Konwersatorium im. Leopolda Infelda

I will present a review of recent developments of a new trend in the physics of ultracold atoms, that concerns studies of the behavior ofquantum degenerate atomic clouds in presence of quantum gauge fields. I will discuss various methods of generating such artificial gaugefields, with special emphasis on the non-Abelian ones. I will then discuss few examples of effects and phenomena expected to occur insuch non-Abelian gauge fields. These include: anomalous quantum Hall effect, emergence of Dirac fermions, novel types of topologicalisolators, etc.