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.
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