  We investigate effects of optical lattice potential in one- and
two-dimensional two-component trapped Fermi gases with population imbalances.
Using the exact diagonalization and the density matrix renormalization group
methods complementarily, we calculate the atom density profile from the ground
state many-body wavefunction as a function of attractive interaction strength
for various population imbalances. The numerical results reveal that although a
phase separation between the superfluid core and the shell cloud of excess
atoms occurs as observed in experiments without the optical lattice, the
population imbalance generally remains in the core region in contrast to the
non-lattice cases. The essence of the numerical results in a strong attractive
regime can be explained by an effective model composed of Cooper pairs and
excess major fermions.
