Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2009-02-18
Phys.Rev.A79:023624,2009
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
12 pages, 2 appendices, 7 figures, extended version of arXiv:0712.2571
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 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.
Gaspard Pierre
Goldman Nathan
Kubasiak A.
Lewenstein Maciej
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