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Physical Review A

Electromagnetic decay into a narrow resonance in an optical cavity

H. M. Lai, P. T. Leung, K. Young

Published Mar 1, 1988• 69 citations
Publisher

Abstract

The spontaneous electromagnetic decay of a two-level atom coupled to a narrow cavity resonance is investigated rigorously in terms of the (Hermitian) modes of the ``universe'' rather than the (dissipative) quasimodes of the cavity. Special attention is paid to the strong-coupling regime (atomic linewidth \ensuremath{\Gamma}\ensuremath{\gtrsim} cavity resonance width \ensuremath{\gamma}), in which there are significant corrections to the golden rule. In particular, spontaneous decay is most rapid for intermediate values of the quality factor Q of the cavity resonance. The photon line shape, the effect of several cavity resonances, and the competition of several transitions are also investigated. The additivity of partial rates does not hold, and in some circumstances, the addition of an extra decay channel may reduce the total decay rate. These results are relevant to optical processes observed in dielectric microspheres, and also to usual laser cavities.

DOI
10.1103/physreva.37.1597

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The spontaneous electromagnetic decay of a two-level atom coupled to a narrow cavity resonance is investigated rigorously in terms of the (Hermitian) modes of the ``universe'' rather than the (dissipative) quasimodes of the cavity. Special attention is paid to the strong-coupling regime (atomic linewidth \ensuremath{\Gamma}\ensuremath{\gtrsim} cavity resonance width \ensuremath{\gamma}), in which there are significant corrections to the golden rule. In particular, spontaneous decay is most rapid for intermediate values of the quality factor Q of the cavity resonance. The photon line shape, the effect of several cavity resonances, and the competition of several transitions are also investigated. The additivity of partial rates does not hold, and in some circumstances, the addition of an extra decay channel may reduce the total decay rate. These results are relevant to optical processes observed in dielectric microspheres, and also to usual laser cavities.
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.
The rates of spontaneous emission and stimulated emission and absorption for a two-level atom in a dielectric microsphere are calculated for weak E1 coupling. The A coefficient for spontaneous emission is proportional to the zero-point fluctuation of the electric field ℰij evaluated in the previous paper [ J. Opt. Soc. Am. B4, 1995 ( 1987)], which shows sharp resonances in frequency (Q > 104). It is verified that the ratio of the A and B coefficients is determined by the spectral density of thermal radiation. The level shift tends to repel the transition line away from the cavity resonance.
Starting from the quantized version of Maxwell's equations for the electromagnetic field in an arbitrary linear Kramers-Kronig dielectric, the Heisenberg equations of motion for a two-level atom resonantly coupled to the radiation field in the presence of dispersive and absorbing dielectric bodies are derived. The theory is applied to the problem of spontaneous decay of excited atoms in absorbing media. The decay rate is calculated for the (Glauber-Lewenstein) real-cavity model, and a comparison with the recently studied (Clausius-Mosotti) virtual-cavity model [S. Scheel, L. Kn\"oll, D.-G. Welsch, and S. M. Barnett, Phys. Rev. A 60, 1590 (1999)] is given. It is shown that owing to nonradiative decay associated with absorption, the rate of spontaneous decay sensitively depends on the cavity radius, particularly when the atomic transition frequency approaches an absorption band of the medium. Only when the effect of absorption is fully disregarded, is the familiar local-field correction factor recovered.
We consider spontaneous emission in dielectric microcavities with multiple resonances that may overlap in both position and frequency. By projecting the Green tensor onto a set of quasimodes associated with the resonances, we derive the reduced spontaneous emission rate. To demonstrate the accuracy and computational efficiency of our approach, we model spontaneous emission in a two-dimensional photonic crystal with two coupled defects. Employing a quantum mechanical interpretation, we show that the spontaneous emission involves both direct decay into the individual quasimodes and photon transfer between the quasimodes. The quantum path interference between these different emission channels can cause the spontaneous emission rate to differ dramatically from the rate obtained by the summation over resonant line shapes. We also show how our approach can be used to determine the emission into particular quasimodes of multiple-resonance microcavities.
The decay characteristics of two-state Rydberg atoms are investigated in a microwave cavity driven simultaneously by two strong rf fields. Tuning one of the driving fields leads to sharp resonances in the decay rate of the upper atomic level. Their width may become smaller than the cavity linewidth and transit time broadening. We present a theoretical model, interpreting the resonances as cavity-induced decay of Floquet states of the composite atom-field system. The observed phenomena arise from the interplay of cavity-modified Bloch-Siegert shifts and dynamic enhancement of spontaneous emission at single-photon and multiphoton resonances.
The interaction between two-state atoms and the modes of an optical cavity has been studied extensively over many years; in particular, in connection with lasers and optical bistability. These are dissipative systems, and it has been usual in their study to assume that dissipation rates are, in some sense, large compared with the coupling strength between the atoms and the field. Recent work has shown that interesting new dynamical behavior occurs when this is not so. For example, spontaneous emission linewidths can be altered,1,2 and if the coupling is very strong, an emission line can be split into a pair of resonances identified with the normal- mode frequencies of coupled oscillators describing the atomic polarization and the cavity field.3.4 Altered linewidths and normal-mode splitting are features of weak excitation; both are explained by a coupled damped harmonic oscillator model. In this paper we report new results obtained for strong excitation.