Quasi-relativistic behavior of cold atoms in light fields

We study the influence of three laser beams on the center of mass motion of cold atoms with internal energy levels in a tripod configuration. We show that similar to electrons in graphene the atomic motion can be equivalent to the dynamics of ultra-relativistic two-component Dirac fermions. We propose and analyze an experimental setup for observing such a quasi-relativistic motion of ultracold atoms. We demonstrate that the atoms can experience negative refraction and focussing by Veselago-type lenses. We also show how the chiral nature of the atomic motion manifests itself as an oscillation of the atomic internal state population which depends strongly on the direction of the center of mass motion. For certain directions an atom remains in its initial state, whereas for other directions the populations undergo oscillations between a pair of internal states.