Fermion pairing with spin-density imbalance in an optical lattice

We consider pairing in a two- component atomic Fermi gas, in a three- dimensional optical lattice, when the components have unequal densities, i. e. the gas is polarized. We show that a superfluid where the translational symmetry is broken by a finite Cooper pair momentum, namely a Fulde Ferrel - Larkin - Ovchinnikov ( FFLO)- type state, minimizes the Helmholtz free energy of the system. We demonstrate that such a state is clearly visible in the observable momentum distribution of the atoms, and analyse the dependence of the order parameter and the momentum distribution on the filling fraction and the interaction strength.