Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials

Abstract

We study the transport of cold fermionic atoms trapped in optical lattices in the presence of artificial Abelian or non-Abelian gauge potentials. Such external potentials can be created in optical lattices in which atom tunneling is laser assisted and described by commutative or non-commutative tunneling operators. We show that the Hall-like transverse conductivity of such systems is quantized by relating the transverse conductivity to topological invariants known as Chern numbers. We show that this quantization is robust in non-Abelian potentials. The different integer values of this conductivity are explicitly computed for a specific non-Abelian system which leads to a fractal phase diagram.

arXiv comment6 pages, 2 figures

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• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
• Topological phase transitions in the non-Abelian honeycomb lattice
• Two-Dimensional Electron Gas with Cold Atoms in Non-Abelian Gauge Potentials
• Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
• Simulation of non-Abelian lattice gauge fields with a single component gas
• Identifying topological edge states in 2D optical lattices using light scattering
• Characterizing the Hofstadter butterfly's outline with Chern numbers
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• Topological phase transition in the quench dynamics of a one-dimensional Fermi gas
• Spatial patterns in optical lattices submitted to gauge potentials
• Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice II
• Spectral Gaps of Spin-orbit Coupled Particles in Deformed Traps
• P-band in a rotating optical lattice
• Mott-Insulator Transition for Ultracold Fermions in Two-Dimensional Optical Lattices
• Hofstadter problem in higher dimensions
• Cold atoms in U(3) gauge potentials
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Detecting degenerate bands topological invariants in optical lattice
• Proposal for realizing and probing topological crystalline insulators in optical lattices