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

2006/09/30 by Nathan Goldman, N. Goldman, Pierre Gaspard +1 · 29 citations
Mathematics · Physics and Astronomy · #Abelian group #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Electron #Gauge theory #Mathematical physics #Mathematics #Noncommutative geometry #Physics #Pure mathematics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum tunnelling #Topological Materials and Phenomena #Ultracold atom #cond-mat.mes-hall

paper · pdf · doi:10.1209/0295-5075/78/60001

published in Europhysics Letters (EPL) 78(6), 60001 (Institute of Physics) · 6 pages, 2 figures

openalex publication_date 2007/05/22 · arxiv created 2007/05/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Geometry, Topology and Physics
• Homotopy and Quantization in Condensed Matter Physics
• Significance of Electromagnetic Potentials in the Quantum Theory
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase
• Fractional Quantum Hall States of Atoms in Optical Lattices
• Quantal phase factors accompanying adiabatic changes
• Light-induced effective magnetic fields for ultracold atoms in planar geometries

Cited by

• SimulatingZ2topological insulators with cold atoms in a one-dimensional optical lattice
• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop