  In this paper we study the superfluid density of the two component Fermi gas
in 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 the
FFLO superfluid density differs from the BCS/Sarma superfluid density in an
important way. Although there are dynamical instabilities in the FFLO phase,
when the interaction is strong or densities are high, on the weak coupling
limit the FFLO phase is found to be stable.
