Quantum Materials and Multimode Photonics in Twisted Optical Cavities

In order to put novel condensed matter physics theories to the test, we turn to simulations and experiments. However, computer simulation is not always feasible due to inherent computational obstructions or the demand for excessive computational resources to calculate the dynamics of many particles, for example. Where computer simulators fail, we turn to "quantum simulators," or experimental model systems. Within these poke-able model systems, we need only set up the experimental conditions that mirrors the physics of interest, then glean information based on measurable quantities of the system. Examples of quantum simulation platforms include trapped ions, cold atoms in optical lattices, superconducting circuits, nitrogen-vacancy centers, and interacting photons in optical cavities—the platform of the work presented in this thesis. This thesis describes the quantum simulation of topologically ordered quantum materials made of light using a twisted optical cavity and Rydberg polaritons. This platform—based in atoms and cavities—additionally enables studies based in the manipulation of atoms using light, leading to the optical mode conversion of photons at high efficiency. The work presented in this thesis provides broad prospects for the study of topologically-ordered states and spatiotemporal modulation of optical susceptibility as a tool for quantum information as well as atomic, molecular, and optical (AMO) systems.