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

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 $\alpha =1\mathrm{/}2$ 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.