Quantum complementarity of cavity photons coupled to a three-level system

Recently a device enabling the ultrafast all-optical control of the wave-particle duality of light was proposed [Ridolfo et al., Phys. Rev. Lett. 106, 013601 (2011)]. It is constituted by a three-level quantum emitter strongly coupled to a microcavity and can be realized by exploiting a great variety of systems ranging from atomic physics and semiconductor quantum dots to intersubband polaritons and Cooper pair boxes. Control pulses with specific arrival times, performing which-path and quantum-eraser operations, are able to destroy and recover interference almost instantaneously. Here we show that the coherence sudden death implies the sudden birth of a higher order correlation function storing coherence. Such storing enables coherence rebirth after the arrival of an additional suitable control pulse. We derive analytical calculations describing the all-optical control of the wave-particle duality and the entanglement-induced switch-off of the strong coupling regime. We also present analytical calculations describing a homodynelike method exploiting pairs of phase locked pulses with precise arrival times to probe the optical control of wave-particle duality of this system.Within such a method the optical control of wave-particle duality can be directly probed by just detecting the photons escaping the microcavity.