Evolution from BCS to BEC superfluidity in the presence of spin-orbit coupling

We discuss the evolution from BCS to BEC superfluids in the presence of spin-orbit coupling, and show that this evolution is just a crossover in the balanced case. The dependence of several thermodynamic properties, such as the chemical potential, order parameter, pressure, entropy, isothermal compressibility and spin susceptibility tensor on the spin-orbit coupling and interaction parameter at low temperatures are analyzed. We studied both the case of equal Rashba and Dresselhaus (ERD) and the Rashba-only (RO) spin-orbit coupling. Comparisons between the two cases reveal several striking differences in the corresponding thermodynamic quantities. Finally we propose measuring the spin susceptibility as a means to detect the spin-orbit coupling effect.