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Physical Review A

Test of the neoclassical theory of radiation in a weakly excited atomic system

Gilbert O. Brink

Published Jul 1, 1975• 1 citation
Publisher

Abstract

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 $^{39}\mathrm{K}$ the decay rate is in agreement with the predictions of quantum electrodynamics and definitely in disagreement with the neoclassical theory.

DOI
10.1103/physreva.12.99

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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.
The neoclassical or semiclassical theory (NCT) of the radiative decay of an isolated atom predicts that the decay rate of an excited state is proportional to the atoms's population in the state to which the atom is decaying. For weak excitation of a two-level system, this prediction is consistent with observations and with the Weisskopf-Wigner theory of decay, which assumes a quantized electromagnetic field as in quantum electrodynamics (QED). But for weak excitation of a system with three or more levels, there can be gross disagreements between NCT and QED. NCT predicts that the lifetime of an excited state depends on the nuclear spin which determines the number of ground states between which the atom's unity population density is divided. Also NCT predicts no fluorescence to a third level not initially populated, even though the transition is highly allowed. Observations in Pb vapor are inconsistent with NCT and consistent with QED. The oscillator strengths of the 2833-, 3640-, and 4058-A transitions were determined to be 0.167(20), 0.061(04), and 0.146(10), respectively, by measuring the ratios of oscillator strengths and using the lifetime measurements of Happer and Saloman.
The resonance-fluorescence experiment described in the preceeding paper and found to be consistent with quantum electrodynamics is analyzed using the neoclassical theory (NCT) of radiation, i.e., the electromagnetic field is not quantized. We have not found a value of the dynamic shift for which the NCT computer simulation is consistent with the data. NCT predicts an increased radiative lifetime as appreciable excitation is achieved; the observed decay curves were simple exponentials with characteristic times independent of the fractional excitation. The observed oscillatory dependence of the integrated fluorescence upon input pulse area has not been reproduced by a NCT simulation either. Objections raised against this disproof of NCT are answered.
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 Jaynes's semiclassical radiation theory, the decay of an excited atomic state depends on its initial population. For the radiative decay of the 2P2P2P level in atomic hydrogen, produced by pulsed excitation from the 2S2S2S level, the theory predicts a decay rate $\ensuremath{\Gamma}=(1\ensuremath{-}f){\ensuremath{\Gamma}}_{0}+\ensuremath{\beta}P$, where $\ensuremath{\beta}=f{\ensuremath{\Gamma}}_{0}$. Here fff is the initial 2S2S2S population, ${\ensuremath{\Gamma}}_{0}$ is the natural 2P2P2P decay rate, and PPP is the 2P2P2P population relative to fff. For $f=0.086\ifmmode\pm\else\textpm\fi{}0.016$, and PPP values in the range 0.15 to 0.64, we have measured $\ensuremath{\beta}=\ensuremath{-}(2.8\ifmmode\pm\else\textpm\fi{}2.8)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. The corresponding value from the semiclassical theory is $\ensuremath{\beta}=+(53.8\ifmmode\pm\else\textpm\fi{}10.0)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$.
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.
We propose and analyze the use of quantum-beat phenomena to test neoclassical radiation theory (NCT) and quantum electrodynamics (QED). For a beam-foil type of experiment with atoms having one upper level and two closely spaced lower levels, all coherently excited, NCT predicts the presence of quantum beats in the emitted radiation; beats are not expected in QED. QED predicts beats when many atoms are present, in agreement with recent photon-echo experiments. An experiment to test NCT and QED is suggested.