  We analyze the evolution of two-band superfluidity from the weak coupling
Bardeen-Cooper-Schrieffer (BCS) to the strong coupling Bose-Einstein
condensation (BEC) limit. When the interband interaction is tuned from negative
to positive values, a quantum phase transition occurs from a 0-phase to a
$\pi$-phase state, depending on the relative phase of two order parameters.
Furthermore, population imbalances between the two bands can be created by
tuning the intraband or interband interactions. We also find two undamped low
energy collective excitations corresponding to in-phase and out-of-phase modes.
Lastly, we derive the coupled Ginzburg-Landau equations, and show that they
reduce to coupled Gross-Pitaevskii equations for two types of bosons in the BEC
limit.
