  Molecules constitute compact hybrid quantum optical systems that can
interface photons, electronic degrees of freedom, localized mechanical
vibrations and phonons. In particular, the strong vibronic interaction between
electrons and nuclear motion in a molecule resembles the optomechanical
radiation pressure Hamiltonian. While molecular vibrations are often in the
ground state even at elevated temperatures, one still needs to get a handle on
decoherence channels associated with phonons before an efficient quantum
optical network based on opto-vibrational interactions in solid-state molecular
systems could be realized. As a step towards a better understanding of
decoherence in phononic environments, we take here an open quantum system
approach to the non-equilibrium dynamics of guest molecules embedded in a
crystal, identifying regimes of Markovian versus non-Markovian vibrational
relaxation. A stochastic treatment based on quantum Langevin equations predicts
collective vibron-vibron dynamics that resembles processes of sub- and
superradiance for radiative transitions. This in turn leads to the possibility
of decoupling intramolecular vibrations from the phononic bath, allowing for
enhanced coherence times of collective vibrations. For molecular polaritonics
in strongly confined geometries, we also show that the imprint of
opto-vibrational couplings onto the emerging output field results in effective
polariton cross-talk rates for finite bath occupancies.
