  On the basis of optimal control theory, we numerically study how to optimally
manipulate molecular vibrational dynamics by using cycle-averaged
polarizability interactions induced by mildly intense non-resonant laser (NR)
pulses. As the essential elements to be controlled are the probability
amplitudes, namely, the populations and the relative phases of the vibrational
eigenstates, we consider three fundamental control objectives: selective
population transfer, wave packet shaping that requires both population control
and relative-phase control, and wave packet deformation suppression that solely
requires relative-phase control while avoiding population redistribution. The
non-trivial control of wave packet deformation suppression is an extension of
our previous study on wave packet spreading suppression. Focusing on the
vibrational dynamics in the B state of I2 as a case study, we adopt optimal
control simulations and model analyses under the impulsive excitation
approximation to systematically examine how to achieve the control objectives
with shaped NR pulses. Optimal solutions are always given by NR pulse trains,
in which each pulse interval and each pulse intensity are adjusted to cooperate
with the vibrational dynamics to effectively utilize the quantum interferences
to realize the control objectives with high probability.
