Phase diagram of imbalanced fermions in optical lattices

The zero-temperature phase diagrams of imbalanced fermions in 3D optical lattices are investigated to evaluate the validity of the Fermi-Hubbard model. It is found that depending on the filling factor, s-wave scattering strength and lattice potential, the system may fall into the normal($N$) phase, magnetized superfluid(SF$_M$) or phase separation of $N$ and BCS state. By tuning these parameters, the superfluidity could be favorable by enhanced effective couplings or suppressed by the increased band gap. The phase profiles in the presence of a harmonic trap are also investigated under LDA, which show some exotic shell structures compared to those without the optical lattice.