Acceleration techniques for semiclassical Maxwell-Bloch systems: An application to discrete quantum dot ensembles'

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. 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 (Glosser et al., 2017). Scaling beyond 10(4) quantum dots tests the limit of computational horsepower, however, due to the O(NtNs2) 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(NtNs 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. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The integral-equation-based framework for solving Maxwell-Bloch systems effectively captures collective features of quantum dots, demonstrating convergence and accuracy in analyzing large ensembles of interacting quantum dots.