Predicting Statistical Signatures of Collective Emission in Disordered Color Center Ensembles

ABSTRACT An efficient simulation framework is proposed to model collective emission in disordered ensembles of color centers. Using a cumulant expansion approach, the computational complexity scales polynomially as opposed to exponentially with the number of emitters, enabling Monte Carlo sampling over a large number of realizations. The framework is applied to model negatively charged silicon‐vacancy () centers inside diamond. Incorporating spatial disorder and inhomogeneous broadening, we obtain statistically averaged responses over hundreds of clusters. These simulations reveal two signatures of collective behavior. First, the dynamics of fully inverted clusters show that superradiant emission occurs only with sufficiently large emitter numbers and high quantum efficiency. Unlike ideal Dicke superradiance, the burst is substantially suppressed by strong near‐field dipole–dipole interaction, consistent with existing theoretical predictions. Second, under continuous‐wave excitation, we compute photoluminescence‐excitation spectra, which exhibit interaction‐induced broadening in the distribution of resonance peaks. The corresponding density of states also displays a non‐zero skewness. Overall, by incorporating realistic inhomogeneities in emitter clusters, our framework is able to predict statistics for disordered ensembles that can be compared to experiments directly. Our approach generalizes to other types of emitters, including atoms and quantum dots, thus providing a practical tool for analyzing collective behavior in realistic quantum systems.