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Stochastic Liouville Equations for Femtosecond Stimulated Raman Spectroscopy

Electron and vibrational dynamics of molecules are commonly studied by subjecting them to two interactions with a fast actinic pulse that prepares them in a nonstationary state and after a variable delay period $T$, probing them with a Raman process induced by a combination of a broadband and a narrowband pulse. This technique known as femtosecond stimulated Raman spectroscopy (FSRS) can effectively probe time resolved vibrational resonances. We show how FSRS signals can be modeled and interpreted using the stochastic Liouville equations (SLE) originally developed for NMR lineshapes. The SLE provides a convenient simulation protocol that can describe complex dynamics due to coupling to collective coordinates at much lower cost that a full dynamical simulation. The origin of the dispersive features which appear when there is no separation of timescales between vibrational variations and dephasing is clarified.