Finite Orbital Angular Momentum Pairing in Atomic Fermi Gases with Spin-Orbital-Angular-Momentum Coupling

Fulde-Ferrell-Larkin-Ovchinnikov states represent superconducting states with finite momentum Cooper pairs and have become one of most sought-after exotic states of matter. The recent realization of a new type of spin-orbit coupling in ultracold atomic gases, namely the spin-orbital-angular-momentum coupling, provides a novel perspective to study Fulde-Ferrell-Larkin -Ovchinnikov states in orbital angular momentum space. In this letter, we demonstrate that the combined effects of spin-orbital-angular-momentum coupling and level detuning can induce an exotic Fulde-Ferrell-Larkin-Ovchinnikov phase, where Cooper pairs have finite center-of-mass angular momenta. This implies that vortex with high-vorticity can be generated without rotation or effective vector potential field. The orientation of the phase winding can be altered by adjusting the sign of level detuning.