Abstract
We study the phase diagram and the collective excitations of an attractive two-component Fermi gas on a double-layer optical lattice at zero temperature. Unlike the single layer case where one typically finds a smooth crossover from a weak pairing state to a strong one, here one uncovers a superfluid-insulator transition at half-filling. In addition, we investigate the collective mode of the system and identify an analogous excitonic mode in the system and compute its gap and effective mass. We propose a many-body wave function for the excitonic mode and show that it gives exactly the excitonic gap in the long wave length limit.
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