We observe multiple excitonic optical Rabi oscillations in a semiconductor
quantum well. Up to eight oscillation periods of the heavy-hole exciton den
sity on a subpicosecond time scale are observed. An approximate linear depe
ndence of the oscillation frequency on the light field amplitude is establi
shed. The experiment is based on a two-color detection scheme which allows
for the observation of the heavy-hole exciton density via transmission chan
ges at the light-hole exciton. The observations are in good agreement with
theoretical computations based on multiband semiconductor Bloch equations.