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