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Optica Acta International Journal of Optics

Quantum-mechanical Long-range Correlations Generated in Optical Beam-splitting

Henryk Paul

Published Jan 1, 1981• 7 citations
Publisher

Abstract

It is pointed out that optical beam splitting, when the number of incident photons is fixed, produces quantum-mechanical correlations of the type discussed by Einstein, Podolsky and Rosen [1]. From this result, it is concluded that conventional interference experiments at large beam separation provide indirect evidence of the actual long-range character of intrinsically quantum-mechanical correlations.

DOI
10.1080/713820437

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It is pointed out that optical beam splitting, when the number of incident photons is fixed, produces quantum-mechanical correlations of the type discussed by Einstein, Podolsky and Rosen [1]. From this result, it is concluded that conventional interference experiments at large beam separation provide indirect evidence of the actual long-range character of intrinsically quantum-mechanical correlations.
Einstein–Podolsky–Rosen (EPR) correlations produced for two-photon entangled wave packets are analyzed by use of optical Wigner functions. In particular, type-II optical parametric downconversion systems are used, and the effects of the length of the crystal and the filter bandwidth on the Wigner functions are studied. The relation between the optical Wigner functions and the interference experiment with a beam splitter is studied. We find that, whereas in first-order correlation experiments (typified, for example, by Young’s interference experiment) the “photon interferes with itself” [ P. A. M. Dirac , The Principles of Quantum Mechanics (Clarendon, Oxford, UK, 1958), p. 9], in the EPR correlations the two-photon amplitude function interferes with itself. Such interference is analyzed by use of the optical Wigner functions.
Simple optical instruments are linear optical networks where the incident light modes are turned into equal numbers of outgoing modes by linear transformations. For example, such instruments are beam splitters, multiports, interferometers, fibre couplers, polarizers, gravitational lenses, parametric amplifiers, phase-conjugating mirrors and also black holes. The paper develops the quantum theory of simple optical instruments and applies the theory to a few characteristic situations, to the splitting and interference of photons and to the manifestation of Einstein–Podolsky–Rosen correlations in parametric downconversion. How to model irreversible devices such as absorbers and amplifiers is also shown. Finally, the paper develops the theory of Hawking radiation for a simple optical black hole. The paper is intended as a primer, as a nearly self-consistent tutorial. The reader should be familiar with basic quantum mechanics and statistics, and perhaps with optics and some elementary field theory. The quantum theory of light in dielectrics serves as the starting point and, in the concluding section, as a guide to understand quantum black holes.