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arXiv:1212.2858 · Physical Review A

Feshbach resonance in a synthetic non-Abelian gauge field

Vijay B. Shenoy

Published Apr 23, 2014• 3 citations
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Abstract

We study the Feshbach resonance of spin-$\frac{1}{2}$ particles in a uniform synthetic non-Abelian gauge field that produces spin-orbit coupling and constant spin potentials. We develop a renormalizable quantum field theory including the closed-channel boson which engenders the resonance. We show that the gauge field shifts the Feshbach field where the low-energy scattering length diverges. In addition the Feshbach field is shown to depend on the center-of-mass momentum of the particles. For high-symmetry gauge fields which produce a Rashba spin coupling, we show that the system supports two bound states over a regime of magnetic fields when the background scattering length is negative and the resonance width is comparable to the energy scale of the spin-orbit coupling. We discuss interesting consequences useful for future theoretical and experimental studies, even while our predictions are in agreement with recent experiments.

DOI
10.1103/physreva.89.043618

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We study the Feshbach resonance of spin-12\frac{1}{2}21​ particles in a uniform synthetic non-Abelian gauge field that produces spin-orbit coupling and constant spin potentials. We develop a renormalizable quantum field theory including the closed-channel boson which engenders the resonance. We show that the gauge field shifts the Feshbach field where the low-energy scattering length diverges. In addition the Feshbach field is shown to depend on the center-of-mass momentum of the particles. For high-symmetry gauge fields which produce a Rashba spin coupling, we show that the system supports two bound states over a regime of magnetic fields when the background scattering length is negative and the resonance width is comparable to the energy scale of the spin-orbit coupling. We discuss interesting consequences useful for future theoretical and experimental studies, even while our predictions are in agreement with recent experiments.
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.
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.
Recent experiments on fermions in synthetic gauge fields result in systems with a spin-orbit coupling along one spatial axis, a detuning field, and a Zeeman field. We show theoretically that the presence of all three results in interesting and unusual phenomena in a system of interacting fermions (interactions described by a scattering length). For two fermions, bound states appear only over a certain range of the center-of-mass momenta. The deepest bound state appears at a nonzero center-of-mass momentum. For center-of-mass momenta without a bound state, the gauge field induces a resonance-like feature in the scattering continuum resulting in a large scattering phase shift. In the case of many particles, we demonstrate that the system, in a parameter range, shows flow-enhanced pairing, i.e., a Fulde-Farrell-Larkin-Ovchnnikov superfluid state made of robust pairs with a finite center-of-mass momentum. Yet another regime of parameters offers the opportunity to study strongly interacting normal states of spin-orbit-coupled fermionic systems utilizing the resonance-like feature induced by the synthetic gauge field.
We investigate the ground state of interacting spin-12\frac{1}{2}21​ 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.
Generation and study of synthetic gauge fields has enhanced the possibility of using cold atom systems as quantum emulators of condensed matter Hamiltonians. In this article we describe the physics of interacting spin -1/2 fermions in synthetic non-Abelian gauge fields which induce a Rashba spin-orbit interaction on the motion of the fermions. We show that the fermion system can evolve to a Bose-Einstein condensate of a novel boson which we call rashbon. The rashbon-rashbon interaction is shown to be independent of the interaction between the constituent fermions. We also show that spin-orbit coupling can help enhancing superfluid transition temperature of weak superfluids to the order of Fermi temperature. A non-Abelian gauge field, when used in conjunction with another potential, can generate interesting Hamiltonians such as that of a magnetic monopole.
Two-body scattering constitutes one of the most fundamental processes in various physical systems ranging from ultracold dilute quantum gases to energetic quark- gluon plasmas. In this dissertation, we study the low-energy atomic collision physics in the presence of synthetic gauge fields, which are generated by atom-light interaction. One category of synthetic gauge fields is the artificial spin-orbit coupling. We discuss three different aspects in scattering theory: ultracold collision, scattering resonance, and bound state formation from a few-body perspective when the atomic spin states are coupled with their center-of-mass motion. The understanding of the spin-orbit effects on the modification of the scattering processes not only builds the foundation of collision physics in the presence of non-abelian gauge fields but also paves the way towards unraveling the few-body correlations in many-body systems.