  Recently, systems with strong coupling between electronic and vibrational
degrees of freedom attract a great attention. In this work, we consider the
transient dynamics of the system consisting of strongly coupled vibron and
exciton driven by external monochromatic field. We show that under coherent
pumping, polarization of exciton exhibits complex quantum dynamics which can be
divided into three stages. At the first stage, exciton oscillations at its
eigenfrequency relax due to the transition to set of shifted Fock states of
vibrons. We demonstrate that these shifted Fock states play the role of an
effective reservoir for the excited exciton state. The time of relaxation to
this reservoir depends on exciton-vibron coupling. At the second stage,
excitation, transferred to the reservoir of the vibronic shifted states at the
first stage, returns into electronic degrees of freedom and revival of
oscillations at exciton eigenfrequency appears. Thus, the dynamics of molecular
polarization exhibit collapses and revivals. At the final stage, these
collapses and revivals dissipate and polarization exhibits Rayleigh response at
the frequency of the external field. Discovered collapses and revivals manifest
in radiation spectrum as multiple splitting of the spectral line near the
exciton transition frequency.
