Mediated Interactions and Damping Effects in Superfluid Mixtures of Bose and Fermi Gases

Abstract: We investigate the homogeneous superfluid mixtures of Bardeen-Cooper-Schrieffer~(BCS) superfluid originating from pairing two-species fermionic atoms and superfluidity stemming from condensation of bosonic atoms. By integrating out the freedoms associated with the BCS superfluid, we derive the fermion-mediated interactions between bosons, which is attractive and can be tuned from long range in the BCS region to short range in the region of Bose-Einstein condensation (BEC) of molecular dimers. By analyzing the Bogoliubov spectrum and the damping rate of bosonic superfluid, we map out the phase diagram spanned by the boson-fermion mass ratio and the boson-fermion coupling strength, which consists of a phase separation region and two phase mixing regions with and without Landau damping. The three different phases can coexist at a tricritical point, which moves toward low boson-fermion mass ratio and high boson-fermion scattering length as the fermion-fermion interaction strength is tuned up on the BCS side.