  We present a microscopic semi-analytical theory for the description of
organic molecules interacting strongly with a cavity mode. Exciton-vibration
coupling within the molecule and exciton-cavity interaction are treated on an
equal footing by employing a temperature-dependent variational approach. The
interplay between strong exciton-vibration coupling and strong exciton-cavity
coupling gives rise to a hybrid ground state, which we refer to as the lower
polaron polariton. Explicit expressions for the ground-state wave function, the
zero-temperature quasiparticle weight of the lower polaron polariton, the
photoluminescence line strength, and the mean number of vibrational quanta are
obtained in terms of the optimal variational parameters. The dependence of
these quantities upon the exciton-cavity coupling strength reveals that strong
cavity coupling leads to an enhanced vibrational dressing of the cavity mode,
and at the same time a vibrational decoupling of the dark excitons, which in
turn results in a lower polaron polariton resembling a single-mode dressed bare
lower polariton in the strong-coupling regime. Thermal effects on several
observables are briefly discussed.
