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Journal of the Optical Society of America B

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

Peter W. Milonni

Published Dec 1, 1985• 2 citations
Publisher

Abstract

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.
DOI
10.1364/josab.2.001953

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Spontaneous emission: vacuum fluctuations or radiation reaction?

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Cambridge University Press eBooks•Sep 2, 1993•0 citations
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.
Introduction Ever since 1916/17 when Einstein argued [45] [46] that spontaneous emission must occur if matter and radiation are to achieve thermal equilibrium, physicists have believed that spontaneous emission is an inherent quantum mechanical property of atoms and that excited atoms inevitably radiate. This view, however, overlooks the fact that spontaneous emission is a consequence of the coupling of quantized energy states of atoms with the quantized radiation field, and is a manifestation of quantum noise or of emission ‘stimulated’ by ‘vacuum fluctuations’. An infinity of vacuum states is available to the photon radiated by an excited atom placed in free space, leading to the effective irreversibility of such emissions. If these vacuum states are modified, as for example by placing an excited atom between closely spaced mirrors or in a small cavity (essentially the Casimir effect), spontaneous emission can be greatly inhibited or enhanced or even made reversible. Recent advances in atomic and optical techniques have made it possible to control and manipulate spontaneous emission. A whole new branch of quantum optics called ‘cavity QED’ has developed since 1987 utilizing these dramatic changes in spontaneous emission rates in cavities to construct new kinds of microscopic masers or micromasers that operate with a single atom and a few photons or with photons emitted in pairs in a two-photon transition.
Spontaneous emission may be regarded as a result of the radiation-reaction fields emitted by an atom acting back on the atom itself. It is commonly (and often implicitly) assumed that the frequencies of different transitions in the atom are sufficiently different that the field radiated by one dipole is not in near resonance with any other transition. The “secular assumption” is then made that the field couples back only on the same dipole that originally sent it. In this work we study spontaneous emission without making the secular approximation.
When you follow two separate chains of thought, Watson, you will find some point of intersection which should approximate the truth. —Sir Arthur Conan Doyle, The Disappearance of Lady Frances Carfax ABSTRACT. It is now well established that effects traditionally associated with vacuum electromagnetic field fluctuations can be described equally well in terms of source fields (radiation reaction). This remarkable reconciliation of two previously unconnected points of view, which was stimulated by Jaynes' neoclassical theory, is reviewed and explained in a general and simple way. Background The Jaynes-Cummings paper seems to have been the first to employ dressed states of two-state atoms in fields (Jaynes 1963). One result found in that paper is that semiclassical radiation theory could serve as an excellent approximation even under certain conditions where the average number of photons in the field is small. The accuracy of semiclassical theory paved the way to Jaynes' “neoclassical theory,” where even spontaneous emission was treated without field quantization (Jaynes 1972, Milonni 1976). The neoclassical theory was a subject of much debate and misunderstanding in the 1970s. It turned out not to be so easy to dismiss it on experimental grounds.