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arXiv:1207.6934 · Physical Review Letters

Experimental Observation of a Skewed X-type Spatiotemporal Correlation of Ultrabroadband Twin Beams

Ottavia Jedrkiewicz, A. Gatti, E. Brambilla, P. Di Trapani

Published Dec 10, 2012• 23 citations
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Abstract

This work presents the experimental observation of the nonfactorable near-field spatiotemporal correlation of ultrabroadband twin beams generated by parametric down-conversion, in an interferometric-type experiment using sum frequency generation, where both the temporal and the spatial degrees of freedom of parametric down-conversion light are controlled with high resolution. The revealed correlation is skewed in space-time in accordance with the X structure predicted by the theory.

DOI
10.1103/physrevlett.109.243901

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This work presents the experimental observation of the nonfactorable near-field spatiotemporal correlation of ultrabroadband twin beams generated by parametric down-conversion, in an interferometric-type experiment using sum frequency generation, where both the temporal and the spatial degrees of freedom of parametric down-conversion light are controlled with high resolution. The revealed correlation is skewed in space-time in accordance with the X structure predicted by the theory.
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.
In this work we propose and analyze a scheme where the full spatiotemporal correlation of twin photons or beams generated by parametric down-conversion is detected by using its inverse process, i.e., sum frequency generation. Our main result is that, by imposing independently a temporal delay $\ensuremath{\Delta}t$ and a transverse spatial shift $\ensuremath{\Delta}x$ between two twin components of PDC light, the up-converted light intensity provides information on the correlation of the PDC light in the full spatiotemporal domain and should enable the reconstruction of the peculiar X-shaped structure of the correlation predicted previously [A. Gatti et al. Phys. Rev. Lett. 102, 223601 (2009); L. Caspani et al. Phys. Rev. A 81, 033808 (2010); E. Brambilla et al. Phys. Rev. A 82, 013835 (2010)]. Through both a semianalytical and a numerical modeling of the proposed optical system, we analyze the feasibility of the experiment and identify the best conditions to implement it. In particular, the tolerance of the phase-sensitive measurement against the presence of dispersive elements, imperfect imaging conditions, and possible misalignments of the two crystals is evaluated.
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.
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.