Efficient simulation framework for modeling collective emission in ensembles of inhomogeneous solid-state emitters

TL;DR

This paper introduces an efficient simulation framework for modeling collective emission in disordered solid-state quantum emitter ensembles, capturing realistic inhomogeneities and enabling analysis of superradiance and spectral features.

Contribution

The framework uses a cumulant expansion to reduce computational complexity, allowing large-scale Monte Carlo simulations of disordered emitter ensembles with realistic inhomogeneities.

Findings

Superradiant emission occurs only with large emitter numbers and high quantum efficiency.

Strong near-field interactions suppress superradiant bursts compared to ideal Dicke superradiance.

Spectra show interaction-induced broadening and skewness in resonance peak distributions.

Abstract

An efficient simulation framework is proposed to model collective emission in disordered ensembles of quantum emitters. 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 (SiV$^{-}$) centers inside diamond. Incorporating spatial disorder and inhomogeneous broadening, we obtain statistically averaged responses over hundreds of SiV$^{-}$ clusters. These simulations reveal two signatures of collective behavior. First, dynamics of fully inverted clusters show that superradiant emission occurs only with sufficiently large emitter number 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, molecules, and quantum dots, thus providing a practical tool for analyzing collective behavior in realistic quantum systems.