Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions

N. Goldman, A. Kubasiak, A. Bermudez, P. Gaspard, M. Lewenstein, M. A. Martin-Delgado

Published 2009-03-13, updated 2009-07-14Version 3

We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.