Theory of vibrational coherence and population decay in isotopically mixed crystal

A simple theoretical description of vibrational coherence decay in isotopically mixed molecular crystals at low temperatures is presented. Dephasing due to impurity scattering is shown to be a slower than exponential decay process for optically excited vibrons lying near band singularities, by analogy with the theory of coherence loss in weakly disordered crystals [I. I. Abram and R. M. Hochstrasser, J. Chem. Phys. 72, 3617 (1970)]. When the nature of the initially excited state is properly taken into account, the rate constant for population decay displays an unexpected interplay between trapping and self-relaxation which can, in principle, lead to a nonmonotonic dependence of the relaxation rate with impurity concentration. Our results are related to recent time resolved CARS measurements in low temperature molecular crystals.