  The interband polarizations induced by two phase-locked pulses in a
semiconductor show strong interference effects depending on the time tau_1
separating the pulses. The four-wave mixing signal diffracted from a third
pulse delayed by tau is coherently controlled by tuning tau_1. The four-wave
mixing response is evaluated exactly for a two-level system coupled to a single
LO phonon. In the weak coupling regime it shows oscillations with the phonon
frequency which turn into sharp peaks at multiples of the phonon period for a
larger coupling strength. Destructive interferences between the two
phase-locked pulses produce a splitting of the phonon peaks into a doublet. For
fixed tau but varying tau_1 the signal shows rapid oscillations at the
interband-transition frequency, whose amplitude exhibits bursts at multiples of
the phonon period.
