Cooperative optical response of two-dimensional atomic arrays in solids

We develop a model describing long-range atom-atom interactions in a two-dimensional periodic or a-periodic lattice of optical centers considering spectral and spatial broadening effects. Using both analytical and numerical Green's function techniques, we develop a mathematical framework to describe effective atom-atom interactions and collective behaviors in the presence of disorder. This framework is applicable to a broad range of quantum systems with arbitrary lattice geometries, including cold atoms, solid-state photonics, and superconducting platforms. The model can be used, for example, to scalably design quantum optical elements, e.g. a quantum lens, harnessing atomistic engineering (e.g. via ion implantation) of collective interactions in materials to enhance quantum properties at scale.