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Optics Express

Mode counting in high-dimensional orbital angular momentum entanglement

Martin P. van Exter, P. S. K. Lee, S. van Doesburg, J. P. Woerdman

Published Jan 1, 2007• 12 citations
Publisher

Abstract

We study the high-dimensional orbital angular momentum OAM) entanglement contained in the spatial profiles of two quantum-correlated photons. For this purpose, we use a multi-mode two-photon interferometer with an image rotator in one of the interferometer arms. By measuring the two-photon visibility as a function of the image rotation angle we measure the azimuthal Schmidt number, i.e., we count the number of OAM modes involved in the entanglement; in our setup this number is tunable from 1 to 8.

DOI
10.1364/oe.15.006431

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•Jul 24, 2012•14 citations
We study the high-dimensional orbital angular momentum OAM) entanglement contained in the spatial profiles of two quantum-correlated photons. For this purpose, we use a multi-mode two-photon interferometer with an image rotator in one of the interferometer arms. By measuring the two-photon visibility as a function of the image rotation angle we measure the azimuthal Schmidt number, i.e., we count the number of OAM modes involved in the entanglement; in our setup this number is tunable from 1 to 8.
We describe a simple experiment that is ideally suited to analyze the high-dimensional entanglement contained in the orbital angular momenta (OAM) of entangled photon pairs. For this purpose we use a two-photon interferometer with a built-in image rotator and measure the two-photon visibility versus rotation angle. Mode selection with apertures allows one to tune the dimensionality of the entanglement; mode selection with spiral phase plates and fibers allows detection of a single OAM mode. The experiment is analyzed in two different ways: either via the continuous two-photon amplitude function or via a discrete modal (Schmidt) decomposition of this function. The latter approach proves to be very fruitful, as it provides a complete characterization of the OAM entanglement.
We put forward an approach to estimate the amount of bipartite spatial entanglement of down-converted photon states correlated in orbital angular momentum and the magnitude of the transverse (radial) wave vectors. Both degrees of freedom are properly considered in our framework, which only requires azimuthal local linear optical transformations and mode selection analysis with two fiber detectors. The coincidence distributions predicted by our approach give an excellent fit to the distributions measured in a recent experiment aimed to show the very high-dimensional transverse entanglement of twin photons from a down-conversion source. Our estimate for the Schmidt number is substantially lower but still confirms the presence of high-dimensional entanglement.
Any practical experiment utilizing the innate DDD-dimensional entanglement of the orbital angular momentum (OAM) of photons is subject to the generation capacity of the entangled photon source and the modal capacity of the detection system. We report an experimental spontaneous parametric-down-conversion system able to generate and detect tunable high-dimensional OAM entanglement. By tuning the phase matching, we demonstrate a factor of 2 increase on the half-width of the OAM-correlation spectrum, from 10 to 20. In terms of quantum mutual information capacity, this is an increase from 3.183.183.18 to 4.954.954.95 bits/photon. Furthermore, we measure correlations in the conjugate variable, angular position, and obtain concurrence values 0.960.960.96 and 0.900.900.90. The good entanglement measures in both OAM and angular position bases indicate bipartite, DDD-dimensional entanglement where DDD is tunable.