  A coherent control scheme for the population distribution in the vibrational
states of nonpolar molecules is proposed. Our theoretical analysis and results
of numerical simulations for the interaction of the hydrogen molecular ion in
its electronic ground state with an infrared laser pulse reveal a selective
two-photon transition between the vibrational states via a coupling with the
first excited dissociative state. We demonstrate that for a given temporal
intensity profile the population transfer between vibrational states, or a
superposition of vibrational states, can be made complete for a single chirped
pulse or a train of chirped pulses, which accounts for the accumulated phase
difference due to the AC Stark effect. Effects of a spatial intensity (or,
focal) averaging are discussed.
