Full characterisation of the quantum spiral bandwidth of entangled biphotons

TL;DR

This paper provides a comprehensive analytical characterization of the orbital angular momentum and radial momentum correlations in entangled biphotons generated via spontaneous parametric down conversion, enabling flexible beam parameter analysis.

Contribution

It derives a general analytical expression for the spiral bandwidth of entangled biphotons without geometric restrictions, advancing understanding of their quantum properties.

Findings

Analytic formula for correlations in orbital and radial momentum

Calculation of spiral bandwidth with arbitrary beam parameters

Full characterization of entangled biphoton state properties

Abstract

Spontaneous parametric down conversion has been shown to be a reliable source of entangled photons. Amongst the wide range of properties that have been shown to be entangled, it is the orbital angular momentum that is the focus of our study. We investigate, in particular, the bi-photon state generated using a Gaussian pump beam. We derive an expression for the simultaneous correlations in the orbital angular momentum and radial momentum of the down-converted Laguerre-Gaussian beams. Our result allows us, for example, to calculate the spiral bandwidth with no restriction on the geometry of the beams: $\ell$, $p$ and the beam widths are all free parameters. Moreover, we show that, with the usual paraxial and collinear approximations, a fully analytic expression for the correlations can be derived.