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We investigate the role of a repulsive s-wave interaction in the two-bodyproblem in the presence of spin orbit couplings, motivated by current interestsin exploring exotic superfluid phases in spin-orbit coupled Fermi gases. Forweak spin orbit coupling where the density of states is not significantlyaltered, we analytically show that the high-energy states become more importantin determining the binding energy when the interaction strength decreases.Consequently, tuning the interaction gives rise to a rich ground statebehavior, including a zigzag of the ground state momentum or inducingtransitions among the meta-stable states. By exactly solving the two-bodyproblem for a spin-orbit coupled Fermi mixture, we demonstrate that ouranalysis can also apply to the case when the density of states is significantlymodified by the spin-orbit coupling. Our findings pave the way forunderstanding and controlling the paring of fermions in the presence of spinorbit couplings.

The Role of Interaction in the Pairing of Two Spin-orbit Coupled Fermions