Correlated Quantum Airy Photons: An Analytical Approach

TL;DR

This paper presents an analytical study of correlated photon pairs generated via spontaneous parametric down-conversion of finite energy Airy beams, revealing detailed spatial and momentum correlations and the effects of crystal length.

Contribution

It provides an analytical framework for understanding the spatial and momentum correlations of biphotons generated from Airy beams, including the effects of crystal length on mode structure.

Findings

Reconstruction of Airy beam in near-field correlations.

Mapping of biphoton momentum anti-correlation in far-field.

Longer crystals yield tighter real-space and higher-dimensional angular correlations.

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.