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 nonadiabatic cavity quantum electrodynamics effects can be observed. We show that control pulses with specific arrival times, performing which-path and quantum-eraser operations, are able to suddenly switch-off and on first-order coherence of cavity photons, without affecting their strong coupling population dynamics. © 2011 The American Physical Society.