  It is known that the more tractable Markovian models of coupling suited for
weak interactions may overestimate the Rabi frequency notably when applied to
the strong-coupling regime. Here, a more significant consequence of the
non-Markovian interaction between a photon emitter and dissipating matter such
as resonant plasmonic nanoparticles is described. A large increase of radiative
decay and a diminished non-radiative loss is shown, which unravels the origin
of unexpected large enhancements of surface-enhanced-Raman-spectroscopy (SERS),
as well as the anomalous enhancements of emission due to extremely small fully
absorbing metal nanoparticles less than 10 nm in dimensions. We construct the
mixture of pure states of the coupled emitter-nanoparticle system, unlike
conventional methods that rely on the orthogonal modes of the nanoparticle
alone.
