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Physical Review Letters

Coherence in Spontaneous Emission in the Presence of a Dielectric

G. S. Agarwal

Published Apr 1, 1974• 40 citations
Publisher

Abstract

A quantum-electrodynamic theory of spontaneous emission in the presence of a dielectric has been worked out, and formulas are presented for the change in the lifetime and the Lamb shift of a two-level atom, as a result of the presence of a dielectric. Curves are given for the behavior of the damping as a function of the distance of the atom from the interface. The frequency shift for the case of a conductor is also evaluated.

DOI
10.1103/physrevlett.32.703

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A quantum-electrodynamic theory of spontaneous emission in the presence of a dielectric has been worked out, and formulas are presented for the change in the lifetime and the Lamb shift of a two-level atom, as a result of the presence of a dielectric. Curves are given for the behavior of the damping as a function of the distance of the atom from the interface. The frequency shift for the case of a conductor is also evaluated.
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 spontaneous emission rate of an atom in a dielectric system with a single interface is calculated using quantum electrodynamics and analyzed using ideas from closed-orbit theory. The spontaneous emission rate is shown to exhibit a damping oscillation as the atomic distance from the interface is varied. The calculated frequency of the oscillation matches very well with the prediction from closed-orbit theory. This study provides a different perspective on the spontaneous emission of atoms in the presence of environments.
We consider the process of spontaneous emission of a two-level atom embedded into a periodic layered dielectric structure. When the resonant atomic frequency lies within the photon-density-of-states gap, of width \ensuremath{\Gamma}, the atom emits light during a time interval t\ensuremath{\Gamma}\ensuremath{\ll}1 until the spontaneous emission becomes fully inhibited. We discuss the enhancing of spontaneous emission by tuning the atomic resonance with a one-mode microcavity. In the \ensuremath{\lambda}/4-shifted distributed feedback microcavities which possess the \ensuremath{\delta}-function-like density of states, in the middle of the gap, the process of spontaneous emission has damped Rabi oscillation behavior; the damping depends on the width of the gap and the height of its walls. A profile of the density-of-states gap can be determined from the experimental data on the temporal behavior of the atomic spontaneous decay.
The rate of spontaneous emission of an atom in the presence of an interface between two dielectrics was calculated using the quantum theory of electromagnetic radiation. Spatial distribution of the field for quasi-continuous spectrum inside an infinite cavity with ideally conducting walls was determined for multiple values of real refractive indices. Spontaneous emission in the continuous spectrum of the field was calculated using the known spatial Green’s function for a one-dimensional dielectric interface. The rate of spontaneous emission of an atom may either be higher or much lower than that in the free space, depending on the refractive indices and the distance between the atom and the interface between dielectrics.
Spontaneous emission and Lamb shift of atoms in absorbing dielectrics and dense atomic gases are discussed using a microscopic Green's-function approach. Uncorrelated and random atomic positions are assumed, and the associated unphysical interactions between different atoms at the same location are eliminated (local field correction). For the case of an atom in a purely dispersive medium, the spontaneous-emission rate is altered by the well-known Lorentz local-field factor. When the mean distance between atoms becomes less than the resonance wavelength, results different from previously suggested expressions are found. In particular, it is shown that nearest-neighbor interactions become important. The results suggest that, for large densities, absorbing disordered dielectrics cannot accurately be described by a macroscopic approach that neglects correlations between atomic positions.