5We investigate the ground state of interacting spin-1 2 fermions in 3D at a finite density (ρ ∼ k 3 F ) 6 in the presence of a uniform non-Abelian gauge field. The gauge field configuration (GFC) described 7 by a vector λ ≡ (λx, λy, λz), whose magnitude λ determines the gauge coupling strength, generates 8 a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel 9 described by a small negative scattering length (kF |as| 1), the ground state in the absence of the 10 gauge field (λ = 0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. 11With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS 12 ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction

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 3D 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 (λx, λy, λz). 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., λx = λy = λz) 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 high-symmetry configurations have nematic spin structure similar to those found in liquid 3 He. Our results show that the BCS-BEC 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.

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In presence of a synthetic non-Abelian gauge field that induces a Rashba like spin-orbit interaction, a collection of weakly interacting fermions undergoes a crossover from a BCS ground state to a BEC ground state when the strength of the gauge field is increased [Phys. Rev. B 84, 014512 (2011)]. The BEC that is obtained at large gauge coupling strengths is a condensate of tightly bound bosonic fermion-pairs whose properties are solely determined by the Rashba gauge field -hence called rashbons. In this paper, we conduct a systematic study of the properties of rashbons and their dispersion. This study reveals a new qualitative aspect of the problem of interacting fermions in non-Abelian gauge fields, i. e, that the rashbon state induced by the gauge field for small centre of mass momenta of the fermions ceases to exist when this momentum exceeds a critical value which is of the order of the gauge coupling strength. The study allows us to estimate the transition temperature of the rashbon BEC, and suggests a route to enhance the exponentially small transition temperature of the system with a fixed weak attraction to the order of the Fermi temperature by tuning the strength of the non-Abelian gauge field. The nature of the rashbon dispersion, and in particular the absence of the rashbon states at large momenta, suggests a regime of parameter space where the normal state of the system will be a dynamical mixture of uncondensed rashbons and unpaired helical fermions. Such a state should show many novel features including pseudogap physics.

Synthetic non-Abelian gauge fields in cold atom systems produce a generalized Rashba spin-orbit interaction described by a vector λ = (λx, λy, λz) that influences the motion of spin-1 2 fermions. It was recently shown [Phys. Rev. B 84, 014512 (2011)] that on increasing the strength of the spinorbit coupling λ = |λ|, a system of fermions at a finite density ρ ≈ k 3 F evolves to a BEC like state even in the presence of a weak attractive interaction (described by a scattering length as). The BEC obtained at large spin-orbit coupling (λ kF ) is a condensate of rashbons -novel bosonic bound pairs of fermions whose properties are determined solely by the gauge field. In this paper, we investigate the collective excitations of such superfluids by constructing a Gaussian theory using functional integral methods. We derive explicit expressions for superfluid phase stiffness, sound speed and mass of the Anderson-Higgs boson that are valid for any λ and scattering length. We find that at finite λ, the phase stiffness is always lower than that set by the density of particles, consistent with earlier work [arXiv:1110.3565] which attributed this to the lack of Galilean invariance of the system at finite λ. We show that there is an emergent Galilean invariance at large λ, and the phase stiffness is determined by the rashbon density and mass, consistent with Leggett's theorem. We further demonstrate that the rashbon BEC state is a superfluid of anisotropic rashbons interacting via a contact interaction characterized by a rashbon-rashbon scattering length aR. We show that aR goes as λ −1 and is essentially independent of the scattering length between the fermions as long as it is nonzero. Analytical results are presented for a rashbon BEC obtained in a spherical gauge field with λx = λy = λz = λ √ 3.