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We first show that the many-body Hamiltonian governing the physicalproperties of an alkaline-earth Yb-173 Fermi gas across the recently-realizedorbital Feshbach resonance is exactly analogous to that of two-band s-wavesuperconductors with contact interactions: i.e., even though the free-particlebands have a tunable energy offset in between and are coupled by aJosephson-type attractive inter-band pair scattering, the intra-bandinteractions have exactly the same strength. We then introduce two intra-bandorder parameters within the BCS mean-field approximation, and investigate thecompetition between their in-phase and out-of-phase (i.e., the so-called\pi-phase) solutions in the entire BCS-BEC evolution at zero temperature.

Two-band superfluidity and intrinsic Josephson effect in alkaline-earth Fermi gases across an orbital Feshbach resonance