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International Conference on Quantum Information

Exploring the spatio-temporal correlation of twin photons via sum frequency generation

A. Gatti, E. Brambilla, O. Jedrkiewicz, Jean-Luc Blanchet, Luigi A. Lugiato

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We describe the X-shaped geometry, non-factorable in space and time, of the spatio-temporal correlation of biphotons, and the temporal localization thereby achievable. We discuss a scheme where the X-correlation is revealed by the inverse process of sum frequency generation
DOI
10.1364/icqi.2011.qtuf2

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The entangled photon pairs (biphotons) produced from parametric down-conversion (PDC) in a χ(2)crystal are the key element for several quantum information and communication schemes. Recent theoretical investigations [1–2] have revealed the peculiar structure of the biphotonic correlation characterizing the entanglement of twin beams in the space-time domain. The biphotonic correlation in type I PDC is characterized in the near field by a X-shaped geometry, which turns out to be non-factorable in space and time, offering thus the relevant possibility of manipulating the temporal bandwidth of biphoton entanglement by acting on their spatial degrees of freedom. The name “X-entanglement” was coined to describe this geometry [1]. An other key feature which emerged is the extreme spatial and temporal localization of the biphotonic correlation, on the micrometer and femtosecond range, respectively.
We investigate the spatio-temporal structure of the bi-photon entanglement in parametric down-conversion (PDC) and we demonstrate its non-factorable X-shaped geometry. Such a structure gives access to the ultra-broad bandwidth of PDC, and can be exploited to achieve a bi-photon temporal localization in the femtosecond range. This extreme localization is connected to our ability to resolve the photon positions in the source near-field. The non factorability opens the possibility of tailoring the temporal entanglement by acting on the spatial degrees of freedom of twin photons.
We draw an intuitive picture of the spatio–temporal properties of the entangled state of twin photons, where they are described as classical wave-packets. This picture predicts a precise relation between their temporal and transverse spatial separations at the crystal output. The space-time coupling described by classical arguments turns out to determine in a precise way the spatio–temporal structure of the quantum entanglement, analyzed by means of the biphotonic correlation and of the Schmidt dimensionality of the entanglement.
In this paper we report about the experimental investigation of the non factorable spatio-temporal correlation of twin beams generated in parametric down conversion (PDC) at the crystal output. We present the correlation features to be reconstructed by means of the inverse process of PDC, that is sum frequency generation, in a scheme based on achromatic imaging. In particular we show the ultra-narrow temporal localization (6fs) observed thanks to the huge spectral bandwidth detected in the near field of the crystal. We illustrate the deteriorating effects of imperfect imaging conditions or spatial modes selection on the temporal correlation, giving evidence of the interdependence of spatial and temporal degrees of freedom in PDC as claimed by the theory. Throughout the paper we shall discuss about the characteristics of the experimental set-up being used for the investigation of the twin beam correlation in both the temporal and spatial domain, highlighting the important features for the success of the experiment and the demonstration of the X-shaped structure of the space-time correlation, already emerging from preliminary results.
We investigate the spatiotemporal structure of the biphoton entanglement in parametric down-conversion (PDC) and we demonstrate its nonfactorable X-shaped geometry. Such a structure gives access to the ultrabroad bandwidth of PDC, and can be exploited to achieve a biphoton temporal localization in the femtosecond range. This extreme localization is connected to our ability to resolve the photon positions in the source near field. The nonfactorability opens the possibility of tailoring the temporal entanglement by acting on the spatial degrees of freedom of twin photons.