Towards strong linear and nonlinear light-matter interactions in hybrid nanostructures of a single molecule and a plasmonic nanocavity

Reaching strong coupling between a single molecule and a plasmonic nanocavity (PNC) at ambient conditions is important for many nanophotonic applications. Many efforts have been devoted towards such a goal. Here, we develop a semi-analytical method which can efficiently calculate the extinction spectrum of a general coupled system of a single molecule and a PNC. The field enhancement and the enhancement efficiency of a PNC are found to be crucial to obtain a clear large Rabi splitting. The bound for the coupling strength can be obtained correspondingly. Specifically, we find that a plasmonic raindrop dimer with a gap size of 1.5 nm can achieve strong coupling with a single common molecule of a transition dipole moment of \ensuremath{\sim}3.8 Debye. The raindrop dimer shows a better performance than the other common experimentally feasible plasmonic nanocavities. The case of a special nonlinear coupling where an additional peak appears at the Rabi splitting dip is also discussed. Our results pave the way for single-emitter quantum optics at ambient conditions.