  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.
