Evolution of Two-Band Superfluidity from Weak to Strong Coupling

Abstract We analyze the evolution of two-band superfluidity from the weak to the strong coupling (Bardeen–Cooper–Schrieffer to Bose–Einstein condensation) limit. We find that population imbalances between the two bands can be created by tuning the intraband or interband (Josephson) interactions. In addition, when the Josephson interband interaction is tuned from negative to positive values, a quantum phase tran-sition occurs from a 0-phase to a π-phase state, depending on the relative phase of the two order parameters. We also find two undamped low energy collective excita-tions corresponding to in-phase phonon (Goldstone) and out-of-phase exciton (finite frequency) modes. Lastly, we derive the coupled Ginzburg–Landau equations, and show that they reduce to coupled Gross–Pitaevskii equations for two types of weakly interacting bosons (tightly bound fermions) in the BEC limit