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CRC Press eBooks

Quantum Interference

F. J. Duarte

Published Apr 10, 2026• 0 citations
Publisher

Abstract

Quantum interference, which is a physical phenomenon, and probability amplitudes à la Dirac are miraculously like synonyms. Indeed, the way probability amplitudes are written down on paper is very much as a single photon, or an ensemble of indistinguishable photons, propagates from one plane to the next. And then, if at one of the planes an N -slit array alternative is offered then the probability amplitude notation à la Dirac cleverly describes the N -path alternative via a mathematical summation. Here we should emphasize that since the photon is a nonlocal quantum entity, all the microscopic slits in the N -slit array, or transmission diffraction grating, are illuminated simultaneously.

DOI
10.1201/9781003649434-5

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Comment on Reflection, refraction and multislit interference

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It is indicated that the generalized interference equation, obtained using the Dirac notation applied to an N-slit interferometer, has already been applied to derive the equation of the diffraction grating, the law of refraction and the law of reflection. The applicability of the Dirac approach to describe interference of large number of indistinguishable photons is also explained.

European Journal of Physics•Jul 9, 2004•13 citations
Quantum interference, which is a physical phenomenon, and probability amplitudes à la Dirac are miraculously like synonyms. Indeed, the way probability amplitudes are written down on paper is very much as a single photon, or an ensemble of indistinguishable photons, propagates from one plane to the next. And then, if at one of the planes an N -slit array alternative is offered then the probability amplitude notation à la Dirac cleverly describes the N -path alternative via a mathematical summation. Here we should emphasize that since the photon is a nonlocal quantum entity, all the microscopic slits in the N -slit array, or transmission diffraction grating, are illuminated simultaneously.
The interaction of coherent light with a set of slits, in the near field, gives rise to an interference pattern. Refraction is the change in the geometrical path, of a beam of light, due to transmission from the original medium of propagation to a second medium with a different refractive index. One of the beauties of the Dirac description of optics is the ability to continuously describe the evolution of the interferometric distribution, as it moves from the near to the far field, with a single mathematical equation. The interferometric distribution, in the near field, is mainly part of a single order. At the boundaries there is an incipient indication that of emerging orders. Explicitly, if a mirror is placed at an infinitesimal distance immediately behind the N-slit array then the transmission interferometer becomes a reflection interferometer.
It is elucidated that N-slit, or N-path, quantum interference utilizes the intrinsic nonlocality of the photon to illuminate simultaneously from the source the entire N-slit array thus allowing the characterization of the interference via the Dirac-Feynman interferometric principle. This simultaneous illumination of N-paths also applies to the Feynman path integral formulation of quantum mechanics. This quantum mechanism of simultaneous and whole illumination of N-slits, or N-paths, is quite different to the sequential illumination of N-paths via the hypergraph methodology where the N is achieved via the classical diagrammatical binary sequence 1, 2, 4, 8, 16, 32, … .
It is elucidated that N-slit, or N-path, quantum interference utilizes the intrinsic nonlocality of the photon to illuminate simultaneously from the source the entire N-slit array thus allowing the characterization of the interference via the Dirac-Feynman interferometric principle. This simultaneous illumination of N-paths also applies to the Feynman path integral formulation of quantum mechanics. This quantum mechanism of simultaneous and whole illumination of N-slits, or N-paths, is quite different to the sequential illumination of N-paths via the hypergraph methodology where the N is achieved via the classical diagrammatical binary sequence 1, 2, 4, 8, 16, 32, … .
It is elucidated that N-slit, or N-path, quantum interference utilizes the intrinsic nonlocality of the photon to illuminate simultaneously from the source the entire N-slit array thus allowing the characterization of the interference via the Dirac-Feynman interferometric principle. This simultaneous illumination of N-paths also applies to the Feynman path integral formulation of quantum mechanics. This quantum mechanism of simultaneous and whole illumination of N-slits, or N-paths, is quite different to the sequential illumination of N-paths via the hypergraph methodology where the N is achieved via the classical diagrammatical binary sequence 1, 2, 4, 8, 16, 32, … .
It is elucidated that N-slit, or N-path, quantum interference utilizes the intrinsic nonlocality of the photon to illuminate simultaneously from the source the entire N-slit array thus allowing the characterization of the interference via the Dirac-Feynman interferometric principle. This simultaneous illumination of N-paths also applies to the Feynman path integral formulation of quantum mechanics. This quantum mechanism of simultaneous and whole illumination of N-slits, or N-paths, is quite different to the sequential illumination of N-paths via the hypergraph methodology where the N is achieved via the classical diagrammatical binary sequence 1, 2, 4, 8, 16, 32,…2^r.