Finite-momentum superfluidity and phase transitions in a p-wave resonant Bose gas

We study a degenerate two-species gas of bosonic atoms interacting through a p-wave Feshbach resonance as for example realized in a Rb85-Rb87 mixture. We show that in addition to a conventional atomic and a p-wave molecular spinor-1 superfluidity at large positive and negative detunings, respectively, the system generically exhibits a finite momentum atomic-molecular superfluidity at intermediate detuning around the unitary point. We analyze the detailed nature of the corresponding phases and the associated quantum and thermal phase transitions.