Superfluid Fermi gases in an optical lattice with random defects

We investigate the superfluidity of Fermi gases in a deep annular optical lattice with random defects, focusing on discussion of the interplay between defects and Fermi atomic interaction along the BCS-BEC crossover. Within a hydrodynamic scheme and a two-mode approximation, we obtain an analytic expression of atomic density as a function of the defects and the Fermi atomic interaction along the BCS-BEC crossover for supporting a superfluid flow. The analytical results are confirmed by direct numerical simulations. We find that there exists a critical atomic density along the BCS-BEC crossover which divided the system into two regimes: a normal regime with disorder induced damping and a superfluid regime with a plane wave travels coherently through the randomly distributed defects. Importantly, the defects and the atomic interaction are coupled, and the superfluidity of the system strongly depends on the properties of the defects and the atomic interaction. The system easily supports the superfluid states on the BCS side than that on the BEC side.