Parametric instabilities in shaken optical lattices

Shaking optical lattices offers an efficient method to devise artificial gauge fields and topological bands for ultracold gases, as was demonstrated through the realisations of the Hofstadter and Haldane models. Adding inter-particle interactions to these systems is expected to lead to strongly-correlated topological states. However, the interplay between interactions and time-periodic drives typically triggers instabilities and heating, hence potentially ruling out the possibility of accessing such states in experiments. I will discuss the early-stage parametric instabilities that occur in systems of periodically-driven Bose-Einstein condensates in optical lattices. I will present a theory, which simply describes these instabilities in terms of abstract parametric oscillators, and will illustrate its general predictions, such as the behaviour of the resulting instability rates and the properties of the most unstable modes. Within this framework, clear signatures of these early-stage instabilities were identified, which can be probed experimentally using time-of-flight imaging. In collaboration with the group of I. Bloch, we have recently revealed these signatures in a BEC experiment.