Density matrix calculation of population transfer between vibrational levels of Na₂ by stimulated Raman scattering with temporally shifted laser beams

We compare the results of full density matrix calculations with recently reported experimental results describing the population transfer in Na ₂ using Raman scattering with the fundamental laser beam temporally shifted relative to the Stokes laser beam. Our calculations confirm the conclusion that almost total transfer of the population into the terminal level of the Raman transition can be achieved when the laser frequencies are tuned to resonance and the fundamental laser beam is temporally delayed relative to the Stokes shifted laser beam but still partially overlapping it. We analyze our results when the frequencies of the lasers are tuned off-resonance as a function of the Rabi frequencies and the detuning, and compare with experimental and theoretical results. The alignment of the terminal level as a function of time displacement of the Stokes and pump beams is predicted.