  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.
