The fifth lesson was devoted to microwave cavity electrodynamics experiments detecting, but not destroying, trapped single photons. The field probes are Rydberg atoms passing one by one through the C cavity. The field leaves an imprint on the phase of a superposition of atomic states, prepared before the atoms enter C by a firstR1 microwave pulse and analyzed, after C, by a secondR2 pulse. The R1-R2 assembly is a Ramsey interferometer. Detector D measures the final state of the atom. The information provided by each atom is binary, which is sufficient to discriminate between 0 and 1 photon. As the photon is not destroyed, the measurement can in principle be repeated indefinitely. Two experiments have been analyzed. The first (1999) exploits a resonant atom-cavity interaction, the QND condition being achieved by adjusting the interaction time so that the atom returns to its initial state, without absorbing the photon (Rabi 2π pulse). The experiment was carried out in a damped cavity in a timeTC = 1 ms, too short for multiple repetitions of the measurement. The second experiment (2006) uses a non-resonant dispersive interaction and a cavity storing photons for a very long time (Tc = 0.13 s). Hundreds of independent measurements of the same photon have enabled us to observe for the first time the quantum jumps associated with the annihilation and creation of photons in the cavity mirrors. Before describing these experiments, we begin with a few theoretical reminders about the states of the atom-field system in the cavity
