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Physical Review A

Atomic Radiation in a Cavity

P. Stehle

Published Jul 1, 1970• 67 citations
Publisher

Abstract

The spontaneous decay of an atom located between two parallel plane mirrors of reflectivity $R$ is calculated using the Weisskopf-Wigner method, both when the two mirrors are very large and when they are small. When the mirrors are large and of high reflectivity, the atom radiates more rapidly than in free space and into the Fabry-Perot modes of the mirror system. When the mirrors are small, their effect on the total radiation rate is small, but radiation into the few modes defined is enhanced if the reflectivity is high. It is concluded that the effect of the presence of a laser etalon is insufficient to justify omitting the coupling of the atom to non-Fabry-Perot modes from the Hamiltonian of an atomic system in a laser etalon.

DOI
10.1103/physreva.2.102

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The spontaneous decay of an atom located between two parallel plane mirrors of reflectivity RRR is calculated using the Weisskopf-Wigner method, both when the two mirrors are very large and when they are small. When the mirrors are large and of high reflectivity, the atom radiates more rapidly than in free space and into the Fabry-Perot modes of the mirror system. When the mirrors are small, their effect on the total radiation rate is small, but radiation into the few modes defined is enhanced if the reflectivity is high. It is concluded that the effect of the presence of a laser etalon is insufficient to justify omitting the coupling of the atom to non-Fabry-Perot modes from the Hamiltonian of an atomic system in a laser etalon.
Enhancement or suppression of spontaneous emission by the presence of a cavity has been a subject of numerous papers [1]. The effective number of radiation modes was estimated in terms of the cavity Q. Sachdev [2] has improved on this by an exact quantum Langevin treatment of a lossy, single-mode cavity and predicted a vacuum Rabi oscillation for high-Q cavities. Cook et al. [3] included retardation effects by incorporating multiple Fabry-Perot modes and treated the coupling loss by a heuristic introduction of the mirror reflectivity. The present author [4] has considered the same problem in perturbation and Wigner-Weisskopf approximations by use of a set of continuously distributed radiation modes which describes a cavity having output coupling.
We revisit the problem of spontaneous emission by a two-level system in a cavity, concentrating in particular on those aspects associated with the finite propagation time of light between the atom and the cavity boundaries. We find that spontaneous emission always occurs first at the free space rate and there is then an abrupt change in these dynamics when light reflected by the cavity mirrors returns to the atom, leading to interference effects that result either in an enhancement or a reduction of this rate or in a periodic exchange of excitation between the atom and the cavity field. From this point of view, reversible spontaneous emission in terms of single-mode ``vacuum Rabi oscillations'' can be interpreted as resulting from the interference between the multimode partial waves reflected at the cavity mirrors and the instantaneously radiated light. \textcopyright{} 1996 The American Physical Society.
A detailed account of the calculation on the spontaneous emission rate in a very short optical cavity with plane-parallel dielectric mirrors is given. A cavity model consisting of a pair of plane dielectric slabs is used. Guided modes as well as outgoing modes are considered. The emission rate from a two-level atom is calculated under quantum-mechanical perturbation approximation. The enhancement factor for the rate is found to be of the order of unity except for extremely short cavities. The concept of quasimodes in a very short cavity and their effective area are discussed in relation to the enhancement factor. The coupling ratios into various quasimodes are derived.
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The inhibition of atomic phase decays by squeezed light, as first predicted by Gardiner [Phys. Rev. Lett. 56, 1917 (1986)], has yet to be confirmed experimentally. A major obstacle to such an experiment is the production of an effective squeezed-vacuum--atom coupling, so that the atom interacts only with squeezed modes of the radiation field. In this paper we propose the use of a microscopic plane-mirror Fabry-P\'erot cavity to effect a strong selection of modes coupling to the atom. It is shown that a significant reduction in fluctuations experienced by the atom can be achieved in one quadrature, with an input squeezed beam of modest angular dimensions, provided that the phase (and to lesser extent the amplitude) characteristics of the input beam are suitably matched to the cavity.
The behavior of a two-level atom in a half-cavity, i.e., a cavity with one mirror, is studied within the framework of a one-dimensional model with respect to spontaneous decay and resonance fluorescence. The system under consideration corresponds to the setup of a recently performed experiment [J. Eschner et al., Nature (London) 413,413,413, 495 (2001)] where the influence of a mirror on a fluorescing single atom was revealed. In the present work special attention is paid to the regime of large atom-mirror distances where intrinsic memory effects can not longer be neglected. This is done with the help of delay-differential equations which contain, for small atom-mirror distances, the Markovian limit with effective level shifts and decay rates leading to the phenomenon of enhancement or inhibition of spontaneous decay. Several features are recovered beyond an effective Markovian treatment, appearing in experimentally accessible quantities like the intensity or emission spectra of the scattered light.