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

Ionization of neutral $D_2$ molecules by a short pump laser pulse may create a vibrational wave packet on the lowest ($1s\sigma_g^+$) adiabatic potential curve of the $D_2^+$ molecular ion. We investigated the possibility of manipulating the bound motion, dissociation, and vibrational--state composition of $D_2^+$ nuclear wave packets with a sequence of ultra--short, intense, near infrared control laser pulses. Our numerical results show that a single control pulse with an appropriate time delay can quench the vibrational state distribution of the nuclear wave packet by increasing the contribution of a selected stationary vibrational state of $D_2^+$ to more than 50\%. We also demonstrate that a second control pulse with a carefully adjusted delay can further squeeze the vibrational-state distribution, suggesting a multi--pulse control protocol for preparing stationary excited nuclear wave functions. With the subsequent fragmentation of the molecular ion with a probe pulse, we suggest a scheme for experimentally assessing the degree at which the nuclear motion in small molecules can be controlled, cf., Phys. Rev. {\bf 77}, 013407 (2008).