  The exact optical response of quantum few-level systems depends crucially on
the exact choice of the incoming pulse areas. We use four-wave mixing (FWM)
spectroscopy to infer the coherent response and dynamics of single InAs quantum
dots (QDs) and study their pulse area dependence. By combining atomic force
microscopy with FWM hyperspectral imaging, we show that the retrieved FWM
signals originate from individual QDs enclosed in natural photonic defects. The
optimized light-matter coupling in these defects allows us to perform our
studies in a wide range of driving field amplitudes. When varying the pulse
areas of the exciting laser pulses the so-called Rabi rotations can be resolved
by the two-pulse FWM technique. We investigate these Rabi rotations within two-
and three-level systems, both theoretically and experimentally, and explain
their damping by the coupling to acoustic phonons. To highlight the importance
of the pulse area influence, we show that the phonon-induced dephasing of QD
excitons depends on the pulse intensity.
