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We investigated possible superfluid phases at finite temperature in atwo-component Fermi gas with density imbalance. In the frame of a generalfour-fermion interaction theory, we solved in the BCS region the gap equationsfor the pairing gap and pairing momentum under the restriction of fixed numberdensities, and analyzed the stability of different phases by calculating thesuperfluid density and number susceptibilities. The homogeneous superfluid isstable only at high temperature and low number asymmetry, the inhomogeneousLOFF survives at low temperature and high number asymmetry, and in between themthere exists another possible inhomogeneous phase, that of phase separation.The critical temperatures and the orders of the phase transitions among thesuperfluid phases and normal phase are calculated analytically and numerically.The phase diagram we obtained in the temperature and number asymmetry plane isquite different from the one in temperature and chemical potential differenceplane for a system with fixed chemical potentials.Comment: Final published versio

Finite-temperature phase diagram of a two-component Fermi gas with density imbalance