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Physical Review A

Quantum electrodynamic and semiclassical interference effects in spontaneous radiation

R. M. Herman, Howard Grotch, R. L. Kornblith, Joseph H. Eberly

Published Apr 1, 1975• 55 citations
Publisher

Abstract

The theory of spontaneous decay is studied using both quantum electrodynamics (QED) and semiclassical theories of radiation. There are qualitative differences between the theories in the prediction of interference phenomena. In QED, systems which have been excited with pulsed laser light do not exhibit quantum interference effects associated with lower state splittings. On the other hand, semiclassical treatments of spontaneous decay do indicate the existence of interference effects not present in QED. In addition to this, differences are found between the predictions of fluorescence intensity in the presence of lower-state level crossings under continuous excitation.

DOI
10.1103/physreva.11.1389

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The theory of spontaneous decay is studied using both quantum electrodynamics (QED) and semiclassical theories of radiation. There are qualitative differences between the theories in the prediction of interference phenomena. In QED, systems which have been excited with pulsed laser light do not exhibit quantum interference effects associated with lower state splittings. On the other hand, semiclassical treatments of spontaneous decay do indicate the existence of interference effects not present in QED. In addition to this, differences are found between the predictions of fluorescence intensity in the presence of lower-state level crossings under continuous excitation.
Many quantum phenomena, traditionally described by quantum electrodynamics, can be calculated within the framework of so-called semiclassical theory, in which atoms are described by the wave equations of quantum mechanics (Schrödinger, Dirac, etc.), while light is described by classical electrodynamics without quantization of the radiation. These phenomena include the photoelectric effect, the Compton effect, the Lamb shift, radiative effects, spontaneous emission, the Hanbury Brown and Twiss effect, etc. In this paper, I show that the double-slit experiment can also be calculated in detail in terms of semiclassical theory if we take into account the discrete (atomic) structure of matter. I show that the results of a semiclassical simulation of the “linear” double-slit experiment coincide with predictions of wave theory only for low-intensity light and for short exposure time, while stricter dependences exist for long-term exposure. The semiclassical theory is used for calculation of the “nonlinear” double-slit experiment with an intense laser beam in which multiphoton and tunnel excitation of atoms on a photographic plate occurs. The Born rule for light is derived from the semiclassical theory.
A semiclassical radiation theory is developed in which the spontaneous emission field of a two-level atom is a quantum entity represented by atomic operators acting in the Hilbert space of the atomic states. The theory is applied to an investigation of the coherence properties of spontaneous emission. It is found that incoherent and coherent components can be identified in the emission field, the former dominating in the early stages of the decay from the excited state and the latter dominating in the later stages or in the emission from a weakly excited atom. The single-atom coherence properties are shown to lead to well-known superradiance phenomena in the spontaneous emission from an assembly of similar atoms. The paper does not use the theory of quantum electrodynamics; it builds on knowledge at the undergraduate level of classical radiation theory and the quantum mechanics of atoms.
Abstract Both quantum-electrodynamical (QED) and semiclassical approaches are applied to study the spontaneous emission of an atom or atomic ensemble driven by the strong external laser field. It is demonstrated that the semiclassical approach typically used for analyzing the emission of dressed atomic systems is inconsistent with the QED approach and does not provide a proper description of the emission of two-level atoms in a strong external laser field. That is, aside from a situation where the external radiation is nonresonant, weak enough and does not cause the essential population of the excited atomic level.
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.
We discuss quantum interference effects in the resonance fluorescence spectrum of a \ensuremath{\Lambda} three-level atom when the lower-level doublet is driven by a coherent field. The interfering pathways that lead to the same final state involve both spontaneous decays and stimulated transitions, and differ from one another by an odd number of stimulated processes induced by the driving field. As a consequence, the interference structures depend upon the phase of the coherent field, an effect that is absent in other resonance fluorescence phenomena. The phase dependence of the quantum interference contribution is especially significant when the level splitting of the driven doublet is comparable to the spontaneous decay rates of the competing optical paths.
An improved form of semiclassical radiation theory is developed which includes the effect of the atom's radiation field back on the atom. This formalism is applied to the problem of a single "two-level atom" interacting with a monochromatic field. The resulting equations are solved without resorting to time-dependent perturbation theory, and are found to predict the behavior of the system over times long compared with the lifetime for spontaneous transitions. Not only stimulated emission and absorption, but also spontaneous emission with the proper Einstein AAA coefficient, and a frequency shift which agrees at least semiquantitatively with the Lamb shift are described. In addition, several nonlinear effects involving the interference between spontaneous and stimulated radiation are described, and new experiments which might detect such effects are suggested.