Quantum description and emergence of nonlinearities in strongly coupled single-emitter nanoantenna systems

Realizing strong coupling between a single quantum emitter (QE) and an optical cavity is of crucial importance in the context of various quantum optical applications. Although Rabi splitting of single quantum emitters coupled to high-Q classical cavities has been reported in numerous configurations, attaining single emitter Rabi splitting with a plasmonic nanostructure remains a challenge. In particular, strong coupling at the single QE regime would open the path for the realization of single-photon nonlinearities. In this paper, we derive a plasmon quantization procedure for systems consisting of a single QE located in the gap of a nanoantenna. This procedure leads to the description of the quantum dynamics by a master equation for the state of the QE and the quantized plasmonic modes, which is crucial to demonstrate the emergence of single-photon nonlinearities. We investigate numerically the optical response and the resulting Rabi splitting in metallic nanoantennas and find the optimal geometries for the emergence of the strong-coupling regime with single QEs. Finally, we demonstrate the saturation of hybridized modes for a chosen configuration. Our results will be useful for implementation of realistic quantum plasmonic nanosystems involving single QEs at room temperature.