# Observation of the density dependence of the closed-channel fraction of a $^6$Li superfluid

## TL;DR

This study measures the closed-channel fraction in a $^6$Li superfluid across the BCS-BEC crossover, revealing its density dependence and agreement with many-body theories, thus providing insights into superfluid pairing physics.

## Contribution

It demonstrates the density dependence of the closed-channel fraction as a probe for many-body effects in a superfluid, with quantitative measurements across the BCS-BEC crossover.

## Key findings

- $Z_{cc}$ scales as $T_F^{1/2}$ at unitarity.
- $Z_{cc}$ increases rapidly into the BCS regime.
- Measurements agree with two-channel pairing fluctuation theory.

## Abstract

Atomic Fermi gases provide an ideal platform for studying the pairing and superfluid physics, using a Feshbach resonance between closed channel molecular states and open channel scattering states. Of particular interest is the strongly interacting regime. We show that the closed-channel fraction $Z_{cc}$ provides an effective probe for the important many-body interacting effects, especially through its density dependence, which is absent from two-body theoretical predictions. Here we measure $Z_{cc}$ as a function of interaction strength and the Fermi temperature $T_\text{F}$ in a trapped $^6$Li superfluid throughout the entire BCS--BEC crossover, in quantitative agreement with theory when important thermal contributions outside the superfluid core are taken into account. Away from the deep BEC regime, the fraction $Z_{cc}$ is sensitive to $T_\text{F}$. In particular, our data show $Z_{cc} \propto T_\text{F}^{\alpha}$ with $\alpha=1/2$ at unitarity, in quantitative agreement with calculations of a two-channel pairing fluctuation theory, and $\alpha$ increases rapidly into the BCS regime, reflecting many-body interaction effects as predicted.