Temporal sorting of optical multi-wave-mixing processes in semiconductor quantum dots

Coherent control of ensembles of light emitters by means of multi-wave mixing processes is key for the realization of high capacity optical quantum memories and information processing devices. In this context, semiconductor quantum dots placed in optical microcavities represent excellent candidates to explore strong light-matter interactions beyond the limits of perturbative non-linear optics and control the unitary evolution of optically driven quantum systems. In this work, we demonstrate that a sequence of two optical picosecond pulses can be used to establish coherent control over the phase evolution of the ensemble of trions in (In,Ga)As quantum dots independent of their initial quantum state. Our approach is based on coherent transfer between degenerate multi-wave-mixing signals in the strong field limit where Rabi rotations in multi-level systems take place. In particular, we use the two-pulse photon echo sequence to uncover the coherent dynamics of the trion ensemble, whereas the areas of two additional control pulses serve as tuning knobs for adjusting the magnitude and timing of the coherent emission. Furthermore, we make use of the spin degeneracy of ground and excited state of trions to control the polarization state of the emitted signal. Surprisingly, we reveal that the use of optical control pulses, whose durations are comparable to the dephasing time of the ensemble, lifts the temporal degeneracy between wave-mixing processes of different order. This phenomenon is manifested in a significant modification of the temporal shape of the coherent optical response for strong optical fields. Lifting the temporal degeneracy allows to smoothly trace the transition from the perturbative to the regime of Rabi rotations and opens up new possibilities for the optical investigation of complex energy level structures in so far unexplored material systems.