  The zero-temperature phase diagrams of imbalanced two-species Fermi gases are
investigated in asymmetric optical lattices with arbitrary potential depths,
based on the exact spectrum instead of the Fermi-Hubbard model. We study the
effect of lattice potentials and atomic densities to the fully paired
Bardeen-Cooper-Schrieffer (BCS) state and particularly the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. It is found that the increasing
lattice potential favors BCS at low densities because of the enhanced effective
coupling; whereas FFLO is favored at intermediate densities when the system
undergoes a dimensional crossover. Finally using local density approximation we
study the evolution of phase profile in the presence of external harmonic traps
by merely tuning the lattice potentials.
