Statistical Theory of a Quantum Emitter Strongly Coupled to Anderson-Localized Modes

A statistical theory of the coupling between a quantum emitter and Anderson-localized cavity modes is presented based on a dyadic Green's function formalism. The probability of achieving the strong light-matter coupling regime is extracted for an experimentally realistic system composed of InAs quantum dots embedded in a disordered photonic crystal waveguide. We demonstrate that by engineering the relevant parameters that define the quality of light confinement, i.e., the light localization length and the loss length, strong coupling between a single quantum dot and an Anderson-localized cavity is within experimental reach. As a consequence, confining light by disorder provides a novel platform for quantum electrodynamics experiments.