Phase diagram of imbalanced fermions in optical lattices

Abstract

The zero-temperature phase diagrams of imbalanced fermions in three-dimensional 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 $({\text{SF}}_{M})$, or phase separation of $N$ and Bardeen-Cooper-Schrieffer 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.