Fulde-Ferrell-Larkin-Ovchinnikov and topological superconducting phase in one dimensional optical lattice

The recent experimental realization of spin-orbit coupling in ultracold atom systems provides new arena for us to explore new quantum states. In this work, we explore the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase and topological superconducting phase of spin-orbital coupled Fermions in one dimensional optical lattice using the Density matrix renormalization group (DMRG) method. We demonstrate that the FFLO phase is energetically favored for in-plane Zeeman field while the topological superconducting phase is favored for out-of-plane Zeeman field. The entanglement entropy for these two phases are also examined.