Two-component Fermi gas with a resonant interaction

TL;DR

This paper analyzes a two-component Fermi gas with resonant interactions, identifying the key energy scale for universality and calculating the energy of the universal state relevant to current experiments.

Contribution

It introduces a critical energy scale for the universal behavior of resonantly interacting Fermi gases and distinguishes this state from molecular gases.

Findings

Universal state occurs when $E_g \, \gg \, \epsilon_F$

Calculated energy of the universal state

Relevance to experiments with $^{6}$Li and $^{40}$K

Abstract

We consider a two-component Fermi gas interacting via a Feshbach molecular state. It is shown that an important energy scale is $E_g=g^4m^3/(64\pi^2)$ where $g$ is the Feshbach coupling constant and $m$ the mass of the particles. Only when $E_g\gg \epsilon_{\rm F}$ where $\epsilon_{\rm F}$ is the Fermi energy can the gas be expected to enter a universal state in the unitarity limit on the atomic side of the resonance where there are no molecules present. The universal state is distinct from the molecular gas state on the other side of the resonance. We furthermore calculate the energy of the gas for this universal state and our results are related to current experiments on $^{6}$Li and $^{40}$K.