Dissociative ionizaiton of $H_2$ in an ultroviolet pulse train and delayed infrared laser pulse*

The ionization of H$_2$ in a single attosecond XUV pulse generates a nuclear wavepacket in H$_2^+$ which is entangled with the emitted photoelectron wavepacket. The nuclear wavepacket dynamics can be observed by dissociating H$_2^+$ in a delayed infrared laser pulse. If H$_2$ is ionized by a sequence of XUV pulses of an attosecond pulse train, whether or not the corresponding sequence of nuclear wavepackets in H$_2^+$ is detected as a coherent or incoherent superposition depends on whether and how the photoelectrons are observed. We simulate the nuclear dynamics in this XUV pump - IR probe scenario and analyze our numerical results, suggesting that interference between coherently launched nuclear wavepackets in H$_2^+$ can be neglected in the recent experiment of Kelkensberg \textit{et al.} [\textbf{103}, 123005 (2009)].