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arXiv:1910.12470 · Physics Letters A

Quantum diffraction of position-momentum entangled photons from a sharp edge

Samridhi Gambhir, Mandip Singh

Published Aug 16, 2019• 1 citation
arXivHTMLPDF
DOI
10.1016/j.physleta.2019.125889

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Previous papers have presented an alternative picture for photon diffraction based on a distribution of photon paths through quantized momentum exchange with probabilities defined at the location of scattering, not the point of detection. This contrasted with the picture from classical optical wave theory that describes diffraction in terms of the Huygens-Fresnel principle and sums the phased contributions of electromagnetic waves at the location of detection to determine probabilities. This alternative picture was termed “Momentum Exchange Theory (MET),” replacing the concept of Huygens wavelets with photon scattering (positive and negative dispersions) through momentum exchange with the scattering lattice. MET assumes a momentum representation for diffracted particles and has been applied to several different optical diffraction experimental configurations. Straight edge diffraction has been a particularly revealing experimental configuration as it provides significant clues to the geometric parameters controlling exchange probabilities. Diffraction by an opaque disc is examined to provide further insight to negative (attractive) dispersions. This analysis indicates that the “diffraction force” is an integration of momentum exchange field interactions to derive an exchange probability at interaction points along the photon path – resembling aspects of the QED path integral formulation for particle interactions.
An alternative picture for photon diffraction had been proposed describing diffraction by a distribution of photon paths determined through a Fourier analysis of a scattering lattice. The momentum exchange probabilities are defined at the location of scattering, not the point of detection. This contrasts with the picture from classical optical wave theory that describes diffraction in terms of the Huygens-Fresnel principle and sums the phased contributions of electromagnetic waves to determine probabilities at detection. This revised picture, termed “Momentum Exchange Theory,” can be derived through a momentum representation of the diffraction formulas of optical wave theory, replacing the concept of Huygens wavelets with photon scattering through momentum exchange with the lattice. Starting with the Rayleigh-Sommerfeld and Fresnel-Kirchoff formulas, this paper demonstrates that diffraction results from positive and negative photon dispersions through virtual particle exchange probabilities that depend on the lattice geometry and are constrained by the Heisenberg uncertainty principle. The positive and negative increments of momentum exchange exhibit harmonic probability distributions characteristic of a “random walk,” dependent on the distance of momentum exchange. The analysis produces a simplified prediction for the observed intensity profile for a collimated laser beam diffracted by a long, straight edge that lends conceptual support for this alternative picture.
Mobley (2018) presented Momentum Exchange Theory (MET) as an alternative picture for photon diffraction, providing comparable predictions to Classical Optical Wave and Boundary Diffraction Wave Theories. MET explains diffraction scattering in terms of momentum transfer probabilities determined by two primary factors: 1) the momentum transfer states of the scattering lattice (aperture); and 2) the distance and location of momentum transfer between the lattice and the scattered photon path. For example, MET was illustrated examining straight edge diffraction where the Fresnel pattern is obtained assuming local maxima in the probability of perpendicular momentum exchange approximated by Δp = ±(2j+1)h/4x, where x is the distance between the photon’s path and the edge, (j = 0, 1, 2, 3…). This study explores diffraction experiments that might discriminate between the predictions of MET and alternative wave theories. This reports preliminary results with novel observations supporting descriptions based upon MET. Experiments examine diffraction of a narrow laser beam by thin aluminum ribbons with a variety of configurations: e.g. diffraction by the edge of an Al ribbon and single-slit diffraction between Al ribbons. Additional fringes are observed in diffraction patterns with a dependence related to Δp = ±(2j+1)h/2L where L is the width of the Al ribbon. Photon scattering exhibits similarities in dependence to multiple-slit diffraction but where the photons only pass through a single slit. Observations suggest the photon scattering probabilities are dependent on the electromagnetic field geometry that determines momentum exchange at the aperture as predicted by MET.