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Springer series on atomic, optical, and plasma physics

Theory of Atomic Photon-Particle Coincidence Measurements

J. H. Macek, D. H. Jaecks

Published Jan 1, 2001• 0 citations
Publisher
DOI
10.1007/978-1-4613-0187-5_26

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Theory of Atomic Photon-Particle Coincidence Measurements

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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.
Spontaneous emission of a photon by an atom is described theoretically in three dimensions with the initial wave function of a finite-mass atom taken in the form of a finite-size wave packet. Recoil and wave-packet spreading are taken into account. The total atom-photon wave function is found in the momentum and coordinate representations as the solution of an initial-value problem. The atom-photon entanglement arising in such a process is shown to be closely related to the structure of atom and photon wave packets which can be measured in the coincidence and single-particle schemes of measurements. Two predicted effects, arising under the conditions of high entanglement, are anomalous narrowing of the coincidence wave packets and, under different conditions, anomalous broadening of the single-particle wave packets. Fundamental symmetry relations between the photon and atom single-particle and coincidence wave-packet widths are established. The relationship with the famous scenario of Einstein-Podolsky-Rosen is discussed.