  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.
