Disorder and Interactions in Topological Floquet Systems

This project aims at studying the topological properties of ultracold atoms in a periodically-driven honeycomb optical lattice in the presence of disorder and interactions.

It relies on an already-existing experimental setup that can routinely create topological Floquet phases with weakly-interacting bosonic potassium atoms.

The development of several technical tools will allow for the investigation of yet-unexplored topological phases of matter and bring solutions to the inherent heating due to the periodic driving.A first task is the direct observation of topological edge states and the realization of a Chern number 2 topological phase.

This requires the implementation of a box potential and a better control of the laser beams providing the optical lattice.

It will provide for the first time a complete picture of the bulk-edge correspondence and of the phase diagram of Floquet systems.A second set of experiments involves the setting of a disorder potential, and will bring into light the interplay between topology and disorder in periodically-driven systems.

In particular the existence of disorder-induced topological phases such as the anomalous Floquet Anderson insulator will be demonstrated.

In this phase, the bulk is fully localized and topologically-protected edge states do exist.In the last part of the project, a vertical confinement will be implemented, and it will be combined with the tuning of interactions with a Feshbach resonance to bring the system to a strongly-interacting regime.

There, interesting phases of matter can be explored, such as a fermionization of the gas loaded in a so-called moat band.

More strikingly, a topological many-body-localized Floquet phase can be realized, where the strongly-interacting particles undergo a periodic driving, but are resilient to heating while supporting a topological edge state.