Effect of high-dimensional entanglement of Laguerre-Gaussian modes in parametric downconversion

Abstract

We calculate the coincidence count probabilities when the photon pairs entangled in orbital angular momentum generated via spontaneous parametric downconversion are measured by using holograms with an m-fold dislocation, considering the nonzero crystal length. We find that the coincidence probabilities related to azimuthal changes in hologram positions deviate significantly from a sinusoidal curve, which has often been assumed in simple analyses. It is found that the main cause of this effect is the high-dimensional entanglement in Laguerre-Gaussian modes. We also find that the crystal length causes the hologram positions to change for the maximum coincidence probabilities.