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arXiv · 0712.2571

Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy

N. Goldman·A. Kubasiak·P. Gaspard·M. Lewenstein
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Abstract

Nowadays it is experimentally feasible to create artificial, and in particular, non-Abelian gauge potentials for ultracold atoms trapped in optical lattices. Motivated by this fact, we investigate the fundamental properties of an ultracold Fermi gas in a non-Abelian U(2) gauge potential characterized by a \emph{constant} Wilson loop. Under this specific condition, the energy spectrum exhibits a robust band structure with large gaps and reveals a new fractal figure. The transverse conductivity is related to topological invariants and is shown to be quantized when the Fermi energy lies inside a gap of the spectrum. We demonstrate that the analogue of the integer quantum Hall effect for neutral atoms survives the non-Abelian coupling and leads to a striking fractal phase diagram. Moreover, this coupling induces an anomalous Hall effect as observed in graphene.

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N. Goldman, A. Kubasiak, P. Gaspard, M. Lewenstein. 2008-09-09. Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy. https://doi.org/10.1103/physreva.79.023624

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