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Physica Scripta

Spontaneous emission and absorber theory

David Thomas Pegg

Published Jan 1, 1997• 3 citations
Publisher

Abstract

One of the long term interests of George Series was the construction of a theory of spontaneous emission which does not involve field quantisation. His approach was written in terms of atomic operators only and he drew a parallel with the Wheeler-Feynman absorber theory of radiation. By making a particular extra postulate, he was able to obtain the correct spontaneous emission rate and the Lamb shift reasonably simply and directly. An examination of his approach indicates that this postulate is physically reasonable and the need for it arises because quantisation in his theory occurs after the response of the absorber has been accounted for by means of the radiative reaction field. We review briefly an alternative absorber theory approach to spontaneous emission based on the direct action between the emitting atom and a quantised absorber, and outline some applications to more recent effects of interest in quantum optics.

DOI
10.1088/0031-8949/1997/t70/016

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One of the long term interests of George Series was the construction of a theory of spontaneous emission which does not involve field quantisation. His approach was written in terms of atomic operators only and he drew a parallel with the Wheeler-Feynman absorber theory of radiation. By making a particular extra postulate, he was able to obtain the correct spontaneous emission rate and the Lamb shift reasonably simply and directly. An examination of his approach indicates that this postulate is physically reasonable and the need for it arises because quantisation in his theory occurs after the response of the absorber has been accounted for by means of the radiative reaction field. We review briefly an alternative absorber theory approach to spontaneous emission based on the direct action between the emitting atom and a quantised absorber, and outline some applications to more recent effects of interest in quantum optics.
The absorber theory of radiation is discussed with particular reference to its application to quantum optical phenomena. The essential feature of the theory is that the absorber is the source of the radiative reaction force. This is an advanced action of the absorber on the emitting atom and, in the quantum version of the theory, is highly directional and polarized. Direct action absorber theory, without fields, can reproduce effects such as spontaneous emission, the Lamb shift, the dynamic Stark effect and photoelectron antibunching, which are often described as properties of the quantized field. Its most interesting application, however, is in calculating the detailed dynamics involved in the Kocher-Commins experiment. It is this experiment which most clearly displays the anti-causal nature of the radiative reaction in absorber theory and shows the advantage of absorber theory over the conventional quantum electrodynamic model in explaining the effect.
We consider the spontaneous emission in an absorbing medium by calculating the quantum flow of energy from an emitting atom. For this purpose, we extend the analysis by Power and Thirunamachandran of quantized Maxwell fields in the vicinity of an atom in the free space to a situation where the emitter is in a dielectric medium. We represent the quantum flow in terms of the non-equal time commutators involving electric and magnetic fields, as well as the local displacement field. The commutators are calculated applying a previously developed microscopic theory of quantization of radiation in dielectrics. Consequently, we derive from first principles the rate of spontaneous emission in an absorbing medium containing local field factors and other refractive contributions. The results support the previous introduction of the (virtual cavity) local field correction by Barnett et al on a phenomenological basis, as well as our previous approach in which the spontaneous emission is considered as a resonance energy transfer to the far-zone atoms. A distinctive feature of the present formalism is that it deals with the spontaneous emission directly by calculating the quantum flow from the emitting atom. Therefore, the method is free from divergences appearing in other approaches analysing the spontaneous decay in absorbing media.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
This paper discusses the nature of the boundary condition applying to the direct-action theory of fields, also known as the 'absorber' theory, first developed in a classical version by Wheeler and Feynman. The traditional understanding of these authors and others who followed is that the direct-action theory requires that 'all emitted radiation be absorbed,' or that 'the universe is a perfect (or complete) of absorber of radiation,' implying the need for a specific sort of cosmological boundary condition that may or may not obtain in our universe. It is pointed out that this interpretation requires critical scrutiny even at the classical level, and in any case does not apply to the fully quantum form of the direct-action theory (QDAT), which involves discrete energy transfers by way of photons. In the latter case, the absorption boundary condition describes a specific interactive relationship between emitters and absorbers that is independent of cosmological boundary conditions. Thus, the quantum direct-action theory does not require any special cosmological boundary condition in order for it describe the physical world.
The recently detected photoelectron antibunching effect is considered to be evidence for the quantised electromagnetic field, i.e. for the existence of photons. Direct-action quantum absorber theory, on the other hand, has been developed on the basis that the quantised field is illusory, with quantisation being required only for atoms. The author shows that photoelectron antibunching is readily explicable in terms of absorber theory and in fact is directly attributable to the quantum nature of the emitting and detecting atoms alone. The physical nature of the reduction of the wavepacket associated with the detection process is briefly discussed in terms of absorber theory.