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We study Rabi rotations arising in intensity-dependent photon echoes from anensemble of self-assembled InGaAs quantum dots. To achieve a uniformdistribution of intensities within the excited ensemble, we introduce flattopintensity profiles of picosecond laser pulses. This allows us to overcome thedamping of Rabi rotations imposed by the spatial inhomogeneity of Rabifrequencies by a Gaussian laser profile. Using photon echo polarimetry, wedistinguish between the coherent optical responses from exciton and trionensembles. Here, we demonstrate that a photo-induced charging of the quantumdots leads to a significant reduction of the number of neutral quantum dotsunder resonant excitation with intensive optical pulses with areas exceeding$\frac{\pi}{2}$. The trion ensemble shows robust Rabi rotations when the areaof the refocussing pulse is increased up to 5.5$\pi$. We analyze the remainingattenuation of Rabi rotations by theoretical modeling of excitation induceddephasing, inhomogeneity of dipole moments, and coupling to acoustic phonons.The latter is identified as the dominating mechanism resulting in a loss ofoptical coherence during the action of the involved optical pulses.

Multiple Rabi rotations of trions in InGaAs quantum dots observed by photon echo spectroscopy with spatially shaped laser pulses