Slow photons as charged quasi-particles, and photonic Aharonov-Bohm effect

Over the past few years several proposals have been made how to realize artifical Abelian and non-Abelian gauge potentials for ultracold atoms. I will give a pedagical introduction to this field and present our own proposal to achieve an analogous effect for quantized light (photons) propagating through an atomic gas. In this case, the dynamical equation for photons is equivalent to the Schroedinger equation for charged particles in two dimensions. The corresponding vector potential is completely determined by a set of classical light fields that are used to manipulate the atomic state. We suggest classical field configurations that generate potentials corresponding to a constant electric and a constant magnetic field. Furthermore we devise a scheme of fields that generates a vector potential of Aharonov-Bohm type which induces a topological phase shift for slow photons.