A quasi-classical model (QCM) of molecular dynamics in intense femtosecond laser fields has been developed, and applied to a study of the effect of an ultrashort `control pulse on the vibrational motion of a deuterium molecular ion in its ground electronic state. A nonadiabatic treatment accounts for the initial ionization-induced vibrational population caused by an ultrashort `pump pulse. In the QCM, the nuclei move classically on the molecular potential as it is distorted by the laser-induced Stark shift and transition dipole. The nuclei then adjust to the modified potential, non-destructively shifting the vibrational population and relative phase. This shift has been studied as a function of control pulse parameters. Excellent agreement is observed with predictions of time-dependent quantum simulations, lending confidence to the validity of the model and permitting new observations to be made. The applicability of the QCM to more complex multi-potential energy surface molecules (where a quantum treatment is at best difficult) is discussed.
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