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Physical Review A

Theory of Atomic Lifetime Measurements

J. H. Macek

Published Mar 1, 1970• 75 citations
Publisher

Abstract

The theory of atomic lifetime measurements is developed on the basis of the quantum theory of radiation. The effect of coherent emission on the shape of the decay curves is studied in detail. It is shown that the light intensity will oscillate in time when two closely spaced levels decay coherently. Oscillations due to interference between fine-structure levels of the hydrogen atom in particular are discussed.

DOI
10.1103/physreva.1.618

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Cascade Effects in Certain Atomic Lifetime Measurements

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Physical Review A•Apr 1, 1971•12 citations
The theory of atomic lifetime measurements is developed on the basis of the quantum theory of radiation. The effect of coherent emission on the shape of the decay curves is studied in detail. It is shown that the light intensity will oscillate in time when two closely spaced levels decay coherently. Oscillations due to interference between fine-structure levels of the hydrogen atom in particular are discussed.
The theory of measurements in which photons are detected in delayed coincidence with a scattered particle is developed in a form specifically applicable to atomic collisions. Equations are obtained which relate the measured coincidence rate to excitation amplitudes. These equations incorporate the polarization of the radiation, the fine and hyperfine structure of the atomic levels, the coherence of the radiation, and the time dependence of the radiation intensity. A semiclassical model for certain transitions is introduced to illustrate new features of coincidence measurements. The $\mathrm{Ly}\ensuremath{-}\ensuremath{\alpha}$ transitions in hydrogen and $^{1}P\ensuremath{\rightarrow}^{1}S$ transitions in He are treated in detail to illustrate the general theory.
In this paper we present a study of the radiative decay of coherently excited, closely spaced, molecular (or atomic) levels. Interference effects in the decay process cannot be treated in general by displaying the damping matrix in a diagonal form, so that each decay channel is assumed to be characterized by its own lifetime. The problem of the radiative decay of coherently excited indistinguishable levels (characterized by the same symmetry) is treated by a self-consistent extension of the Wigner-Weisskopf method, or alternatively, by the ‘unitarity relations’ method, developed in elementary particles physics. Finally, the Fano configuration interaction method is applied for the decay of a manifold of states characterized by the same polarization. General expressions for photon counting rates are derived and the nature of a general quantum beat experiment is discussed.
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.
Variations in the spatial intensity distribution of light caused by coherent interaction with two-level atoms are determined by semi-classically calculating a term for interference between incident light and spherical radiation from the atom. The interference term is divided into two components: one oscillates at the Rabi frequency corresponding to absorption and stimulated emission, and the other contributes to dispersion. The spatial distribution of both components involves alternation of constructive and destructive parts in the form of parabolic surfaces where light energy flows. Although the time average over the Rabi oscillation of the former component vanishes at every position, that of the latter remains. The light-related reaction of a dipole force acting on an atom is considered to appear in the non-vanishing latter component.
A semiclassical discussion is given of a simple case of the Hanle effect when the population of the level of interest varies with time because of decays to it from higher levels excited by collisions. It is found that the width of the intensity-vs-applied-field curve is no longer simply related to the lifetime of this single level, but depends on the relative populations and lifetimes of all other participating levels. It is shown by examples that, unless these effects are taken into account, the lifetimes deduced from the measurements can be greatly in error.