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We benchmark a selection of semiclassical and perturbative dynamicstechniques by investigating the correlated evolution of a cavity-bound atomicsystem to assess their applicability to study problems involving stronglight-matter interactions in quantum cavities. The model system of interestfeatures spontaneous emission, interference, and strong coupling behaviour, andnecessitates the consideration of vacuum fluctuations and correlatedlight-matter dynamics. We compare a selection of approximate dynamicsapproaches including fewest switches surface hopping, multi-trajectoryEhrenfest dynamics, linearized semiclasical dynamics, and partially linearizedsemiclassical dynamics. Furthermore, investigating self-consistent perturbativemethods, we apply the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in thesecond Born approximation. With the exception of fewest switches surfacehopping, all methods provide a reasonable level of accuracy for the correlatedlight-matter dynamics, with most methods lacking the capacity to fully captureinterference effects.

Benchmarking Semiclassical and Perturbative Methods for Real-time Simulations of Cavity-Bound Emission and Interference