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Physica Scripta

Absorber Theory in Quantum Optics

David Thomas Pegg

Published Jan 1, 1986• 13 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/1986/t12/002

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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.

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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.
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 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.
An attempt is made to present a consistent detailed theory of optical phenomena, based on the suggestion recently made by the author in collaboration with Bohr and Kramers. This suggestion is that atoms are radiating or absorbing continuously, during their stationary states, and that transitions influence radiation only in terminating the radiation characteristic of the old state, and substituting that of the new. The atoms, on the other hand, are supposed not to change their energy while radiating, but to change it discontinuously on transition. This necessitates giving up the detailed application of the conservation of energy in interaction between atoms and radiation. In the present paper, an additional suggestion is made, namely that resonance radiation is to be identified with the radiation carried out by the spherical wavelets which, by their interference with the external field, also produce absorption. This is practically a return to the classical picture of resonance radiation. Statement of the theory consists formally of two parts: the description of the behavior of atoms, and of radiation, when the two interact. The first involves the statement of the probabilities of transition of atoms, and is taken without change from Einstein. The probability of interruption of coherent vibrations is also discussed. The second requires the specification of the fields emitted by atoms in any steady state under the influence of any external field. These consist of spherical wavelets of the frequencies of the various quantum lines which the atom can emit or absorb in the stationary state in which it is. For emission frequencies, wavelets are emitted even in the absence of an external field; for absorption frequencies, external fields induce wavelets, similar to the wavelets of linearly bound electrons in electron theory, which on the one hand interfere with the external field to produce the phenomena of dispersion, etc., and on the other carry out the resonance radiation in all directions. Detailed descriptions of these fields are given. In a discussion of the theory, it is first shown that the assumptions which have been made about the field satisfy the correspondence principle, in that for large quantum numbers the field aproaches that which would be emitted classically on account of the interaction of an external field and a multiply periodic atom. On the other hand, it is shown that the field has a character essentially like that of classical electron theory, which is known to be in general agreement with experiments. Next, the energy and momentum relations at interaction of atoms and light are investigated, and it is shown that, although these quantities are not precisely conserved, still the assumptions as to atomic and radiation processes have been so made that they are conserved on an average over a great number of atomic processes. Finally the spectral resolution of emitted and absorbed radiation is considered; the theory gives a minimum breadth for the lines, depending on the finite length of wave trains resulting from the finite life in stationary states, and it is shown that Kirchhoff's law is obeyed, the emission and absorption lines being of the same breadth. By way of illustration, specific application of the theory is made to the simple examples of emission of light by bombardment of electrons at the resonance potential, resonance radiation, its quenching by presence of foreign gases, absorption, scattering, and disperison.
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 quantum theory of radiation was formulated by Dirac in 1927, when he combined the wave nature of light with the particle behavior and could explain the interference phenomena. He also explained the atomic behavior of absorbing a discrete quantum of radiation for excitation from one level to another. The Michelson-Morley experiment on light led to the formulation of special theory of relativity, while Rayleigh-Jeans formulation on Black Body radiation led Planck to propose the quantum of action that finally marked the beginning of quantum mechanics. The energy of the radiation field of the classical wave has been expressed as the sum of the energies of individual modes in the cavity. The interaction of atom with radiation field was explained by Einstein in terms of stimulated emission, absorption and spontaneous emission. After the development of quantum mechanics, perturbation theory could be used to describe the Einstein B-coefficients.