It has been observed that the spontaneous-emission lifetime of Rydberg atoms is shortened by a large ratio when these atoms are crossing a high-Q superconducting cavity tuned to resonance with a millimeter-wave transition between adjacent Rydberg states.

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A collection of N Rydberg atoms and a resonant millimeter-wave cavity are shown to exchange energy back and forth at a rate 2{d/%)S^N 9 where d is the electric dipole matrix element of the atomic transition and < § 0 the "field per photon" in the cavity. This experiment is a demonstration of self-induced Rabi oscillations in a two-level atom system coupled to a single electromagnetic field mode and can also be considered as a very simple illustration of "ringings" in superradiant emission. PACS numbers: 42.50. + q, The simplest quantum mechanical model dealing with atom-radiation interaction is the Jaynes-Cummings one, 1 which describes an isolated twolevel atom coupled to a single mode of the electromagnetic (em) field resonant with the atomic transition. In this model, atomic radiation appears as a very simple process: If the field-defined as an eigenmode of an em cavity-is undamped and initially empty and if the atom is excited in its upper state, an oscillatory exchange of energy between the atomic and field systems is expected, 2 corresponding to a succession of emission and absorption of a single photon by the atom. This exchange should occur at a rate ft 0 = (2d/H) £ 0 , where d is the electric dipole matrix element of the atomic transition, h the Planck constant, and S 0 = (Hco/2e 0 V) l/2 the "electric field per photon" in the mode (oo and V are, respectively, the transition frequency and the effective volume of the cavity mode). This regime of Rabi oscillation induced by the self-radiated atomic field in the cavity has never been observed so far because it occurs at a rate usually too small compared to the rates T c _1 and T A~X at which the field and the atoms, respectively, escape from the cavity (T c -1 = co/Q, Q being the cavity-mode quality factor). Clearly, if the condition Wc >1(1)is not fulfilled, the singie-atom-single-photon Rabi oscillation cannot occur since the radiated photon decays in the cavity mirrors before being reabsorbed by the atom. In this case, the cavity mode becomes a "reservoir" in which the atom radiates irreversibly at a rate T c = & 0 2 T C which can be much larger than the spontaneous emission rate of the same transition in free space. This enhancement of spontaneous emission due to the atomic coupling with a damped resonator, predicted long ago, 3 has been recently observed by our group 4 in an experiment involving Rydberg atoms excited in a millimeter-wave cavity with Q = 10 6 . In Ref. 4, it has been pointed out that a tenfold increase of the resonator Q should allow us to fulfill condition (1) and to observe the fundamental regime of single-atom self-induced Rabi oscillation,The purpose of this Letter is to report an alternative experiment in which we have observed a closely related self-induced Rabi-oscillation effect in a cavity with a "moderately" high Q. The main idea of the experiment is that an ensemble of N atoms radiates in the cavity a field whose amplitude is JN times larger than a single-photon field, thus increasing the Rabi-exchange frequency to £l 0 JN. C...