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Physical Review A

Quantum-beat phenomena described by quantum electrodynamics and neoclassical theory

Weng W. Chow, Marlan O. Scully, John O. Stoner

Published Apr 1, 1975• 100 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.11.1380

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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.
This dissertation may be divided into three parts. In the first part we propose and analyze the use of quantum beat phenomena to test neoclassical radiation theory (NCT) and quantum electrodynamics CQED). 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 pres­ ent, in agreement with recent photon-echo experiments. An experiment to test NCT and QED is suggested. In the second part of this dissertation we calculate, via the quantum noise operator approach, the power spectral density of a laser subjected to a symmetry-breaking injected signal. The resulting spec­ trum is sharpened. It is further noted that these considerations are potentially of interest in producing high intensity fields in small focal volumes. The final portion of this dissertation contains a description of a high power CO2 TEA laser that was built for use in laser isotope separation experiments. This laser, whose output pulses are each of the order of a few joules, will be used in studies concerning the laser enrichment of SF^ and the temporal behavior of hot electrons in InSb.
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.
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.
Quantum beats in the radiation field of "three-level" atoms are analyzed by means of a previously developed boson-second-quantization (BSQ) formalism. Two types of atoms are considered: type I, in which beats are due to transitions from each of two closely spaced upper levels to a single lower level, and type II, in which beats are due to transitions between a single upper level and each of two closely spaced lower levels. This classification is motivated by the claim found in the literature that semiclassical theory and quantum theory give qualitatively different results concerning the existence of beats in the case of type-II atoms. The terminology associated with beats is made precise by distinguishing between amplitude modulation at the beat frequency of the transition frequency field EEE, and the existence of a spectral component at the beat frequency in E2{E}^{2}E2. With respect to the former, no qualitative difference is found in the predictions from semiclassical theory and quantum theory; with respect to the latter, results that appear paradoxical from an intuitive viewpoint are discussed. It is shown that for the case in which the atoms are all in the same coherent superposition of energy states, with all levels occupied, semiclassical and quantum-mechanical results become equivalent as the number of atoms increases. Reference is made to the disturbance caused by the measurement processes in the case of a single atom. The essential difference in spontaneous emission beats between type-I and type-II atoms [with the ground state(s) unoccupied] is explained by the fact that the phase of the beat amplitude may be determined by preparation of the initial state in type-I atoms but may not be determined in type-II atoms.
We use a self-field approach to quantum electrodynamics (QED) to show how one may obtain spontaneous emission and the Lamb shift in a two-level atom without second quantization of the radiation field. In addition, we compare the self-field formalism to that of the neoclassical theory of electrodynamics advanced by Crisp and Jaynes [Phys. Rev. 179, 1253 (1969)]. We show that the neoclassical model can be obtained from the self-field approach used here, but that the two are not equivalent. In particular, the self-field approach appears to give a more complete description of radiative processes. Finally, we show that the neoclassical theory's prediction of a nonexponential ``chirruped'' decay is most likely a mathematical artifact of the improper application of the superposition principle in a nonlinear model where such a principle does not hold. A correct treatment with self-field QED yields the usual exponential decay dynamics.