ratio and diverges at Efimov threshold.

Equilibrium polarization is zero for equal masses and finite otherwise, favoring heavy particles.

Abstract

We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging s-wave scattering length $a_s$, i.e., with $1/a_s=0$. The high temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio $\kappa$ increases, and diverges when Efimov physics sets in at $\kappa=13.61$. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for $\kappa=1$, but finite for $\kappa \ne 1$ (with a majority of heavy particles). Compared to the equilibrium polarization of the non-interacting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations.