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Annual Meeting Optical Society of America

Spontaneous emission from a moving atom in a standing-wave cavity

Wensheng Ren, H. J. Carmichael

Published Jan 1, 1990• 0 citations
Publisher

Abstract

The spectrum of spontaneously emitted photons from an atom interacting with a single cavity mode depends on the relative sizes of the mode coupling constant and the cavity loss rate. If the coupling constant is not too large, perturbation theory can he used to show that the atomic linewidth is either increased (enhanced spontaneous emission) or decreased (inhibited spontaneous emission) by the presence of the cavity. When the coupling constant is so large that perturbation theory cannot be used, the spontaneous- emission spectrum forms a doublet, with peaks located at the normal-mode frequencies for the coupled-dipole and cavity-mode oscillators (the so-called "vacuum" Rabi splitting).

DOI
10.1364/oam.1990.tur3

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The spectrum of spontaneously emitted photons from an atom interacting with a single cavity mode depends on the relative sizes of the mode coupling constant and the cavity loss rate. If the coupling constant is not too large, perturbation theory can he used to show that the atomic linewidth is either increased (enhanced spontaneous emission) or decreased (inhibited spontaneous emission) by the presence of the cavity. When the coupling constant is so large that perturbation theory cannot be used, the spontaneous- emission spectrum forms a doublet, with peaks located at the normal-mode frequencies for the coupled-dipole and cavity-mode oscillators (the so-called "vacuum" Rabi splitting).
We present a nonperturbative result for the spectrum of spontaneous photons emitted by an atom coupled on resonance to a standing-wave cavity mode. Motion of the atom through the standing-wave mode function is included in a classical way. We discuss the form of the spectrum as a function of the velocity of the atom in the limit of strong dipole coupling. For slow atoms the normal-mode doublet (``vacuum'' Rabi spectrum) survives with small changes. The motion of a fast atom through the standing wave averages the coupling constant to zero, and the spectrum reverts to a single peak. At intermediate velocities the spectrum has a complicated multipeaked structure that can be understood in terms of interfering probability amplitudes for different quantum-mechanical emission paths or as a frequency-modulation spectrum for radiating coupled oscillators.
A brief review is given of theoretical and experimental investigations of the spontaneous emission from an atom in a resonator cavity. A theory of spontaneous emission from a two-level atom in free space and in a cavity is presented in a methodical unified manner. In a single-mode resonator the structure of the spectrum of the emitted photons is a singlet or a doublet, depending on the ratio of the cavity damping to the constant of the interaction of an atom with a field. The emission spectrum of an atom in a cavity with two modes with similar frequencies may have a triplet structure.
It is well known that spontaneous emission is not an intrinsic atomic property, but rather results from the coupling of the atom to the vacuum modes of the electromagnetic field. As such, it can be modified by tailoring the electromagnetic environment into which the atom can radiate. This was already realized by Purcell, who noted that the spontaneous emission rate can be enhanced if the atom placed inside a cavity is resonant with one of the cavity is resonant with one of the cavity modes, and by Kleppner, who discussed the opposite case of inhibited spontaneous emission. It has also been recognized that spontaneous emission need not be an irreversible process. Indeed, a system consisting of a single atom coupled to a single mode of the electromagnetic field undergoes a periodic exchange of excitation between the atom and the field. This periodic exchange remains dominant as long as the strength of the coupling between the atom and a cavity mode is itself dominant. 23 refs., 6 figs.