Two-photon optics of Bessel-Gaussian modes

TL;DR

This paper develops a theoretical framework for two-photon quantum optics involving Bessel-Gaussian modes, demonstrating control over orbital angular momentum spectra and bandwidth through radial mode parameters, with experimental validation.

Contribution

It introduces a general theory for the OAM spectrum and Schmidt number of Bessel-Gaussian modes in quantum optics, and experimentally verifies the control over quantum correlations and mode bandwidth.

Findings

Theoretical expression for OAM spectrum and Schmidt number derived.

Experimental confirmation of spectrum flattening and increased bandwidth.

Control over quantum state dimensionality demonstrated.

Abstract

In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks, a blazed axicon, binary axicon and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states.