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Journal of the Physical Society of Japan

Radiative Lifetime of an Atom In- and Outside of Planar/Spherical Dielectrics

Jun Ushida, T. Ohta, Kikuo Cho

Published Jul 15, 1999• 6 citations
Publisher

Abstract

Radiative lifetime of an atom is theoretically studied in the presence of neighboring dielectrics in terms of a microscopic semiclassical theory where the effect of dielectrics is renormalized into radiation Green's function. Some results are presented for the cases of planar (semi-infinite and slab) and spherical dielectrics. A QED calculation in the semi-infinite case confirms the semi-classical result. The interaction of atom resonance and a whispering gallery mode of a sphere leads to “vacuum Rabi” splitting and a cross-over behavior of their radiative widths.

DOI
10.1143/jpsj.68.2439

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Radiative lifetime of an atom is theoretically studied in the presence of neighboring dielectrics in terms of a microscopic semiclassical theory where the effect of dielectrics is renormalized into radiation Green's function. Some results are presented for the cases of planar (semi-infinite and slab) and spherical dielectrics. A QED calculation in the semi-infinite case confirms the semi-classical result. The interaction of atom resonance and a whispering gallery mode of a sphere leads to “vacuum Rabi” splitting and a cross-over behavior of their radiative widths.
We present a formalism for studying the influence of dispersive and absorbing dielectric bodies on a radiating atom in the framework of quantization of the phenomenological Maxwell equations for given complex permittivities of the bodies. In Markov approximation, the rate of spontaneous decay and the line shift associated with it can then be related to the complex permittivities and geometries of the bodies via the dyadic Green function of the classical boundary value problem of electrodynamics -- a result which is in agreement with second-order calculations for microscopic model systems. The theory is applied to an atom near a planar interface as well as to an atom in a spherical cavity. The latter, also known as the real-cavity model for spontaneous decay of an excited atom embedded in a dielectric, is compared with the virtual-cavity model. Connections with other approaches are mentioned and the results are compared.
Spontaneous decay behavior from an assembly of atoms (or molecules) in a dielectric slab sandwiched by two dielectric semi-infinite spaces with arbitrary refractive indices is investigated. We introduce a lifetime distribution function to describe decay kinetics. The zero-point fluctuations of the electromagnetic field are calculated as a function of the position of atom in the slab. They display a symmetric profile with respect to the central plane of the slab in symmetric structure sample and the contributions of the guided modes and the radiation modes components both exhibit cosinelike variation with a base but with a phase difference of \ensuremath{\pi}. With the increase of the thickness of the slab, the oscillations become dense. In contrast, for the asymmetric structure case, the related curves are asymmetric with respect to the middle plane of slab and exhibit considerably distorted cosinelike oscillations. The dependence of the spontaneous emission rate of atoms on the thickness of the slab and the refractive indices of substrate also is surveyed. Our calculations show that quite wide or narrow lifetime distribution can occur for different thicknesses of the slab. The coexistence of both accelerated and inhibited decay processes appears. The calculated results are in good agreement with experimental results.
A quantum-electrodynamic theory of spontaneous emission in presence of dielectrics and conductors is developed. The theory makes use of the master-equation techniques and the response-function formalism of part I of this series of papers. Various observable entities such as damping coefficients (lifetimes), Lamb shifts, and frequency shifts are related to the appropriate surface-dependent response functions. The results are valid for arbitrary geometries (involving linear dielectrics) and naturally contain, as a special case, the usual results of spontaneous emission in free space. As explicit examples we consider a two-level atom (also the multilevel atom) in presence of a plane dielectric interface and between two conducting plates. Formulas for the shifts and widths are given and their asymptotic behavior for large and short distances is discussed. The behavior when the atom is embedded inside the dielectric is different than when the atom is outside the dielectric. The origin of coherence in the present model is discussed and the coherence effects in this model are contrasted with those in Dicke's model. The results are also compared with those obtained by the image method. Exact expressions for the operator radiation-reaction fields are obtained in terms of the atomic polarization operators and response functions. Approximate results for such fields are also given. The far-zone behavior of the radiation fields is obtained in terms of response functions and the polarization operators. Some of the normally ordered correlation functions are also calculated. The connection of some of the theoretical results with a recent experimental work of Carniglia, Mandel, and Drexhage is discussed. The effect of anisotropy of the dielectric function on the lifetimes as well as on the far-field correlation functions is also considered. Finally the contribution to the shifts and widths due to the excitation of surface polariton modes is computed and the results are compared with those obtained by the quantization of surface polariton field. It is found that such surface modes contribute significantly to widths.
The interaction is considered between a two-level atom and the continuum of electric field modes falling within the profile of one of the resonance modes of a dielectric microsphere (a whispering gallery mode). Subject to minimal assumptions, simple equations are obtained on first principles, which describe the spectral properties of the one-photon continuum and the relaxation processes occurring therein. If the initial state of the atom is excited, a doublet structure is formed in the emitted photon spectrum, provided that the interaction is strong enough. If it is the microsphere that is excited at the initial instant, the excited photon spectrum depends substantially on the excitation method used. When excitation is optimal, the atom is effectively excited, and a Rabi-doublet is then formed in the fluorescence spectrum. When the excitation conditions are other than optimal, the spectrum becomes of triplet character, and when the deviation from the optimal excitation conditions is strong enough, the atom practically fails to get excited, and the fluorescence spectrum is of singlet type. A considerable part of the results obtained is of a general nature and can easily be applied to other cases of strong interaction between atoms and resonators.
The transition rates of atoms inside spherical dielectric particles are computed and studied as functions of the transition frequency and of the physical properties of the host particle. The rates are found to range from about 0.2 to more than 1500 times the free-space value, depending on the location of the atom and other relevant physical parameters. The radiation from distributions of atoms inside liquid drops is also studied. Analytic and numerical results are given for the case of a uniform distribution of excited atoms. Large enhancements of the power output (some 100 times the value for the same distribution in bulk material) are found to occur under resonant conditions.
We study the spontaneous emission rate of excited atoms in a dielectric microcavity sandwiched by two dielectric semi-infinite spaces and introduce a lifetime distribution function to reveal decay kinetics in this paper.The spontaneous emission rate of atoms is calculated as a function of the position of atom in the microcavity in both symmetric and asymmetric structure cases.Our calculations show that the spontaneous emission rate of atoms depends on the thickness of the microcavity and the refractive indices of substrate.Both accelerated and inhibited decay processes appear.The lifetime distribution with a single-exponential decay can be observed in the much thicker microcavity.The calculated results are in good agreement with experimental results.