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Journal of the Optical Society of America A

Nonlocal optical vortices of any order in spontaneous parametric down-conversion

Austin Puckett, Greg Gbur

Published May 2, 2025• 0 citations
Publisher

Abstract

We theoretically demonstrate a method for generating and detecting nonlocal optical vortices of any order produced through spontaneous parametric down-conversion. These vortices arise in a nonlocal coordinate system consisting of a single coordinate from each photon. It is shown that independent vortices can be imposed on different sets of nonlocal coordinates.

DOI
10.1364/josaa.562335

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We theoretically demonstrate a method for generating and detecting nonlocal optical vortices of any order produced through spontaneous parametric down-conversion. These vortices arise in a nonlocal coordinate system consisting of a single coordinate from each photon. It is shown that independent vortices can be imposed on different sets of nonlocal coordinates.
The achievement of optimum conversion efficiency in conventional spontaneous parametric down-conversion requires consideration of quantum processes that entail multisite electrodynamic coupling, actively taking place within the conversion material. The physical mechanism, which operates through virtual photon propagation, provides for photon pairs to be emitted from spatially separated sites of photon interaction; occasionally pairs are produced in which each photon emerges from a different point in space. The extent of such nonlocalized generation is influenced by individual variations in both distance and phase correlation. Mathematical analysis of the global contributions from this mechanism provides a quantitative measure for a degree of positional uncertainty in the origin of down-converted emission.
We demonstrate that the phenomenon known as Spontaneous Parametric Down Conversion is really an amplification, in a nonlinear crystal pumped by a laser, of certain pairs of modes of the electromagnetic zeropoint field. The demonstration is achieved by showing the existence of a related phenomenon, Spontaneous Parametric Up Conversion. This phenomenon, once observed, will cast doubt on the quantum-optical theory, which treats photons as the elementary objects of the light field. It will also lend greater credibility to the zeropoint-field description of optical entanglement phenomena. That description is based on the unquantized light field and is consistently local, in contrast with the nonlocal description of Quantum Optics.
Optical vortices are lines of phase singularity which percolate through all optical fields. We report the entanglement of linked optical vortex loops in the light produced by spontaneous parametric down-conversion. As measured by using a Bell inequality, this entanglement between topological features extends over macroscopic and finite volumes. The entanglement of photons in complex three-dimensional topological states suggests the possibility of entanglement of similar features in other quantum systems describable by complex scalar functions, such as superconductors, superfluids, and Bose-Einstein condensates.
A. Zeilinger proposed that photon pairs with entanglement of the orbital angular momentum (OAM) states could be detected in the course of spontaneous parametric down-conversion by illuminating a "fork" hologram (used for generating optical vortices) by a shifted Gaussian beam. Most closely related to the topic of this work are some early papers of the present authors. This chapter discusses both theoretically and experimentally, transformations of optical vortices which occur due to a complex Cartesian shift of the original functions of the complex amplitude. It theoretically and experimentally studies the transformation of the optical vortex proposed, by illuminating an amplitude "fork" hologram by a Gaussian beam with its waist center being shifted in the transverse plane from the hologram center. The chapter considers asymmetric Gaussian optical vortices that can be generated experimentally by diffraction of a Gaussian beam by an amplitude hologram with a typical "fork" at the point of singularity.