Coupling $N$ identical emitters to the same field mode is well-established method to enhance light matter interaction. However, the resulting $\sqrt{N}$ boost of the coupling strength comes at the cost of a "linearized" (effectively semi-classical) dynamics. Here, we instead demonstrate a new approach for enhancing the coupling constant of a \textit{single} quantum emitter, while retaining the nonlinear character of the light-matter interaction. We consider a single quantum emitter with $N$ nearly degenerate transitions that are collectively coupled to the same field mode. We show that in such conditions an effective Jaynes-Cummings model emerges, with a boosted coupling constant of order $\sqrt{N}$. The validity and consequences of our general conclusions are analytically demonstrated for the instructive case $N=2$. We further observe that our system can closely match the spectral line shapes and photon autocorrelation functions typical of Jaynes-Cummings physics, hence proving that quantum optical nonlinearities are retained. Our findings match up very well with recent broadband plasmonic nanoresonator strong-coupling experiments and will therefore facilitate the control and detection of single-photon nonlinearities at ambient conditions.

Improved abstract and introduction. 12 pages, 6 figures, comments still welcome!