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Physical Review A

Comment on the radiative level shift in the neoclassical radiation theory

R. van den Doel, J.J.J. Kokkedee

Published Mar 1, 1974• 6 citations
Publisher

Abstract

It is shown that when spin currents are included in the neoclassical radiation theory of Jaynes et al., radiative atomic level shifts are obtained which in the case of hydrogen are in strong disagreement with experiment.
DOI
10.1103/physreva.9.1468

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The neoclassical theory of radiation predicts that the decay rate of an excited atomic state depends on the population density of the lower state. Experimental evidence is presented here which shows that in the case of 39K^{39}\mathrm{K}39K the decay rate is in agreement with the predictions of quantum electrodynamics and definitely in disagreement with the neoclassical theory.
We discuss some implications of the description of spontaneous emission of radiation which has been offered by Jaynes and his collaborators in their "neoclassical" extension of semiclassical electrodynamics. In particular, we examine the thermal-equilibrium condition of radiation interacting with a tenuous gas of atoms. We argue that rate equations may be used to describe the interaction of such atoms with the chaotic thermal radiation field. For this situation the neoclassical spontaneous emission rate is incompatible with the well-secured laws of Boltzmann and Planck. Experimental evidence bearing on the accuracy of those laws as well as on the accepted level population dependence of the induced emission rate is reviewed.
In our preceding treatments of the interaction of radiation with matter, we assumed that the electric field is classical. In most cases, this assumption is validated by experiment. There are several instances, however, for which a classical field fails to give experimentally observed results, whereas a quantized field succeeds. This is true, for example, of spontaneous emission, a phenom­ enon which was described phenomenologically in our earlier work (see Chaps. 2 and 7). Another case involves the 2 and 2p \ states in the hydrogen atom, which are predicted to have the same energy not only by the simple theory of Chap. 1, but also by the more sophisticated Dirac theory. In both cases, a classical electric field was assumed. Experimentally, the two levels differ by approximately the Lamb shift, 1057 MHz. A fully quantized treatment of the field and atom system gives impressive agreement with the experimentally observed shift. Derivation of the fluctuations in intensity of a laser near threshold requires the quantum theory o f radiation. In addition there are other problems for which the concept of a “particle,” the photon, is either necessary or convenient. Despite a popular impression to the contrary, however the explanation of the photoelectric effect is not one of these (see Prob. 2-10).
Recently Cardimona and Stroud emphasized that, when the energy levels of an atom are degenerate or nearly so, there can exist a strong radiative interaction between different spontaneous transitions of the atom. This interaction is described by the generalized damping terms and generalized frequency-shift terms in the equation of motion for the atomic density matrix. We here point out that the generalized damping terms can play an important role in the absence of degeneracy for systems other than atoms, and cite the harmonic oscillator as an example. Specifically, we show that these terms are needed for a proper classical limit of radiation damping, and that a small anharmonicity can have a very large effect on the radiative decay rate of the oscillator's amplitude.
The neoclassical theory of the interaction of radiation with matter, introduced by its authors as a potentially viable alternative to quantum electrodynamics, is examined in the case of a multilevel atom interacting with blackbody radiation. The stationary statistical states of the atom and the field are derived, and two independently untenable results emerge. First, the stationary blackbody law turns out to be that of Rayleigh and Jeans, rather than that of Planck. Second, the mean energy of a harmonic oscillator, which interacts with the field only near a single frequency, turns out to be infinite. These results are discussed in the light of the neoclassical description of spontaneous emission.