Localization and delocalization in kicked quantum matter

A sizable fraction of the vast field of condensed matter physics consists of the exploration of the effects of spatial periodicity on quantum mechanics. It is now widely recognized that the effects of temporal periodicity give rise to a related array of phenomena, and that the interplay of temporal and spatial periodicity with many-body interactions creates particularly rich new possibilities. In this talk I will describe some recent experiments on kicked quantum matter, including a study of many-body delocalization in an interacting ensemble of kicked quantum rotors, the first experimental observation of the recently-predicted "quantum boomerang effect," and realization of a kicked quasicrystal which exhibits an extended multifractal phase intermediate between localized and delocalized regimes. The results illuminate a variety of phenomena ranging from the interplay of ergodicity and localization to fractal wavefunctions to new techniques of quantum control.