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arXiv:1104.5633 · Physical Review B

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

Jayantha P. Vyasanakere, Shizhong Zhang, Vijay B. Shenoy

Published Jul 25, 2011• 161 citations
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Abstract

We investigate the ground state of interacting spin-$\frac{1}{2}$ fermions in three dimensions at a finite density ($\ensuremath{\rho}\ensuremath{\sim}{k}_{F}^{3}$) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector $\ensuremath{\lambda}\ensuremath{\equiv}({\ensuremath{\lambda}}_{x},{\ensuremath{\lambda}}_{y},{\ensuremath{\lambda}}_{z})$, whose magnitude $\ensuremath{\lambda}$ 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 $({k}_{F}|{a}_{s}|\ensuremath{\lesssim}1)$, the ground state in the absence of the gauge field ($\ensuremath{\lambda}=0$) 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 $(\ensuremath{\lambda}=0)$. For large gauge couplings $(\ensuremath{\lambda}/{k}_{F}\ensuremath{\gg}1)$, 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 (${a}_{s}={0}^{\ensuremath{-}}$), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling ${\ensuremath{\lambda}}_{T}$. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of $\ensuremath{\lambda}$ near ${\ensuremath{\lambda}}_{T}$. 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.

DOI
10.1103/physrevb.84.014512

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Recent advances in the generation of synthetic gauge fields in cold atomic systems have stimulated interest in the physics of interacting bosons and fermions in them. In this paper, we discuss interacting two-component fermionic systems in uniform non-Abelian gauge fields that produce a spin-orbit interaction and uniform spin potentials. Two classes of gauge fields discussed include those that produce a Rashba spin-orbit interaction and the type of gauge fields (SM gauge fields) obtained in experiments by the Shanxi and MIT groups. For high symmetry Rashba gauge fields, a two-particle bound state exists even for a vanishingly small attractive interaction described by a scattering length. Upon increasing the strength of a Rashba gauge field, a finite density of weakly interacting fermions undergoes a crossover from a BCS like ground state to a BEC state of a new kind of boson called the rashbon whose properties are determined solely by the gauge field and not by the interaction between the fermions. The rashbon Bose-Einstein condensate (RBEC) is a quite intriguing state with the rashbon-rashbon interactions being independent of the fermion-fermion interactions (scattering length). Furthermore, we show that the RBEC has a transition temperature of the order of the Fermi temperature, suggesting routes to enhance the transition temperatures of weakly interacting superfluids by tuning the spin-orbit coupling. For the SM gauge fields, we show that in a regime of parameters, a pair of particles with finite centre-of-mass momentum is the most strongly bound. In other regimes of centre-of-mass momenta, there is no two-body bound state, but a resonance like feature appears in the scattering continuum. In the many-body setting, this results in flow enhanced pairing. Also, strongly interacting normal states utilizing the scattering resonance can be created opening the possibility of studying properties of helical Fermi liquids. This paper contains a general discussion of the physics of Feshbach resonance in a non-Abelian gauge field, where several novel features such as centre-of-mass-momentum-dependent effective interactions are shown. It is also shown that a uniform non-Abelian gauge field in conjunction with a spatial potential can be used to generate novel Hamiltonians; we discuss an explicit example of the generation of a monopole Hamiltonian.
In the presence of a synthetic non-Abelian gauge field that produces a Rashba-like spin-orbit interaction, a collection of weakly interacting fermions undergoes a crossover from a Bardeen-Cooper-Schrieffer (BCS) ground state to a Bose-Einstein condensate (BEC) ground state when the strength of the gauge field is increased (Vyasanakere et al 2011 Phys. Rev. B 84 014512). The BEC that is obtained at large gauge coupling strengths is a condensate of tightly bound bosonic fermion pairs. The properties of these bosons 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 ceases to exist when the center-of-mass momentum of the fermions exceeds a critical value that 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 in 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.
We study the bound states of two spin-12\frac{1}{2}21​ 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 $({\ensuremath{\lambda}}_{x},{\ensuremath{\lambda}}_{y},{\ensuremath{\lambda}}_{z})$. 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., ${\ensuremath{\lambda}}_{x}={\ensuremath{\lambda}}_{y}={\ensuremath{\lambda}}_{z}$) for which there is a two-body bound state for anyscattering 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^{3}\mathrm{He}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.
In the presence of a synthetic non-Abelian gauge field that produces a Rashba-like spin–orbit interaction, a collection of weakly interacting fermions undergoes a crossover from a Bardeen–Cooper–Schrieffer (BCS) ground state to a Bose–Einstein condensate (BEC) ground state when the strength of the gauge field is increased (Vyasanakere et al 2011 Phys. Rev. B 84 014512). The BEC that is obtained at large gauge coupling strengths is a condensate of tightly bound bosonic fermion pairs. The properties of these bosons 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 ceases to exist when the center-of-mass momentum of the fermions exceeds a critical value that 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 in 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.
We present a systematic theoretical study of the BCS-BEC crossover problem in three-dimensional atomic Fermi gases at zero temperature with a spherical spin-orbit coupling which can be generated by a synthetic non-Abelian gauge field coupled to neutral fermions. Our investigations are based on the path-integral formalism, which is a powerful theoretical scheme for the study of the properties of the bound state, the superfluid ground state, and the collective excitations in the BCS-BEC crossover. At large spin-orbit coupling, the system enters the BEC state of a novel type of bound state (referred to as rashbon), which possesses a nontrivial effective mass. Analytical results and interesting universal behaviors for various physical quantities at large spin-orbit coupling are obtained. Our theoretical predictions can be tested in future experiments of cold Fermi gases with three-dimensional spherical spin-orbit coupling.