Volume 78, Number 6, June 2007
Article Number 60001
Number of page(s) 6
Section General
Published online 22 May 2007
EPL, 78 (2007) 60001
DOI: 10.1209/0295-5075/78/60001

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

N. Goldman and P. Gaspard

Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.) Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium

received 30 November 2006; accepted in final form 27 April 2007; published June 2007
published online 22 May 2007

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.

03.65.Vf - Phases: geometric; dynamic or topological .
03.75.Ss - Degenerate Fermi gases .
05.60.Gg - Quantum transport .

© Europhysics Letters Association 2007