Generic phase diagram of Fermion superfluids with population imbalance.

It is shown by microscopic calculations for trapped imbalanced Fermi superfluids that the gap function always has sign changes, i.e., the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state, up to a critical imbalance P(c), beyond which normal state becomes stable, at temperature T=0. A temperature-versus-pressure phase diagram is constructed, where the BCS state without sign change is stable only at T not equal to 0. We reproduce the observed bimodality in the density profile to identify its origin and evaluate P(c) as functions of T and the coupling strength. These dependencies match with the recent experiments.