  We show that Larkin-Ovchinnikov (LO) states with modulated superfluid order
parameters have a considerably larger range of stability in a lattice than in
the continuum. We obtain the phase diagram for the 3D cubic attractive Hubbard
model with an unequal population of up and down fermions using the
Bogoliubov-de Gennes fully self-consistent method. We find a strong modulation
of the local polarization that should provide a distinct signature for
detection of the LO phase. The shell structure in the presence of a trap
generates singularities in the density at the phase boundaries and provide
additional evidence for the LO phase. Depending on specific parameters, the LO
ground state occurs over a large range of population imbalance, involving 80%
of the atoms in the trap, and can exist up to an entropy s ~ 0.5 k_B per
fermion.
