Picosecond optical excitation was used to coherently control the excit
ation in a single quantum dot on a time scale that is short compared w
ith the time scale for loss of quantum coherence. The excitonic wave f
unction was manipulated by controlling the optical phase of the two-pu
lse sequence through timing and polarization. Wave function engineerin
g techniques, developed in atomic and molecular systems, were used to
monitor and control a nonstationary quantum mechanical state composed
of a superposition of eigenstates. The results extend the concept of c
oherent control in semiconductors to the limit of a single quantum sys
tem in a zero-dimensional quantum dot.