One-dimensional Spin-orbit Coupled Fermi Gas In Optical Lattice

We employ the density-matrix renormalization group to investigate one-dimensional spin-orbit coupled degenerate Fermi gas, with an attractive on-site interaction and a Zeeman field, in an optical lattice. In the presence of spin-orbit coupling (SOC) and the strong Zeeman field, the interband Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing has an intrinsic competition with the intraband Bardeen-Cooper-Schrieffer (BCS) pairing. As a consequence, we predict rich phase diagrams, including a quantum phase called the FFLO-BCS phase, at near half filling. In this FFLO-BCS phase, the system exhibits an exotic coexistence of the FFLO pairing and the BCS pairing, and more importantly, the pairing correlation function in momentum space exhibits a three-peak structure (two peaks at nonzero momentum and one at zero momentum), superfluidity and magnetism can coexist.The effect of the SOC with of the phase separation in trap system, we found phase separation can be suppressed until the phase separation disappeared. SOC can enhance the competitive of BCS pairing.With the in-plane Zeeman field,the Fermi surface becomes asymmetric along the y direction,the FFLO pairing can occur between atoms with momenta k and -k+Q,with finite momentum Q, although there is no imbalance. The system exhibits three-peak structure called the FFLO-BCS phase. In the strong SO coupling regime, only independent BCS pairing in each band is allowed in the whole parameter regime.