  Optically controlled coherent dynamics of charge (excitonic) degrees of
freedom in a semiconductor quantum dot under the influence of lattice dynamics
(phonons) is discussed theoretically. We show that the dynamics of the lattice
response in the strongly non-linear regime is governed by a semiclassical
resonance between the phonon modes and the optically driven dynamics. We stress
on the importance of the stability of intermediate states for the truly
coherent control.
