  We investigate the quantum-optical properties of the light emitted by a
nanoparticle-on-mirror cavity filled with a single quantum emitter. Inspired by
recent experiments, we model a dark-field set-up and explore the photon
statistics of the scattered light under grazing laser illumination. Exploiting
analytical solutions to Maxwell's equations, we quantize the nanophotonic
cavity fields and describe the formation of plasmon exciton polaritons (or
plexcitons) in the system. This way, we reveal that the rich plasmonic spectrum
of the nanocavity offers unexplored mechanisms for nonclassical light
generation that are more efficient than the resonant interaction between the
emitter natural transition and the brightest optical mode. Specifically, we
find three different sample configurations in which strongly antibunched light
is produced. Finally, we illustrate the power of our approach by showing that
the introduction of a second emitter in the platform can enhance photon
correlations further.
