By solving the Bogoliubov -- de Gennes equations at zero temperature, westudy the effects of a one-dimensional optical lattice on the behavior of asuperfluid Fermi gas at unitarity. We show that, due to the lattice, at lowdensities the gas becomes highly compressible and the effective mass is large,with a consequent significant reduction of the sound velocity. We discuss therole played by the lattice in the formation of molecules and the emergence oftwo-dimensional effects in the equation of state. Predictions for the densityprofiles and for the frequency of the collective oscillations in the presenceof harmonic trapping are also given.
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