Wave packet theory of dynamic stimulated Raman spectra in femtosecond pump-probe spectroscopy.

The quantum theory for stimulated Raman spectroscopy from a moving wave packet using the third-order density matrix and polarization is derived. The theory applies, in particular, to the new technique of femtosecond broadband stimulated Raman spectroscopy (FSRS). In the general case, a femtosecond actinic pump pulse first prepares a moving wave packet on an excited state surface which is then interrogated with a coupled pair of picosecond Raman pump pulse and a femtosecond Raman probe pulse and the Raman gain in the direction of the probe pulse is measured. It is shown that the third-order polarization in the time domain, whose Fourier transform governs the Raman gain, is given simply by the overlap of a first-order wave packet created by the Raman pump on the upper electronic state with a second-order wave packet on the initial electronic state that is created by the coupling of the Raman pump and probe fields acting on the molecule. Calculations are performed on model potentials to illustrate and interpret the FSRS spectra.