Equation of state and effective mass of the unitary Fermi gas in a 1D   periodic potential
  By solving the Bogoliubov -- de Gennes equations at zero temperature, we study the effects of a one-dimensional optical lattice on the behavior of a superfluid Fermi gas at unitarity. We show that, due to the lattice, at low densities the gas becomes highly compressible and the effective mass is large, with a consequent significant reduction of the sound velocity. We discuss the role played by the lattice in the formation of molecules and the emergence of two-dimensional effects in the equation of state. Predictions for the density profiles and for the frequency of the collective oscillations in the presence of harmonic trapping are also given. 
Gentaro Watanabe, Giuliano Orso, Franco Dalfovo, Lev P. Pitaevskii,   Sandro Stringari