Controlled vibrational quenching of nuclear wave packets in $D_2^+$

The sudden ionization of neutral $D_2$ molecules by a short and intense pump laser pulse may create a wave packet as a coherent superposition of vibrational states on the lowest ($1s\sigma_g^+$) adiabatic potential curve of the $D_2^+$ molecular ion. We investigate the possibility of manipulating the bound motion, dissociation, and vibrational-state composition of such nuclear wave packets with one (or several) ultra-short (6 fs) intense (1 x 10$^{14}$ W/cm$^2$) near infrared (800 nm) control laser pulses. We show numerically that a single control pulse with an appropriately tuned time delay can significantly quench the vibrational state distribution of the nuclear wave packet by increasing the contribution of a selected stationary vibrational state of the molecular ion to more than 50\%. We also show that a second control pulse with a carefully adjusted delay can further squeeze the vibrational state distribution and suggest a scheme for a multi control pulse ``Raman shaping''. Since the resulting nuclear wave function is almost stationary, fragmentation of the molecular ion with a final intense probe pulse can be used to project its nodal structure onto the measurable kinetic energy release, thereby suggesting a tool for assessing the degree at which the nuclear motion in a small molecule can be controlled.