ended after 1st funding period

In this project, we use neutral atoms in one- and two-dimensional optical lattices to investigate the topological properties underlying discrete-time quantum walks (DTQWs). Like in condensed matter physics, where insulators with nontrivial topological phases exist, DTQWs also exhibit in their eigenstates a rich topological structure. This project focuses on the measurement of topological properties of DTQWs in lower dimensionality. We study the so-called bulk-boundary correspondence principle in these systems by undertaking two complementary approaches: first, a detection of topologically protected edge states at the boundary between distinct topological phases, and second, an identification of topological invariants associated to the bulk by interferometric measurement of geometric phases. Our investigation shows that DTQWs possess a richer topology in comparison to that observed in conventional materials: we classify the distinct topological phases using the Floquet theory suited for periodically-driven systems. This project sets the stage for future quantum walk experiments, which will explore topological phenomena in the presence of particle-particle interactions as well as of dissipative processes.