A quantum simulator has the potential to deepen our understanding of complex quantum dynamics in a way that could be transformative for other fields of research, particularly condensed-matter physics. This project will build on new possibilities in our quantum-gas microscope setups [1] to generate arbitrary light potentials at the single-lattice-site scale [2]. These light patterns are generated by a spatial light modulator and projected onto the atoms with the high-resolution microscope, thereby creating repulsive or attractive light potentials with sub-lattice-spacing resolution.

We will use this technique to tailor the tunnel coupling between lattice sites, creating double-well or ladder structures, or disordered light potentials [3]. A regular pattern of repulsive potentials can be used to block, e.g., the centre site in each 3 x 3 subcell of a square lattice, forming a Lieb lattice. These lattices exhibit interesting properties such as flat bands, localization and edge states. Based on model calculations, we will use the quantum-gas microscope in the first instance to prepare and see the stability of the edge states. Quantitative studies could involve measurements of the corner distance as a function of time, or the time evolution of the probabilities to find certain edge states. Further studies will include lattice geometries of a higher complexity such as Lieb-lattice chains and diamond chains. 

In a second strand of work, within the framework of a recent EPSRC-funded project, we will investigate whether ordered states can be generated from non-equilibrium dynamics well above the phase transition temperature. Such effects have recently been observed in the form of short-lived superconducting states in transition-metal oxides far above their equilibrium critical temperature. However, to date, there exists no basic quantitative many-body theory describing whether and how such dynamic orders can emerge in 2D and 3D, due to the challenge in computing the real-time dynamical evolution in these systems. In collaboration with our theory colleagues, we aim to investigate whether superconducting, superfluid, and insulating orders can be induced above their equilibrium critical temperatures through out-of-equilibrium dynamics.