Spin-orbit Coupling Effects In One Dimensional Quantum Fermion Gases

Based on the experimental realization of artificial spin-orbit coupling (SOC) effects in cold atom physics, we have concerned the influence of this effect on the dispersion relation of one-dimensional Fermion gases and studied the phase diagrams of this system by calculating four fluctuation correlation functions:the charge-density wave (CDW), spin-density wave (SDW), singlet superfliud (SS) and triplet superfliud (TS). Firstly, there are five categories of Fermi levels according to the number and properties of the Fermi points of the new dispersion relation. Through Luttinger liq-uid theory, the effective Hamiltonian of the system with δ-interaction has been derived when its Fermi Level is the highest one. Then the correlation functions and phase diagrams are obtained by path integral. One find that the introduction of SOC effects make the structure of the phase diagrams much richer than the ones without it. As to δ-interaction, the backscat-tering term is suppressed for long wave length limit because of SOC effects, the relations between the Luttinger parameters and the strength of inter-action can be derived without renormalization. So, we have also studied the phase diagram of interaction vs SOC and find that, for attractive in-teraction the system tends to be SS phase with singlet cooper pair similar to BCS theory; for repulsive interaction, However, the system prone to be SDW phase which are more easy to transport spin-density wave; the CDW phase shows up only when a weak SOC term was introduced; when the strength of SOC increases to strong coupling region, the triplet superfliud (TS) phase would comes into being.