  We observe the phase space trajectory of an entangled wave packet of a
trapped ion with high precision. The application of a spin dependent light
force on a superposition of spin states allows for coherent splitting of the
matter wave packet such that two distinct components in phase space emerge. We
observe such motion with a precision of better than 9% of the wave packet
extension in both momentum and position, corresponding to a 0.8 nm position
resolution. We accurately study the effect of the initial ion temperature on
the quantum entanglement dynamics. Furthermore, we map out the phonon
distributions throughout the action of the displacement force. Our
investigation shows corrections to simplified models of the system evolution.
The precise knowledge of these dynamics may improve quantum gates for ion
crystals and lead to entangled matter wave states with large displacements.
