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 in this area, including realization of a many-body kicked quantum rotor with tunable interparticle interactions, and exploration of Aubry-André localization in a kicked lattice which is "almost always" periodic. The results illuminate a variety of phenomena ranging from the interplay of ergodicity and localization to new techniques of quantum control. Time permitting, I will present a very recent observation of the “quantum boomerang effect,” a fundamental feature of Anderson-localized matter which was only recently theoretically predicted and has not to our knowledge been observed before.
