Evaluating the phase diagram of superconductors with asymmetric spin populations

The phase diagram of a non-relativistic fermionic system with imbalanced state populations interacting via a short-range S-wave attractive interaction is analyzed in the mean field approximation. We determine the energetically favored state for different values of the mismatch between the two Fermi spheres in the weak and strong coupling regime considering both homogeneous and non-homogeneous superconductive states. We find that the homogeneous superconductive phase persists for values of the population imbalance that increase with increasing coupling strength. In the strong coupling regime and for large population differences the energetically stable homogeneous phase is characterized by one gapless mode. We also find that the inhomogeneous superconductive phase characterized by the condensate $\Delta({\bf x}) \sim \Delta~\exp{(i \bf{q \cdot x})}$ is energetically favored in a range of values of the chemical potential mismatch that shrinks to zero in the strong coupling regime.