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

Abstract

We investigate the ground state of interacting spin-12 fermions in three dimensions at a finite density (ρ∼kF3) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector λ?(λx,λy,λz) , whose magnitude λ 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 (k F|as|?1), the ground state in the absence of the gauge field (λ=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 (λ=0). For large gauge couplings (λ/kF?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 (as=0 -), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling λT. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of λ near λT. 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. © 2011 American Physical Society.