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Physical Review A

Radiation reaction and vacuum fluctuations in spontaneous emission

Peter W. Milonni, Wallace Arden Smith

Published Mar 1, 1975• 124 citations
Publisher

Abstract

A Heisenberg-picture treatment of spontaneous emission is given, and the origin of radiative line shifts and widths is discussed. It is shown that radiation reaction and vacuum fluctuations provide complementary conceptual bases for the interpretation of these radiative corrections. Alternative approaches are discussed, including the use of a random classical field to simulate the effects of the quantum-electrodynamical radiation field.

DOI
10.1103/physreva.11.814

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Comment on “Spontaneous emission: vacuum fluctuations or radiation reaction” by R R Puri

Peter W. Milonni

It has recently been claimed that the vacuum field does not contribute explicitly, in any operator ordering, to spontaneous emission. This claim is based on a trivial observation that misses the point of a whole series of independent investigations.

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identification of their respective contributions

Jean Dalibard, J. Dupont-Roc, Claude N. Cohen-Tannoudji

It is generally considered that there exists in quantum radiation theory an indetermination in the separation of the respective effects of vacuum fluctuations and radiation reaction. We show in this paper that such an indetermination can be removed by imposing to the corresponding rates of variation to be Hermitian (this is necessary if we want them to have a physical meaning). Such a procedure is generalized to the case of a small system S interacting with a large reservoir R and allows the separation of two types of physical processes, those where R fluctuates and polarizes S (effects of reservoir fluctuations), those where it is S which polarizes R (effects of self reaction). We apply this procedure to an atomic electron interacting with the radiation field and we then identify the contribution of vacuum fluctuations and self reaction to radiative corrections and spontaneous emis- sion of radiation. The analysis of the results obtained in this way allows us to specify the physical pictures which must be associated with the various radiative processes.

•Jan 1, 1982•2 citations
A Heisenberg-picture treatment of spontaneous emission is given, and the origin of radiative line shifts and widths is discussed. It is shown that radiation reaction and vacuum fluctuations provide complementary conceptual bases for the interpretation of these radiative corrections. Alternative approaches are discussed, including the use of a random classical field to simulate the effects of the quantum-electrodynamical radiation field.
The role of vacuum fluctuations and radiation reaction in the process of spontaneous emission is examined with particular reference to the Heisenberg picture of quantum electrodynamics. In this picture the radiation reaction is found to be responsible for spontaneous emission if the equations are ordered normally. However, in the case of nonnormally ordered equations there appears to be an explicit contribution to the observable effects from vacuum fluctuations as well. We point out that this contribution from the vacuum field is an artifact of the approximation methods employed for eliminating the free-field variables from the nonnormally ordered equations These approximations are the same as those used in the master-equation approach, in which spontaneous emission appears to be due solely to the vacuum fluctuations. We show that the vacuum field does not contribute explicitly in any ordering if it is eliminated nonperturbatively and the approximation methods are invoked only after its elimination from the equations of motion.
Abstract The atom-field interaction is formulated within the fully quantized-field theory, starting from a detailed analysis of the transformation from the fundamental minimal coupling interaction Hamiltonian to the electric dipole Hamiltonian used extensively in quantum optics. Spontaneous emission, radiative level shifts, and the natural radiative lineshape are treated in both the Schrodinger and Heisenberg pictures, with emphasis on the roles of vacuum field fluctuations, radiation reaction, and the fluctuation-dissipation relation between them. The shortcomings of semiclassical radiation theories are discussed.
Dalibard, Dupont-Roc and Cohen-Tannoudji (J. Physique 43 (1982) 1617; 45 (1984) 637) used the Heisenberg picture to show that the atomic transitions, and the stability of the ground state, can only be explained by introducing radiation reaction and vacuum fluctuation forces. Here we consider the simple case of nonrelativistic charged harmonic oscillator, in one dimension, to investigate how to take into account the radiation reaction and vacuum fluctuation forces within the Schrodinger picture. We consider classical vacuum fields and large mass oscillator.
It is generally considered that there exists in quantum radiation theory an indetermination in the separation of the respective effects of vacuum fluctuations and radiation reaction. We show in this paper that such an indetermination can be removed by imposing to the corresponding rates of variation to be Hermitian (this is necessary if we want them to have a physical meaning). Such a procedure is generalized to the case of a small system S interacting with a large reservoir R and allows the separation of two types of physical processes, those where R fluctuates and polarizes S (effects of reservoir fluctuations), those where it is S which polarizes R (effects of self reaction). We apply this procedure to an atomic electron interacting with the radiation field and we then identify the contribution of vacuum fluctuations and self reaction to radiative corrections and spontaneous emis- sion of radiation. The analysis of the results obtained in this way allows us to specify the physical pictures which must be associated with the various radiative processes.