Determine the actual superfluid fraction in the cavity-coupled Fermi gas

Determine the actual superfluid fraction of the cavity-coupled two-component Fermi gas beyond the Leggett-type pairing diagnostic used to characterize spatial inhomogeneity.

Background

The paper introduces a Leggett-type fraction based on the spatial profile of the pairing gap, f_L^pair, as a diagnostic for pairing-field inhomogeneity. The authors explicitly caution that this quantity is not the exact superfluid fraction. They compare it with the conventional Leggett bound based on the fermionic density and show that the two quantities can differ, particularly in regimes where pairing is absent or strongly localized.

A rigorous determination of the superfluid fraction would require an observable or calculation that directly captures global phase stiffness or superfluid response, rather than relying on the pairing-field diagnostic. This remains unresolved within the mean-field analysis presented in the paper.