Vibrational relaxation and dephasing of two-phonon bound states in molecular crystals

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Abstract
The vibrational relaxation and dephasing of two-phonon states in the region of combinations or overtones of intramolecular vibrations in molecular crystals are discussed. The model Hamiltonian used includes (1) a harmonic part comprehensive of two-body intermolecular interactions that are responsible for the phonon dispersion; (2) a single-site intramolecular anharmonic term that can give rise to the formation of resonances or bound states; (3) cubic and quartic terms coupling internal modes to the lattice phonons. These latter terms give rise to depopulation and dephasing processes, respectively, of the bound states. Explicit expressions for the shift and linewidth of the bound states are obtained. It is shown that the relaxation processes are mixed processes involving both the intra- and the intermolecular anharmonicity. The relaxation follows multistage routes. Besides contributions due to scattering diagrams of single-phonon lines there are relaxation processes that are peculiar to the bound states. Calculations of the shift and linewidths of bound states have been performed on a model system and the general trend of the shift and linewidth as a function of temperature and of the strength of anharmonic interactions has been studied. It is shown that the contribution of depopulation and dephasing processes can be comparable. The model calculations are discussed in connection with available experimental results.