Three-component ultracold Fermi gases with spin-orbit coupling.

We investigate the pairing physics in a three-component Fermi-Fermi mixture, where a few fermionic impurities are immersed in a noninteracting two-component Fermi gas with synthetic spin-orbit coupling (SOC), and interact attractively with one spin species in the Fermi gas. Because of the interplay of SOC and the spin-selective interaction, the molecular state intrinsically acquires a nonzero center-of-mass momentum, which results in a new type of Fulde-Ferrell (FF) pairing in spin-orbit coupled Fermi systems. The existence of the Fermi sea can also lead to the competition between FF-like molecular states with different center-of-mass momenta, which corresponds to a first-order transition between FF phases in the thermodynamic limit. As the interaction strength is tuned, a polaron-molecule transition occurs in the highly imbalanced system, where the boundary varies nonmonotonically with SOC parameters and gives rise to the reentrance of polaron states. The rich physics in this system can be probed using existing experimental techniques.