Imaging of OAM-entangled photon pairs in the Bessel-Gauss basis with full index control

Abstract

In this paper, we directly image the orbital angular momentum (OAM) correlations, expressed in the Bessel-Gauss (BG) basis, present in quantum-entangled photon pairs produced by the process of spontaneous parametric downconversion (SPDC). We use a spatial light modulator that displays an appropriate phase mask, followed by coupling into a single-mode fiber, so as to project the signal, or heralding, photon onto a BG mode, and verify that the idler, or heralded, photon is projected non-locally as expected. In contrast with similar experiments relying on Laguerre-Gauss (LG) modes, our current experiment permits, firstly, full index control (allowing the experimenter to define both the azimuthal index ℓ s and the continuous radial index k rs , also referred to as scaling parameter). Importantly, while not resolving the radial index leaves the heralded single photon in a statistical mixture of all available radial modes, the ability to determine both indices allows us to herald single photons in a particular BG mode, described by a quantum-mechanically pure state. Our use of BG modes permits, secondly, the spatially-resolved detection of the heralded single photon, both in the near and far fields, with a time-gated intensified CCD camera, making it possible to experimentally determine both the radial and azimuthal indices of the heralded single photon. Thirdly, the fact that for BG modes the radial index (scaling parameter) is continuous makes it possible to use the scaling parameter as a continuous adjustment in quantum state engineering, for precise mode matching, or for the selection of photon-pair properties such as the spiral bandwidth, as we experimentally demonstrate. We believe that our work opens up interesting new possibilities in the field of quantum communications based on the spatial degree of freedom of photon pairs.