Bound states of two spin-1/2 fermions in a synthetic non-Abelian gauge field

Abstract

We study the bound states of two spin-1/2 fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters(λ_x,λ_y,λ_z). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the “BCS side” of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., λ_x=λ_y=λ_z) for which there is a two-body bound state for any scattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid ³He. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.