  We consider the full driven quantum dynamics of a qubit realized as spin of
electron in a one-dimensional double quantum dot with spin-orbit coupling. The
driving perturbation is taken in the form of a single half-period pulse of
electric field. Spin-orbit coupling leads to a nontrivial evolution in the spin
and charge densities making the dynamics in both quantities irregular. As a
result, the charge density distribution becomes strongly spin-dependent. The
transition from the field-induced tunneling to the strong coupling regime is
clearly seen in the charge and spin channels. These results can be important
for the understanding of the techniques for the spin manipulation in
nanostructures.
