Physical Review A

Classical limit and quantum measurements in the detection of photons

J. C. Houard

Published Dec 1, 1996• 0 citations

Abstract

The detection process of photons is studied at the limit of a vanishing Planck's constant. The detectors are conceived as particular cases of systems composed of atomic entities, called sources, acting in some given regions of space-time. When these regions are small and when their number is large with respect to the number of atoms of a real detector, we speak of a many-source system. The observable detection probabilities at given times are defined in general in an S-matrix formalism. It is shown that, in the case of a many-source system, these probabilities satisfy the same relations as those valid for a classical statistical system. When Planck's constant goes to zero, the energy density of the radiation remaining finite, an approximate expression of the amplitudes is constructed, which preserves the unitarity of the S matrix, and therefore the conservation of probability. Consequently, no recourse to the attenuation of the radiation field is necessary to ensure a coherent set of probabilities. Due to a factorization property of the amplitudes, it is then shown that the behavior of a real detector is nearly the same as that of a many-source system, namely, a classical behavior. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physreva.54.4719

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Appendix 33 — Quantum Correspondence Tests 33.2 Unitarity and Norm Preservation Conditions 33.2.1 Objective This section establishes the requirement that BSFM must preserve total probability (norm) under evolution in the quantum correspondence regime. 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