We benchmark a selection of semiclassical and perturbative dynamics techniques by investigating the correlated evolution of a cavity-bound atomic system to assess their applicability to study problems involving strong light-matter interactions in quantum cavities. The model system of interest features spontaneous emission, interference, and strong coupling behavior and necessitates the consideration of vacuum fluctuations and correlated light-matter dynamics. We compare a selection of approximate dynamics approaches including fewest switches surface hopping (FSSH), multitrajectory Ehrenfest dynamics, linearized semiclassical dynamics, and partially linearized semiclassical dynamics. Furthermore, investigating self-consistent perturbative methods, we apply the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the second Born approximation. With the exception of fewest switches surface hopping, all methods provide a reasonable level of accuracy for the correlated light-matter dynamics, with most methods lacking the capacity to fully capture interference effects.

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We have verified that in the parameter regimes studied in this work including the quadratic term into adjusted eigenstates, according to the Hamiltonian ĤA+α=12N12(λαμ^)2, has no qualitative influence on the time-evolution of the observables associated with the cavity-bound emission process.

79.

As the exponential scaling permits the inclusion of higher photon states for the given model, we ensured convergence investigating a related 3-level system based on a screened Hydrogen atom with 1/10 of the atomic binding potential coupled to the 100 lowest harmonics of the former cavity. Including the three-photon states resulted in marginal numerical changes such that we deem the selected two-photon states sufficient for the investigated model.

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