BCS pairing state in an asymmetric binary Bose gas

The BCS pairing state has been predicted to be stable in a symmetric binary Bose gas with the intraspecies repulsion and interspecies attraction. In experiments, the binary Bose gases are generally asymmetric. In this work, we study the pairing state in a dilute asymmetric binary Bose system with the intraspecies repulsions and interspecies attraction and show that it is stable in a certain region of the phase space. We find that there always exists a best density ratio for given total density and coupling constants, where the temperature width of the BCS region is maximized. At the best density ratio, both components have the almost same ideal BEC temperature. We also found that there are two critical density ratios where the BCS phase vanishes. The stability of the BCS state against pairing fluctuations is shown by expanding the Helmholtz free energy of BCS state near the normal state and proving that it is a local minimum point.