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Experimental Investigation of Continuous Variable Entanglement with Spatial Degrees of Freedom of Photon Pairs

I will present several recent experiments performed in our group with the objective of studying continuous variable entanglement. To do this we employ the spatial degrees of freedom of pairs of photons produced by spontaneous parametric down-conversion. This system is particularly suited for these investigations due to the simplicity with which one can produce entangled states with a high degree of entanglement, and due to the large amount of control one has over the quantum state. We show how spatial “quadrature” measurements can be performed, and how one can verify spatial entanglement. We investigate also some aspects of “genuine non-Gaussian entanglement”-entanglement which appears only in the higher order correlation functions, and provide and experimental verification of this entanglement using a recent criteria of Shchukin and Vogel. It has been shown that non-Gaussianity (states or operations), is required for some quantum information tasks, such as universal quantum computation and violation of Bell's inequality. We show the appearance of a non-local optical vortex, which appears in the two-photon spatial correlations of the non-Gaussian state.