Capturing the Feshbach-induced Pairing Physics in the BEC-BCS Crossover

TL;DR

This paper models Feshbach resonance physics in a trapped Fermi gas to accurately reproduce the closed-channel fraction Z across the BEC-BCS crossover, aligning well with experimental data and resolving previous discrepancies.

Contribution

It introduces a two-channel model incorporating trap effects to match experimental Z measurements throughout the crossover, including the BCS regime.

Findings

Reproduces the experimental Z across the BEC-BCS crossover.

Confirms Z ∝ √T_F at unitarity with correct proportionality.

Aligns with recent measurements on the BCS side, resolving prior theory-experiment discrepancies.

Abstract

By including the effect of a trap with characteristic energy given by the Fermi temperature $T_F$ in a two-body two-channel model for Feshbach resonances, we reproduce the experimental closed-channel fraction $Z$ across the BEC-BCS crossover and into the BCS regime of a $^6$Li atomic Fermi gas. We obtain the expected behavior $Z \propto \sqrt{T_F}$ at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the $Z$ dependency on $T_F$ on the BCS side, where a significant discrepancy between experiments and theory has been repeatedly reported.