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In this paper we study the superfluid density of the two component Fermi gasin optical lattices with population imbalance. Three different type of phases,the BCS-state (Bardeen, Cooper, and Schrieffer), the FFLO-state (Fulde, Ferrel,Larkin, and Ovchinnikov), and the Sarma state, are considered. We show that theFFLO superfluid density differs from the BCS/Sarma superfluid density in animportant way. Although there are dynamical instabilities in the FFLO phase,when the interaction is strong or densities are high, on the weak couplinglimit the FFLO phase is found to be stable.

Superfluid-density of the ultra-cold Fermi gas in optical lattices