We investigate the ground state of interacting spin-$\frac{1}{2}$ fermions in three dimensions at a finite density ($\rho \sim k_F^3$) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector $\lambda \equiv ({\lambda }_x,{\lambda }_y,{\lambda }_z)$, whose magnitude $\lambda$ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length $\left(k_F\right|a_s|\lesssim 1)$, the ground state in the absence of the gauge field ($\lambda =0$) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum $(\lambda =0)$. For large gauge couplings $(\lambda /k_F\gg 1)$, the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)—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 GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $\lambda$ near ${\lambda }_T$. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.

• Received 6 May 2011

DOI:https://doi.org/10.1103/PhysRevB.84.014512