Entanglement of orbital angular momentum for the signal and idler beams in parametric down-conversion

Abstract

We calculate the anticipated correlation between measurements of the orbital angular momentum of the signal and idler beams for parametric down-conversion. These calculations apply to the experiments where the orbital angular momentum state is measured by the use of computer-generated holograms. Displacement of these holograms with respect to the beam axis allows the measurement of superpositions of Laguerre—Gaussian modes. The correlations between such superposition modes of the signal and idler beams show their entanglement and could be used for Bell-type tests of nonlocality.