Abstract: In the past decade, quantum simulators have increased in their power and scope, offering exquisite dynamical control of tens or even hundreds of individual atoms. Concurrently, a topological revolution in our understanding of electronic band structures has taken place, driven by the discovery of topological insulators, graphene and other topological materials. Remarkably, these advances can be connected --- the dynamics of driven few level systems can be described using band structures in "synthetic dimensions," one per driving tone. Topological order in the synthetic band structure then leads to quantized dynamical responses in the quantum simulator.
In this talk, I will use a unifying frequency lattice construction to reveal nonadiabatic topological responses in quasiperiodically driven systems. We will find that quasi-periodically driven qubits already exhibit topologically distinct dynamical phases, and that a 2-tone driven inhomogenous wire can function as a quantized energy pump at any temperature. The latter system provides one of the few examples of many-body localization protected order that is absolutely stable. I will argue that the quantized energy pumping regime is accessible in near-term optical and microwave cavity-QED experiments, and that furthermore, it is useful to prepare highly excited non-classical cavity states.
Location: ATL 4402