  We study the all-optical time-control of the strong coupling between a single
cascade three-level quantum emitter and a microcavity. We find that only
specific arrival-times of the control pulses succeed in switching-off the Rabi
oscillations. Depending on the arrival times of control pulses, a variety of
exotic non-adiabatic cavity quantum electrodynamics effects can be observed. We
show that only control pulses with specific arrival times are able to suddenly
switch-off and -on first-order coherence of cavity photons, without affecting
their strong coupling population dynamics. Such behavior may be understood as a
manifestation of quantum complementarity.
