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

N. Goldman·P. Gaspard
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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.

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N. Goldman, P. Gaspard. 2007-05-23. Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials. https://doi.org/10.1209/0295-5075%2F78%2F60001

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