  We consider a two-component gas of fermions in optical lattices in the
presence of a population imbalance within a mean-field theory. We study phase
transitions from a normal gas of unpaired fermions to a superfluid phase of
Bose-condensed Cooper pairs. The possibility of Cooper pairs with a nonzero
center-of-mass momentum is included, which corresponds to a so-called
Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state. We find that for population
imbalanced systems such states can form the ground state. The FF and LO state
are compared and it is shown that actually the LO state is energetically more
favorable. We complete the mean-field phase diagram for the LO phase and show
that it is qualitatively in excellent agreement with recent diagrammatic Monte
Carlo calculations. Subsequently, we calculate the atomic density modulations
in the LO phase.
