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International Conference on Quantum Information

Two-photon speckles as a probe of spatial entanglement

H. Di Lorenzo Pires, Wouter H. J. Peeters, J. Woudenberg, Martin P. van Exter

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We experimentally study the statistics of spatially entangled photon pairs scattered by a disordered medium. Striking differences arise between highly entangled and almost separable states. The Schmidt number can be extracted from the speckle visibility.
DOI
10.1364/icqi.2011.qme4

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We experimentally study the statistics of two-photon speckle patterns, obtained when spatially entangled photon pairs are scattered through a random medium. Striking differences arise between the scattering of highly entangled states and almost separable states. Both the purity of the field and the Schmidt number, which quantifies the number of entangled modes, can be obtained from the visibility of the speckles. We observe nonexponential statistics for both the intensities and the two-photon correlations.
We report the observation of speckle patterns in quantum correlations within light that is scattered by a disordered medium. The random medium is illuminated with spatially entangled photon pairs, and fourth-order speckle patterns are spatially resolved by two independently scanning detectors. Spatial entanglement gives two-photon speckle a much richer structure than ordinary one-photon speckle. Our experiments demonstrate that two-photon speckle from a surface scatterer and a volume scatterer look entirely different.
We calculate the statistical distribution P2(I2) of the speckle pattern produced by a photon pair current I2 transmitted through a random medium, and compare it with the single-photon speckle distribution P1(I1). We show that the purity of a two-photon density matrix can be directly extracted from the first two moments of P1 and P2. A one-to-one relationship is derived between P1 and P2 if the photon pair is in an M-dimensional entangled pure state. For M>>1 the single-photon speckle disappears, while the two-photon speckle acquires an exponential distribution.
This dissertation contains scientific research within the realm of quantum optics, which is a branch of physics. An experimental and theoretical study is made of two-photon interference phenomena in various optical systems. Spatially entangled photon pairs are produced via the nonlinear optical process of spontaneous parametric down-conversion. These entangled photons are then passed through different optical systems to study various aspects of two-photon interference. Firstly, an experimental analysis is made of the high-dimensional entanglement that is present in the orbital angular momentum of the photons. Secondly, we present a comprehensive description of two-photon quantum interference behind a double slit. We demonstrate how to control the quantum correlations and present the first observations of complete two-photon diffraction patterns behind a double slit. Finally, we present pioneering experiments on spatially entangled two-photon states that are scattered of random media. We have observed and theoretically analyzed the structure in the random two-photon interference patterns called two-photon speckle patterns. Spatial entanglement gives two-photon speckle a much richer structure than ordinary one-photon speckle. Our experiments also demonstrate a two-photon interference phenomenon that survives averaging over different realizations of disorder. The latter results are closely related to bosonic, fermionic, and anyonic particle exchange symmetries.