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The solution to Maxwell-Bloch systems using an integral-equation-based framework has proven effective at capturing collective features of laser-driven and radiation-coupled quantum dots, such as light localization and modifications of Rabi oscillations [1]. Importantly, it enables observation of the dynamics of each quantum dot in large ensembles in a rigorous, error-controlled, and self-consistent way without resorting to spatial averaging. Indeed, this approach has demonstrated convergence in ensembles containing up to 10 4 interacting quantum dots [1]. Scaling beyond 10 4 quantum dots tests the limit of computational horsepower, however, due to the O(N t N 2 s ) scaling (where N t and N s denote the number of temporal and spatial degrees of freedom). In this work, we present an algorithm that reduces the cost of analysis to O(N t N s log 2 N s ). While the foundations of this approach rely on well-known particle-particle/particle-mesh and adaptive integral methods, we add refinements specific to transient systems and systems with multiple spatial and temporal derivatives. Accordingly, we offer numerical results that validate the accuracy, effectiveness and utility of this approach in analyzing the dynamics of large ensembles of quantum dots.

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We introduce a computational Maxwell-Bloch framework for investigating out of equilibrium optical emitters in open cavity-less systems. To do so, we compute the pulse-induced dynamics of each emitter from fundamental light-matter interactions and self-consistently calculate their radiative coupling, including phase inhomogeneity from propagation effects. This semiclassical framework is applied to open systems of quantum dots with different density and dipolar coupling. We observe that signatures of superradiant behavior, such as directionality and faster decay, are weak for systems with extensions comparable to λ/2. In contrast, subradiant features are robust and can produce long-term population trapping effects. This computational tool enables quantitative investigations of large optical ensembles in the time domain and could be used to design new systems with enhanced superradiant and subradiant properties.