BCS-BEC crossover induced by a synthetic non-Abelian gauge field

We investigate the ground state of interacting spin-$half$ fermions(3D) at a finite density ($\rho \sim k_F^3$) in the presence of a uniform non-Abelian gauge field (with magnitude $\lambda$) that generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length $(k_F |a_s| \la 1)$, the ground state in the absence of the gauge field ($\lambda=0$) is a BCS superfluid with large overlapping pairs. With increasing $\lambda$, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC ground state of bosons even with a weak attractive interaction. For large gauge couplings $(\lambda/k_F \gg 1)$, the BEC attained is a condensate of bosons whose properties are solely determined by the gauge field (and not by the scattering length); we call these bosons ``rashbons.'' In the absence of interactions ($a_s = 0^-$), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling $\lambda_T$. For high symmetry gauge field configurations we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $\lambda$ near $\lambda_T$.