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Collective light emission and multi-qubit dynamics of solid-state quantumemitters are affected both by their coupling to the light field and to latticevibrations. The effect of phonons on quantum emitters is twofold: polaronformation is described by ultrafast non-markovian dynamics, while slowerdephasing is well described by exponential decay. Both temperature-dependentprocesses will affect collective emission and entanglement, but they areusually not modeled, probably due to a lack of efficient methods especially formore than two emitters. So here we propose and compare two methods: the firstmethod concatenates the fast and slow phonon dynamics, and the second is thepolaron method. For a single quantum emitter, we show that the dynamicalequations are identical in both methods, while predictions for two or moreemitters also agree very well. Both of our methods incorporate non-markoviandynamics due to phonons demonstrating the temperature sensitivity of thecollective photon emission. Utilizing a simplified markovian model instead maynot be accurate enough especially for quantum information applications: forexample, we show how the markovian model may considerably overestimate thetwo-emitter concurrence, except at very low temperatures. Our concatenation andpolaron methods can be applied to an arbitrary number and type of quantumemitters, and beyond the bulk GaAs environment that we consider here.Especially the concatenation method can take phonon effects into account at thesame computational cost as modelling the emitter-photon interaction alone.Finally, we present approximate analytical expressions for the collectiveemission spectrum for N emitters on a one-dimensional chain.

Collective photon emission in solid state environments: Concatenating non-markovian and markovian dynamics