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Superposition is the fundamental signature of quantum behavior. A quantum system can exist in a superposition of different eigenstates of an observable. Only after the measurement process, the system will collapse on one of the eigenvalues of the measured observables. We propose the realisation of the counterintuitive superposition of On and Off strong light-matter interaction using an optical resonator and a generic three-level quantum system. Leaked cavity photons can be detected and collected in order to post-select the events and to choose if we want to observe interacting or non-interacting photons. Such proposal can be readily realised within the present technology. Finally we will show that the cavity field can have a morphing behavior between On and Off interaction, by changing the area of the control pulse. [ABSTRACT FROM AUTHOR]