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arXiv:2512.08174

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

Zhou, Qingyi, Wu, Wenxin, Maryam Zahedian, Zongfu Yu, Choy, Jennifer T.

Published Dec 9, 2025• 0 citations
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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.

DOI
10.48550/arxiv.2512.08174

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Collective superradiant decay of a tightly packed inverted quantum emitter ensemble is among the most intensely studied phenomena in quantum optics. Since the seminal work of Dicke more than half a century ago, a plethora of theoretical calculations in quantum many-body physics have followed. Widespread experimental efforts range from the microwave to the X-ray regime. Nevertheless, accurate calculations of the time dynamics of the superradiant emission pulse still remain a challenging task requiring approximate methods for large ensembles. Here, we benchmark the cumulant expansion method for describing collective superradiant decay against a newly found exact solution. The application of two variants of the cumulant expansion exhibits reliable convergence of time and magnitude of the maximum emission power with increasing truncation order. The long-term population evolution is only correctly captured for low emitter numbers, where an individual spin-based cumulant expansion proves more reliable than the collective spin-based variant. Surprisingly, odd orders show unphysical behavior. At sufficiently high spin numbers, both chosen cumulant methods agree, but still fail to reliably converge to the numerically exact result. Generally, on longer time scales the expansions substantially overestimate the remaining population. While numerically fast and efficient, cumulant expansion methods need to be treated with sufficient caution when used for long-time evolution or reliably finding steady states.