A numerically exact solution to the many emitter -cavity problem as an open many body system is presented. The solution gives access to the full, nonperturbative density matrix and thus the full quantum statistics and quantum correlations. The numerical effort scales with the third power in the number of emitters. Notably the solution requires none of the common approximations like good/bad cavity limit. As a first application the recently discussed concept of coherent surface plasmon amplification -spaser -is addressed: A spaser consists of a plasmonic nanostructure that is driven by a set of quantum emitters. In the context of laser theory it is a laser in the (very) bad cavity limit with an extremely high light matter interaction strength. The method allows us to answer the question of spasing with a fully quantized theory.

Hybrid nanosystems composed of excitonic and plasmonic constituents can have different properties than the sum of of the two constituents, due to the exciton-plasmon interaction. Here, we report on a flexible model system based on colloidal nanoparticles that can form hybrid combinations by self-organization. The system allows us to tune the interparticle distance and to combine nanoparticles of different sizes and thus enables a systematic investigation of the exciton-plasmon coupling by a combination of optical spectroscopy and quantum-optical theory. We experimentally observe a strong influence of the energy difference between exciton and plasmon, as well as an interplay of nanoparticle size and distance on the coupling. We develop a full quantum theory for the luminescence dynamics and discuss the experimental results in terms of the Purcell effect. As the theory describes excitation as well as coherent and incoherent emission, we also consider possible quantum optical effects. We find a good agreement of the observed and the calculated luminescence dynamics induced by the Purcell effect. This also suggests that the self-organized hybrid system can be used as platform to address quantum optical effects.

We investigate the influence of the Förster 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 Förster interaction between the semiconductor quantum dots. Surprisingly, the influence of the Förster interaction is barely seen in the Rayleigh spectra whereas the second-order correlation function is strongly affected. In particular, we show that the Förster interaction is capable to tune the emission statistics: depending on the system parameters, the Förster 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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