  Quantum plasmonics extends cavity quantum electrodynamics (cQED) concepts to
the nanoscale, taking benefit from the strongly subwavelength confinement of
the plasmon modes supported by metal nanostructures. In this work, we describe
in detail collective strong coupling to a plasmonic nanocavity. Similarities
and differences to cQED are emphasized. We notably observe that the Rabi
splitting can strongly deviate from the standard $\sqrt{N_e}\Delta \Omega_1$
law, where $N_e$ is the number of emitters and $\Delta \Omega_1$ the Rabi
splitting for a single emitter. In addition, we discuss the collective Lamb
shift and the role of quantum corrections to the emission spectra.
