Floquet-Band Engineering of Shaken Bosonic Condensates

Abstract: Optical control and manipulation of cold atoms has become an important topic in condensed matter. Widely employed are optical lattice shaking experiments which allow the introduction of artificial gauge fields, the design of topological bandstructures, and more general probing of quantum critical phenomena. Here we develop new numerical methods to simulate these periodically driven systems by implementing lattice shaking directly. As a result we avoid the usual assumptions associated with a simplified picture based on Floquet dynamics. A demonstrable success of our approach is that it yields quantitative agreement with experiment, including Kibble-Zurek scaling. Importantly, we argue that because their dynamics corresponds to an effective non-linear Schr\"{o}dinger equation, these particular superfluid studies present a unique opportunity to address how general Floquet band engineering is affected by interactions. In particular, interactions cause instabilities at which the behavior of the system changes dramatically.