Two-band atomic superfluidity in the presence of an orbital Feshbach resonance

We study static superfluid properties of alkali-earth-like Fermi atomic systems in the presence of orbital Feshbach resonance. Using a two-band description of the ground state and excited state and a mean-field approximation of the intraband atomic pairing, we investigate the phase transitions and crossover between BCS and Bose-Einstein-condensate (BEC) superfluidity. At zero temperature, we find exact BCS analytical solutions for the mean-field gap equations and number equations. Using these exact solutions, we calculate various static properties, such as superfluid order parameters, chemical potentials, density variations, density profiles, correlation and coherence lengths, ground-state energy, and Tan's contact density across the entire BCS-BEC crossover region. We anticipate that our closed-form analytical results can be used as a benchmark for future experimental and theoretical investigations and will have an impact on the current understanding of two-band superconductors such as ${\mathrm{MgB}}_{2}$.