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