Engineering Many-Body Dynamics with Quantum Light Potentials and Measurements

Interactions between many-body atomic systems in optical lattices and light in cavities induce long-range and correlated atomic dynamics beyond the standard Bose-Hubbard model, due to the global nature of the light modes. We characterise these processes, and show that uniting such phenomena with dynamical constraints enforced by the backaction resultant from strong light measurement leads to a synergy that enables the atomic dynamics to be tailored, based on the particular optical geometry, exploiting the additional structure imparted by the quantum light field. This leads to a range of tunable effects such as long-range density-density interactions, perfectly correlated atomic tunnelling, superexchange, and effective pair processes. We further show that this provides a framework for enhancing quantum simulations to include such long-range and correlated processes, including reservoir models and dynamical global gauge fields.