Abstract
We investigate the influence of the F\"orster interaction between semiconductor quantum dots on the quantum light emission in proximity to a metal nanoparticle. A fully quantized theory for the excitons in the quantum dots, the plasmons in metal nanoparticles, and their interaction is used. Using an operator equation approach, we derive the Rayleigh emission spectra and the corresponding quantum statistics of the emission. For both observables, we investigate the influence of the exciton-plasmon coupling and the F\"orster interaction between the semiconductor quantum dots. Surprisingly, the influence of the F\"orster interaction is barely seen in the Rayleigh spectra whereas the second-order correlation function is strongly affected. In particular, we show that the F\"orster interaction is capable to tune the emission statistics: depending on the system parameters, the F\"orster interaction between the semiconductor quantum dots induces strong bunching and antibunching of the emission, respectively. We analyze the quasiparticles formed in the coupled system to explain the observed features.
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