Strongly correlated matter with ultracold atoms: From the Hubbard model to Z₂ lattice gauge theory

Ultracold atoms in optical potentials have made great progress over the past few years, and provide the most promising platform for quantum simulations of strongly correlated quantum matter. Indeed, these platforms have already begun to study some of the most challenging open problems in theoretical physics, including the search for the origin of high-temperature superconductivity in the Fermi-Hubbard model and the realization of quantum spin liquids hosting non-trivial topological excitations. I will start this talk by giving a brief overview how far the quantum simulation of the doped Fermi-Hubbard model has already come. Then I will explain how such doped quantum magnets can, in some instances, be directly mapped to Z₂ lattice gauge theories with dynamical matter. On the one hand this allows for an elegant description of hidden string order in these systems and lends a natural explanation to stripe phases. On the other hand, it motivates the search for meson-type excitations - a hallmark feature of lattice gauge theories - in a larger class of doped quantum magnets. I will present recent numerical results pointing to a rich emergent structure of charge carriers in strongly correlated quantum materials, and discuss how these theoretical predictions can result in direct experimental verifications using ultracold atoms. I will close the talk with an outlook how a paradigmatic Z₂ lattice gauge theory with dynamical matter can be realized with current technology in 2D Rydberg arrays.