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arXiv:0905.4830 · Journal of Modern Optics

Two-dimensional characterization of spatially entangled photon pairs

Martin R. Ostermeyer, D. Korn, Dirk Puhlmann, Carsten Henkel, Jens Eisert

Published Oct 10, 2009• 11 citations
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Abstract

We characterize the entanglement in position and momentum of photon pairs generated in type-II parametric down-conversion. Coincidence maps of the photon positions in the near-field and far-field planes are observed in two transverse dimensions using scanning fiber probes. We estimate the covariance matrix of an effective two-mode system and apply criteria for entanglement based on covariance matrices to certify space–momentum entanglement. The role of higher-order spatial modes for observing spatial entanglement between the two photons is discussed.

DOI
10.1080/09500340903359962

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Abstract We experimentally demonstrate the quantum entanglement in various spatial modes of the correlated photons generated via spontaneous parametric down-conversion in a type-II phase-matched periodically-poled KTP crystal. The two-fold coincidence measurement reveals the spatial entanglement between the photon pairs by projecting one of the correlated photons onto a Gaussian mode while scanning the spatial mode of its partner photon through selective projection (Gaussian, Laguerre–Gaussian (LG), Bessel-Gaussian (BG), and Airy–Gaussian (AG)) using a spatial light modulator (SLM). We also show the spatially resolved measurement of the non-conservation of orbital angular momentum via modal decomposition of the correlated photon in LG and BG bases.
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We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations.
We demonstrate EPR entanglement by detecting purely spatial quantum correlations in the near and far-field of spontaneous parametric down conversion generated in a type II BBO crystal. Full field imaging is performed in the photon counting regime with an electron-multiplying CCD (EMCCD) camera. The data are used without any post-selection and we obtain a violation of Heisenberg inequalities with inferred quantities in both transverse dimensions taking into account all the biphoton pairs in both the near and far field, by integration on the entire two dimensional transverse planes. This ensures a rigorous demonstration of the EPR paradox in its original position-momentum form.
Using an electron multiplying CCD camera we observe both image plane (position) and far field (momentum) correlations between photon pairs produced from spontaneous parametric down-conversion when using a 201 x 201 bi-dimensional array of pixels and a flux of around 0.02 photons/pixel. After background subtraction we characterize the strength of signal and idler correlations in both transverse dimensions by applying entanglement and EPR criteria, showing good agreement with the theoretical predictions. The application of such devices in quantum optics could have a wide range, including quantum computation with spatial degrees of freedom of single photons.