Abstract
In this talk I will give an introduction to the emerging field of topological phenomena in periodically-driven quantum systems. Here, robust phenomena are identified through analogies between the Floquet spectra of driven systems and the band structures of static Hamiltonians. Intriguingly, these works have revealed that the topological characterization of driven systems is even richer than that of static systems. I will review the key ideas behind the topological characterization of band structures for non-driven systems, and discuss the similarities and differences with the driven case. In driven systems in two dimensions (2D), we will see that robust chiral edge states can appear even though the Chern numbers of all the bulk Floquet bands are zero. Through explicit examples I will show how this behavior arises, and will present a new topological invariant that yields the correct edge state structure in the driven case. Formulations in both the time and frequency domains afford complementary insight into the origins of the "anomalous" spectra which arise in driven systems. Possibilities for realizing these phenomena in solid state and cold atomic systems will be discussed.
Coffee and tea will be served 20 minutes prior to the seminar.