Ultrafast pump-probe spectroscopy: femtosecond dynamics in Liouville space

A theory for ultrafast pump-probe spectroscopy is developed using a correlation function description of molecular nonlinear optical processes which is based on the density matrix and its evolution in Liouville space. The Liouville space description applies to isolated small molecules as well as complex systems in condensed phases. We identify a condition, called ultrafast dephasing, which allows the probe absorption to be written in terms of an intuitive picture of instantaneous preparation, field-free evolution, and instantaneous detection. The probe absorption is calculated by following a phase-space doorway function which is prepared by the pump, propagates for a specified delay, and is finally projected into a window function which depends on the probe frequency. We find that the doorway and window functions have well-known classical limits: the delta functions in coordinate appearing in the classical Condon approximation. The deviation of the doorway and window functions from their classical limits is a direct and visual measure of the importance of quantum corrections in pump-probe spectroscopy. The signal consists of a sequential term and a tunneling (coherent) term which are formally analogous to fluorescence and Raman line shapes, respectively. Application is made to the femtosecond photodissociation of ICN, where the importance of quantum corrections and the tunneling term is assessed. The role of dephasing processes and the relation to other spectroscopic techniques related to the nonlinear susceptibility χ⁽³⁾ are discussed.