Superradiation of three dimensional Fermi gases with one dimensional spin orbit coupling supported by a cavity

Based on the method of mean field theory, the superradiation transition of a cavity supported three-dimensional Fermi gas coupled with a one dimensional spin-orbit-coupling (SOC) is systematically studied. The superradiation transition behavior of Fermi gas is obviously changed by the introduction of SOC. Due to the interplay between the single-particle energy spectrum change caused by SOC and Pauli exclusion principle, the superradiation threshod of the system will increase with the increase of SOC intensity, meaning that SOC tends to suppress the occurrence of superradiation. The effect of atom-light detuning is further analyzed, and the ground state phase diagram of the system without considering the interaction between atoms is obtained. The evolution characteristics of chemical potential, superradiation order parameters, average photon number and atomic polarization of observable measurements before and after the superradiation transition are discussed. The results show that the SOC provides an effective way to manipulate the superradiant behavior of Fermi gas, which is also helpful for the further study on the non-equilibrium many-body states of the cavity and fermion coupling system.