The fundamental properties of matter are generally well described in terms of the underlying symmetries of the system. However, the discovery of the quantized Hall conductivity marked the beginning of a new classification of phases of matter and phase transitions of materials: Topological insulators (TIs). At present, band theory models describe the physics of non-interacting topological insulators; nevertheless, the rich and still not well-understood connection between topology and interactions represent a new paradigm in modern condensed matter physics. In our project, we have developed an experimental setup to bridge this gap.
In this action, we have built the first Cesium quantum gas microscope in the Hubbard regime. Thanks to a novel transport scheme and a high numerical aperture objective we were able to obtain fluorescence images of single Cs atoms. As a proof-of-concept, we reached the strongly correlated regime by controlling the atomic interactions of our atomic cloud after loading the system in a square optical lattice (383.5 nm periodicity). In this fully controllable environment we have probed the superfluid-to-Mott insulator transition. To reach single-site resolution at the short lattice wavelength, we implemented machine learning techniques to extract the lattice occupation, overcoming the optical resolution limit. Overall, the results associated with this action will allow observing the physics of phase transitions, edge states, and site-to-site density and spin correlations. Our research establishes the starting point to study fascinating, yet poorly understood, topological states of matter in the presence of interactions. These systems are prominent building blocks for fault-free topological quantum computing.
