Precise Control of Molecular Dynamics with a Femtosecond Frequency Comb - A Weak Field Route to Strong Field Coherent Control

We present a general and highly efficient scheme for performing narrow-band Raman transitions between molecular vibrational levels using a coherent train of weak pump-dump pairs of shaped ultrashort pulses. The use of weak pulses permits an analytic description within the framework of coherent control in the perturbative regime, while coherent accumulation of many pulse pairs enables near unity transfer efficiency with a high spectral selectivity, thus forming a powerful combination of pump-dump control schemes and the precision of the frequency comb. The concept is presented analytically and its feasibility and robustness are verified by simulations of dynamics in Rb$_2$. We consider application of this concept to the formation of stable, deeply bound, ultracold molecules.