  We investigate the role of nuclear motion and strong-field-induced electronic
couplings during the double ionization of deuterated water using
momentum-resolved coincidence spectroscopy. By examining the three-body
dicationic dissociation channel, D$^{+}$/D$^{+}$/O, for both few- and
multi-cycle laser pulses, strong evidence for intra-pulse dynamics is observed.
The extracted angle- and energy-resolved double ionization yields are compared
to classical trajectory simulations of the dissociation dynamics occurring from
different electronic states of the dication. In contrast with measurements of
single photon double ionization, pronounced departure from the expectations for
vertical ionization is observed, even for pulses as short as 10~fs in duration.
We outline numerous mechanisms by which the strong laser field can modify the
nuclear wavefunction en-route to final states of the dication where molecular
fragmentation occurs. Specifically, we consider the possibility of a
coordinate-dependence to the strong-field ionization rate, intermediate nuclear
motion in monocation states prior to double ionization, and near-resonant
laser-induced dipole couplings in the ion. These results highlight the fact
that, for small and light molecules such as D$_2$O, a vertical-transition
treatment of the ionization dynamics is not sufficient to reproduce the
features seen experimentally in the strong field coincidence double-ionization
data.
