Simulation of non-Abelian lattice gauge fields with a single component gas

Abstract

We show that non-Abelian lattice gauge fields can be simulated with a single component ultra-cold atomic gas in an optical lattice potential. An optical lattice can be viewed as a Bravais lattice with a $N$-point basis. An atom located at different points of the basis can be considered as a {\it particle} in different internal states. The appropriate engineering of tunneling amplitudes of atoms in an optical lattice allows one to realize U$(N)$ gauge potentials and control a mass of {\it particles} that experience such non-Abelian gauge fields. We provide and analyze a concrete example of an optical lattice configuration that allows for simulation of a static U(2) gauge model with a constant Wilson loop and an adjustable mass of {\it particles}. In particular, we observe that the non-zero mass creates large conductive gaps in the energy spectrum, which could be important in the experimental detection of the transverse Hall conductivity.

6 pages, 5 figures, version accepted for publication in EPL

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• Digital quantum simulation of lattice gauge theories in three spatial dimensions
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• Quantum Simulation of the Abelian-Higgs Lattice Gauge Theory with Ultracold Atoms
• Confinement and string breaking for QED${}_2$ in the Hamiltonian picture
• Spin Orbit Coupling in Periodically Driven Optical Lattices
• Toolbox for Abelian lattice gauge theories with synthetic matter
• Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension
• Unruh effect for interacting particles with ultracold atoms
• Different lattice geometries with synthetic dimension
• Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Loading Ultracold Gases in Topological Floquet Bands: Current and Center-of-Mass Responses
• Nonequilibrium phases of ultracold bosons with cavity-induced dynamic gauge fields
• Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice
• Artificial magnetic field induced by an evanescent wave
• $SU(3)$ Topological Insulators in the Honeycomb Lattice
• Determination of Chern numbers with a phase retrieval algorithm
• Three-dimensional non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly trios