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

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

2007-12-16

arxiv.org/abs/0712.2571v5

Phys. Rev. A. 79, 023624 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages, 5 figures

Scientific paper

10.1103/PhysRevA.79.023624

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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