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In a minimal 2-band model with attractive interactions between fermions, wecalculate the gap to single and two-particle excitations, the band-dependentspectral functions, the superfluid density and compressibility using quantumMonte Carlo (QMC) methods. We find Fermi and Bose insulating phases withsignatures of incipient pairing evident in the single-particle spectralfunctions, and a superconducting state with three different spectral functions:(i) both bands show "BCS" behavior in which the minimum gap locus occurs on aclosed contour on the underlying Fermi surface; (ii) both bands show "BEC"behavior in which the minimum gap occurs at a point; and (iii) band selectivespectral characteristics, in which one band shows "BCS" while the other shows"BEC" behavior. At large interactions, we find a Mott phase of rung bosons inwhich the filling is one boson for every two sites, half the typical densityconstraint for Mott insulators.

Spectral functions across an Insulator to Superconductor Transition