  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.
