A quantum/semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested and applied to simulate and interpret ultrafast optical signals. Linear wave-packet interferometry and time-resolved coherent anti-Stokes Raman scattering signals for a model of molecular iodine in a 2D krypton lattice are calculated and used to study the vibrational decoherence and energy dissipation of iodine molecules in condensed media. The total wave function of the whole model is approximately obtained instead of a reduced system density matrix, and therefore the theory enables us to analyze the behavior and the role of the host matrix in quantum dynamics.This dissertation includes previously published co-authored material.
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