  Plasmonic dimer cavities can induce extreme electric-field hot spots that
allow one to access ultrastrong coupling regimes using Raman-type spectroscopy
on single vibrating molecules. Using a generalized master equation, we study
resonant Raman scattering in the strong coupling regime of cavity-QED, when
also in the vibrational ultrastrong coupling regime, leading to "phonon-dressed
polaritons". The master equation rigorously includes spectral baths for the
cavity and vibrational degrees of freedom, as well as a pure dephasing bath for
the resonant two level system, which play a significant role. Employing
realistic parameters from gold dimer cavity modes, we investigate the emission
spectra in several characteristic strong-coupling regimes, leading to extremely
rich spectral resonances due to an interplay of phonon-modified polariton
states and bath-induced resonances.
