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The Quantum Regime Operation of Beam Splitters and Interference Filters

Andre Vatarescu

Published Feb 2, 2023• 10 citations
Publisher

Abstract

The presence of the quantum Rayleigh scattering, or spontaneous emission, inside a dielectric medium such as a beam splitter or an interferometric filter, prevents a single-photon from propagating in a straight-line. Modelling a beam splitter by means of a unitary transformation is physically meaningless because of the loss of photons. Additional missing elements from the conventional theory are: 1) the quantum Rayleigh stimulated emission which can form groups of photons of the same frequencies, and 2) the unavoidable parametric amplification of single-photons in the original parametric crystal. An interference filter disturbs, through multiple internal reflections, the original stream of single-photons, thereby confirming the existence of groups of photons being spread out to lengthen the coherence time. The approach of modelling individual, single measurements with statistical ensemble probability amplitudes leads to the counterintuitive explanations of the experimental outcomes and should be replaced with pure states describing instantaneous measurements which are afterwards averaged.

DOI
10.20944/preprints201909.0191.v2

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The presence of the quantum Rayleigh scattering, or spontaneous emission, inside a dielectric medium such as a beam splitter or an interferometric filter, prevents a single-photon from propagating in a straight-line. Modelling a beam splitter by means of a unitary transformation is physically meaningless because of the loss of photons. Additional missing elements from the conventional theory are: 1) the quantum Rayleigh stimulated emission which can form groups of photons of the same frequencies, and 2) the unavoidable parametric amplification of single-photons in the original parametric crystal. An interference filter disturbs, through multiple internal reflections, the original stream of single-photons, thereby confirming the existence of groups of photons being spread out to lengthen the coherence time. The approach of modelling individual, single measurements with statistical ensemble probability amplitudes leads to the counterintuitive explanations of the experimental outcomes and should be replaced with pure states describing instantaneous measurements which are afterwards averaged.
The presence of quantum Rayleigh scattering, or spontaneous emission, inside a dielectric medium such as a beam splitter or an interferometric filter prevents a single photon from propagating in a straight line. Modelling a beam splitter by means of a unitary transformation is physically meaningless because of the loss of photons. Additional missing elements from the conventional theory are the quantum Rayleigh-stimulated emission, which can form groups of photons of the same frequency, and the unavoidable parametric amplification of single photons in the original parame-tric crystal. An interference filter disturbs, through multiple internal reflections, the original stream of single photons, thereby confirming the existence of groups of photons being spread out to lengthen the coherence time. The approach of modelling individual, single measurements with probability amplitudes of a statistical ensemble leads to counterintuitive explanations of the experimental outcomes and should be replaced with pure states describing instantaneous measurements whose values are afterwards averaged.
Three physical elements are missing from the conventional formalism of quantum photonics: 1) the quantum Rayleigh spontaneous and stimulated emissions; 2) the unavoidable parametric amplification; and 3) the mixed time-frequency spectral structure of a photonic field which specifies its duration or spatial extent. As a single photon enters a dielectric medium, the quantum Rayleigh scattering prevents it from propagating in a straight-line, thereby destroying any possible entanglement. A pure dynamic and coherent state composed of two consecutive number states, delivers the correct expectation values for the number of photons carried by a photonic wave front, its complex optical field, and phase quadratures. The intrinsic longitudinal and lateral field profiles associated with a group of photons for any instantaneous number of photons are independent of the source. These photonic properties enable a step-by-step analysis of the correlation functions characterizing counting of coincident numbers of photons or intensities with unity visibility interference, spanning the classical and quantum optic regimes
The quantum Rayleigh spontaneous emission replaces entangled photons with independent ones in homogeneous dielectric media where single photons cannot propagate in a straight line. Single and independent groups of photons, described by the original bare states of Jaynes-Cummings model, deliver the correct expectation values for the number of photons carried by a photonic wavefront, its complex optical field, and phase quadratures. The intrinsic longitudinal field profile associated with a photonic wavefront is derived for any instantaneous number of photons. These photonic properties enable a step-by-step analysis of various beam splitters and interferometric filters. As a result, generalized expressions are derived for the correlation functions characterizing counting of coincident numbers of photons for fourth-order interference, whether classical or quantum optical, without entangled photons.
Three physical elements are missing from the conventional formalism of quantum photonics: 1) the quantum Rayleigh spontaneous and stimulated emissions; 2) the unavoidable parametric amplification; and 3) the mixed time-frequency spectral structure of a photonic field which specifies its duration or spatial extent. As a single photon enters a dielectric medium, the quantum Rayleigh scattering prevents it from propagating in a straight-line, thereby destroying any possible entanglement. A pure dynamic and coherent state composed of two consecutive number states, delivers the correct expectation values for the number of photons carried by a photonic wave front, its complex optical field, and phase quadratures. The intrinsic longitudinal and lateral field profiles associated with a group of photons for any instantaneous number of photons are independent of the source. These photonic properties enable a step-by-step analysis of the correlation functions characterizing counting of coincident numbers of photons or intensities with unity visibility interference, spanning the classical and quantum optic regimes
Three physical elements are missing from the conventional formalism of quantum photonics: 1) the quantum Rayleigh spontaneous and stimulated emissions; 2) the unavoidable parametric amplification; and 3) the mixed time-frequency spectral structure of a photonic field which specifies its duration or spatial extent. As a single photon enters a dielectric medium, the quantum Rayleigh scattering prevents it from propagating in a straight-line, thereby destroying any possible entanglement. A pure dynamic and coherent state composed of two consecutive number states, delivers the correct expectation values for the number of photons carried by a photonic wave front, its complex optical field, and phase quadratures. The intrinsic longitudinal and lateral field profiles associated with a group of photons for any instantaneous number of photons are independent of the source. These photonic properties enable a step-by-step analysis of the correlation functions characterizing counting of coincident numbers of photons or intensities with unity visibility interference, spanning the classical and quantum optic regimes
The quantum Rayleigh scattering of single photons, which is absent from the physical analyses of quantum optic experiments, destroys the mathematical concept of entangled photons. The quantum Rayleigh spontaneous and stimulated emissions provide physically meaningful interpretations for both polarization-based quantum correlations and beam splitter-based anti-correlations by means of groups of identical photons, commonly mistaken for one photon. These can overcome the quantum Rayleigh scattering of single photon in a dielectric medium. The random phases of spontaneously emitted photons play a critical role in obtaining visibility of unity with intensity correlations or number of photons. It is the ratio of physically present photon numbers that determine the visibility rather than a superposition of randomly detected numbers of photons. The intrinsic field of a photon is the same regardless of the optical source. The evolution of the photonic properties of each input of a pure quantum dynamic and coherent number state is described by the Ehrenfest theorem breaking away from the Copenhagen approach of time- and space-independent inputs of mixed density matrices which appear to lead to physically counter-intuitive interpretations.