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.

6 pages, 2 figures

References in corpus (4)

• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Evidence for Superfluidity of Ultracold Fermions in an Optical Lattice
• Molecules of Fermionic Atoms in an Optical Lattice
• Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials

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• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
• Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
• Two-Dimensional Electron Gas with Cold Atoms in Non-Abelian Gauge Potentials
• Identifying topological edge states in 2D optical lattices using light scattering
• Characterizing the Hofstadter butterfly's outline with Chern numbers
• Spatial patterns in optical lattices submitted to gauge potentials
• Topological phase transition in the quench dynamics of a one-dimensional Fermi gas
• Mott-Insulator Transition for Ultracold Fermions in Two-Dimensional Optical Lattices
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Detecting degenerate bands topological invariants in optical lattice