Probing quantum dynamics in strongly-driven optical lattices

Degenerate quantum gases in modulated optical lattices provide a near-ideal testbed for the experimental study of quantum matter driven far from equilibrium. I will discuss a sequence of recent experimental results along these lines: flexible Floquet engineering of band structure and transport properties, observation of relativistic harmonic motion, detailed experimental mapping of the properties of prethermal Floquet matter, and a measurement of anomalously slow heating in a rapidly driven interacting gas. Time permitting, I will discuss some recent results on driven quasicrystals and indicate possible future directions of research.