Population of closed-channel molecules in trapped Fermi gases with broad Feshbach resonances

TL;DR

This paper calculates the fraction of closed-channel molecules in trapped Fermi gases across various fields and temperatures, linking it to the pairing gap and validating results with experimental data.

Contribution

It introduces a parameter-free two-channel BCS-BEC crossover model to predict the closed-channel molecule fraction in Fermi gases.

Findings

Good quantitative agreement with low T $^6$Li measurements.

Provides predictions for temperature and Fermi momentum dependencies.

Establishes the closed-channel fraction as a measure of the pairing gap.

Abstract

We compute the fraction of closed-channel molecules in trapped atomic Fermi gases, over the entire range of accessible fields and temperatures. We use a two-channel model of BCS--Bose-Einstein condensation (BEC) crossover theory at general temperature $T$, and show that this fraction provides a measure of the $T$ dependent pairing gap. Our calculations, containing no free parameters, are in good quantitative agreement with recent low $T$ measurements in $^6$Li. We present readily testable predictions for the dependencies of the closed-channel fraction on temperature and Fermi momentum.