Trapped fermions in a synthetic non-Abelian gauge field

Abstract

On increasing the coupling strength ($\lambda$) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density $ρ\sim \kf^3$ undergoes a change at a critical value, $λ_T \approx \kf$ [Phys. Rev. B {\bf 84}, 014512 (2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-$\half$ fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulae for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a {\em characteristic fashion with increasing $\lambda$}. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud for all gauge field configurations, which are anisotropic in general. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling $\lambda$. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians (eg. quantum hall spherical geometry) by using a non-Abelian gauge field in conjunction with another potential.

10 Pages, 4 figures

References in corpus (6)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Spin-Orbit Coupled Spinor Bose-Einstein Condensates
• A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• BCS-BEC crossover induced by a synthetic non-Abelian gauge field

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• Chaos-driven dynamics in spin-orbit coupled atomic gases
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• 2D and 3D topological insulators with isotropic and parity-breaking Landau levels
• Rashbons: Properties and their significance
• Collective excitations across the BCS-BEC crossover induced by a synthetic Rashba spin-orbit coupling
• Three-Dimensional Spin-Orbit Coupling in a Trap
• Vortex line in spin-orbit coupled atomic Fermi gases
• Statistical properties of spectra in harmonically trapped spin-orbit coupled systems
• Spectral Gaps of Spin-orbit Coupled Particles in Deformed Traps
• Trapped Fermi gases with Rashba spin-orbit coupling in two dimensions
• Tuning the Topological Features of Quantum-Dot Hydrogen and Helium by a Magnetic Field
• Synthetic-gauge-field-induced resonances and Fulde-Ferrell-Larkin-Ovchinnikov states in a one-dimensional optical lattice
• Weyl spin-orbit-coupling-induced interactions in uniform and trapped atomic quantum fluids
• Artificial Magnetic Fields in Momentum Space in Spin-Orbit Coupled Systems
• Counterflow of spontaneous mass currents in trapped spin-orbit coupled Fermi gases
• Universal properties of boundary and interface charges in multichannel one-dimensional continuum models
• Spectral intensity distribution of trapped fermions
• Orbital ferromagnetism in interacting few-electron dots with strong spin-orbit coupling