Two-Dimensional Electron Gas with Cold Atoms in Non-Abelian Gauge Potentials

Abstract

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of non-interacting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In the continuum limit, a non-Abelian system characterized by a two-component "magnetic flux" describes a harmonic oscillator existing in two different charge states (mimicking a particle-hole pair) where the coupling between the states is determined by the non-Abelian parameter, namely the difference between the two components of the "magnetic flux." A key feature of the non-Abelian system is a splitting of the Landau energy levels, which broaden into bands, as the spectrum depends explicitly on the transverse momentum. These Landau bands result in a coarse-grained "moth," a continuum version of the generalized Hofstadter butterfly. Furthermore, the bands overlap, leading to effective relativistic effects. Importantly, similar features also characterize the corresponding two-dimensional lattice problem when at least one of the components of the magnetic flux is an irrational number. The lattice system with two competing "magnetic fluxes" penetrating the unit cell provides a rich environment in which to study localization phenomena. Some unique aspects of the transport properties of the non-Abelian system are the possibility of inducing localization by varying the quasimomentum, and the absence of localization of certain zero-energy states exhibiting a linear energy-momentum relation. Furthermore, non-Abelian systems provide an interesting localization scenario where the localization transition is accompanied by a transition from relativistic to non-relativistic theory.

A version with higher resolution figures is available at http://physics.gmu.edu/~isatija/NALFinal.pdf

References in corpus (5)

• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials
• Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials
• Spatial patterns in optical lattices submitted to gauge potentials

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• Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
• Rydberg-Atom Quantum Simulation and Chern Number Characterization of a Topological Mott Insulator
• Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
• Relativistic quantum effects of Dirac particles simulated by ultracold atoms
• Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms
• Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
• Chains with loops - synthetic magnetic fluxes and topological order in one-dimensional spin systems
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Spin-selective localization due to intrinsic spin-orbit coupling
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Bose-Einstein Condensates in Non-abelian Gauge Fields