  We studied the semiconductor response with respect to high intensity resonant
excitation on short time scale when the contribution of the Fermi statistics of
the electrons and holes prevails. We studied both the single and double pulse
excitations. For the latter case we considered the time evolution of the
multi-wave mixing exciton polarization. The main difference between the
excitation by a single pulse or by two non-collinear pulses is that the Rabi
oscillations of the multi-wave mixing response are characterized by two
harmonics. Analyzing the operator dynamics governed by the external excitation
we found that there are three invariant spin classes, which do not mix with the
evolution of the system. Two classes correspond to the bright exciton states
and one contains all dark states. We found that the dynamics of the classes is
described by six frequencies and the Rabi frequencies are only two of them (one
for each bright class). We discuss the effect of the dispersion of the
electrons and holes and the Coulomb interaction describing the semiconductor by
the semiconductor Bloch equation (SBE). We show that if initially the system is
in the ground state then the SBE preserves the invariant spin classes thus
proving absence of the dark excitons in the framework of this description. We
found that due to the mass difference between holes of different kind
additional Rabi frequencies, two of those present in the operator dynamics,
should appear in the evolution of the exciton polarization.
