Engineering Floquet Hamiltonians in Cold Atom Systems

In this talk I will first give a brief overview of the Floquet theory, describing periodically driven systems. Then I will introduce the concept of the high-frequency expansion and will show how it generalizes the celebrated Schrieffer-Wolff transformation to driven systems. Using these tools I will illustrate how one can engineer non-trivial interacting Hamiltonians mostly in the context of cold atom systems and discuss some experimental examples. In the end I will talk about issues of heating and adiabaticity and show that there are very strong parallels between Floquet systems and disordered systems. In particular, I will argue that the heating transition is closely analogous to the many-body localization transition.