VOLUME 74, NUMBER 8 PH YS ICAL REVIEW LETTERS 20 FEBRUARY 1995 Sudden Replacement of a Mirror by a Detector in Cavity QED: Are Photons Counted Immediately' ? Heidi Fearn Department of Physics, California State University, Fulierton, California 92634 9480- Richard J. Cook Department of Physics, United States Air Force Academy, Colorado Springs, Colorado 80840 Peter W. Milonni Theoretical Division (T 4), Lo-s Alamos National Laboratory, Los Alamos, lVew Mexico 87545 (Received 19 September 1994) We consider an excited atom in a cavity such that spontaneous emission is inhibited, and address the question of whether a sudden replacement of one of the cavity mirrors by a detector can result in a photon count immediately or only after some retardation time. The feasibility of an experiment of this type has led to considerable discussion as to its outcome. Following a brief summary of the conflicting arguments, we show that it is possible to count a photon immediately following the substitution of a photodetector for a mirror. PACS numbers: 42. 50. — p, 12. 20. — m Recent experiments on two-photon down-conversion [1] have extended the domain of cavity QED to include nonlin- ear optical processes and much larger emitter-mirror sepa- rations than have been possible in experiments with atoms in cavities [2]. Such experiments also allow the possibil- ity, through the use of polarization-sensitive mirrors and fast Pockels cells, of investigating effects associated with the sudden replacement of a cavity mirror by a detector [3]. This possibility has stimulated considerable discus- sion about whether photons, under conditions of cavity- inhibited emission, can be counted immediately following the substitution of a photodetector for a mirror or only after some retardation time relating to the propagation of light between the emitter and the detector. The same question can be raised in the context of ordinary cavity QED involving a single excited atom in a cavity. Suppose that spontaneous emission is completely inhibited by the cavity and that at time T one of the mirrors is suddenly replaced by a photodetector. Can a photon be counted immediately at time T, or is the photon count ideally zero until some time T' = T + TR, where T& is a retardation time determined by the distance between the atom and the detector that has replaced the mirror [4]? Two plausible explanations, leading to different an- swers, have been proposed. According to one argument, the inhibited atom cannot "know" the mirror has been re- moved until the time t = T + d/c, where d is the atom- mirror distance, and the atom can begin to radiate only after this time. Since the propagation time to the detec- tor is d/c, a photon can be detected only after a time t + d/c = T + 2d/c, i.e. , after a time 2d/c following the mirror switchout. The second viewpoint holds that, as in the case of a classical dipole radiator in a cavity, there are always fields E, (z, t) = 2~i p, dt'[o (t') + o t (t')]-- x g ~oaUk(z)Ua(zo)e' " ' ' + H. c. (1) k (or, more precisely, probability amplitudes) propagating from the atom to the removable mirror and back to the atom, and that the inhibition of spontaneous emission im- plies a destructive interference of the two counterpropa- gating fields. The sudden removal of the mirror allows that part of the field propagating toward the mirror to es- cape from the cavity, so that a photon can be counted immediately following the switchout of the mirror. In the absence of detailed calculations or an experiment, objections can be raised against either prediction. The first argument makes no reference to counterpropagating, destructively interfering waves or probability amplitudes. The second argument might appear to violate energy conservation, since it apparently predicts an immediately nonvanishing photon counting rate at time T while the atom is held in its excited state, spontaneous emission being inhibited until the atom can somehow receive the information that the mirror has been switched out. We will show that a photon can be counted immediately following the replacement of a mirror by a detector. Because the analysis of any specific, real experiment will involve complications irrelevant to the question of interest, we consider an idealized model. This model consists of a two-level atom in the presence of a single plane mirror, and an electric-dipole atom-field interaction restricted to singly polarized field modes propagating only in the two directions normal to the mirror (Fig. 1). The Heisenberg-picture electric field operator is E(z, t) = Eo(z, t) + E, (z, t), where Eo(z, t) is the free field in the absence of any sources and 0031-9007/95/74(8)/1327(4)$06. 00 1995 The American Physical Society 1327