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arXiv:2511.09334 · Physical Review A

Correlated Quantum Airy Photons: An Analytical Approach

V. Sau, R. Giustozzi, P. Piergentili, D. Vitali, G. Di Giuseppe, S. Ghosh, U. Roy

quant-phSubmitted Nov 12, 2025• Announced Nov 13, 2025• 0 citations
arXivHTMLPDF

Abstract

We describe the generation of correlated photon pairs by means of spontaneous parametric down-conversion of an optical pump in the form of a finite energy Airy beam. The optical system function, which contributes to the propagation of the down-converted beam before being registered by the detectors, is computed. The spectral function is utilized to calculate the biphoton amplitude for finding the coincidence count of the inbound Airy photons in both far-field and near-field configurations. We report the reconstruction of the finite energy Airy beam in the spatial correlation of the down-converted beams in near field scenario. In far field, the coincidence counts resembles the probability density of the biphoton in momentum space, revealing a direct mapping of the anti-correlation of the biphoton momentum. By examining the spatial Schmidt modes, we also demonstrate that longer crystals have tighter real-space correlations, but higher-dimensional angular correlations, whereas shorter crystals have fewer modes in momentum space and broader multimode correlations in position space.

DOI
10.1103/9lvb-qrl3
Comments
Submitted to Physical Review A

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We describe the generation of correlated photon pairs by means of spontaneous parametric down-conversion of an optical pump in the form of a finite energy Airy beam. The optical system function, which contributes to the propagation of the down-converted beam before being registered by the detectors, is computed. The spectral function is utilized to calculate the biphoton amplitude for finding the coincidence count of the inbound Airy photons in both far-field and near-field configurations. We report the reconstruction of the finite energy Airy beam in the spatial correlation of the down-converted beams in near field scenario. In far field, the coincidence counts resembles the probability density of the biphoton in momentum space, revealing a direct mapping of the anti-correlation of the biphoton momentum. By examining the spatial Schmidt modes, we also demonstrate that longer crystals have tighter real-space correlations, but higher-dimensional angular correlations, whereas shorter crystals have fewer modes in momentum space and broader multimode correlations in position space.
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Abstract With exotic propagation properties, optical Airy beams have been well studied for innovative applications in communications, biomedical imaging, micromachining, and so on. Here we extend those studies to the quantum domain, creating quantum correlated photons in finite-energy Airy transverse modes via spontaneous parametric down conversion and subsequential spatial light modulation. Through two-photon coincidence measurements, we verify their Airy spatial wavefunctions, propagation along a parabolic trajectory, and that the spatial modulation does not introduce any observable degradation of quantum correlation between the photons. These results suggest the feasibility of using spatially structured photons for practically advantageous quantum applications.
Abstract We experimentally demonstrate the quantum entanglement in various spatial modes of the correlated photons generated via spontaneous parametric down-conversion in a type-II phase-matched periodically-poled KTP crystal. The two-fold coincidence measurement reveals the spatial entanglement between the photon pairs by projecting one of the correlated photons onto a Gaussian mode while scanning the spatial mode of its partner photon through selective projection (Gaussian, Laguerre–Gaussian (LG), Bessel-Gaussian (BG), and Airy–Gaussian (AG)) using a spatial light modulator (SLM). We also show the spatially resolved measurement of the non-conservation of orbital angular momentum via modal decomposition of the correlated photon in LG and BG bases.
We directly observe far-field correlations of x-ray photon pairs generated by spontaneous parametric down-conversion (SPDC). Using an energy-resolved, two-dimensional photon counting detector we record the full ring-shaped emission of both photons across a broad bandwidth and extract pair correlations directly from raw events without imposing angular constraints. The ring radii scale with photon energy, in quantitative agreement with transverse phase matching, providing a stringent momentum-space validation of x-ray SPDC. These observations open a route to leveraging quantum correlations in x-ray imaging and metrology, including correlation-enhanced magnification and reduced blurring.