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arXiv · 1312.1092

Separable Schmidt modes of a non-separable state

Alessio Avella·Marco Gramegna·Alexander Shurupov·Giorgio Brida·Maria Chekhova·Marco Genovese
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Abstract

Two-photon states entangled in continuous variables such as wavevector or frequency represent a powerful resource for quantum information protocols in higher-dimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering two-photon spectral amplitude in such a way that it contains several non-overlapping Schmidt modes, each of which can be filtered losslessly. The method is based on spontaneous parametric down-conversion (SPDC) pumped by radiation with a comb-like spectrum. There are many ways of producing such a spectrum; here we consider the simplest one, namely passing the pump beam through a Fabry-Perot interferometer. For the two-photon spectral amplitude (TPSA) to consist of non-overlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the Fabry-Perot free spectral range and its finesse should satisfy certain conditions. We experimentally demonstrate the control of TPSA through these parameters. We also discuss a possibility to realize a similar situation using cavity-based SPDC.

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Alessio Avella, Marco Gramegna, Alexander Shurupov, Giorgio Brida, Maria Chekhova, Marco Genovese. 2013-12-04. Separable Schmidt modes of a non-separable state. https://doi.org/10.1103/physreva.89.023808

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