Engineering Collective Light-Atom Interactions in Solid State

Collective interactions between atoms have been proposed as one method to improve the performance of photonic quantum technologies. In solids, an ensemble of atoms exhibits inhomogeneous broadening that allows high-bandwidth interactions to be achieved in small crystals. Using optical resonators to reach the strong-coupling regime, in this case, limits the interaction bandwidth imposed by the resonator linewidth. Therefore, exploring interaction mechanisms that enable strong light-atom coupling over a wide range of frequencies is desirable to advance quantum photonic technology and achieve broadband control of quantum optical information. We present developments in the theory of solid-state systems to model collective emissions in an array of atoms coupled to a 1D ring waveguide, focusing on the impact of array properties on collective emissions. We expand upon prior results by considering the influence of an optical cavity and inhomogeneous broadening of the atoms. In particular, these effects are realized in computation of the operators associated with the system and their application to correlation functions.