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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Experimental investigation of the X-shaped spatio-temporal correlation of twin photons via sum frequency generation

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

Published Oct 15, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.929537

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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.
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.
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.
In this paper we show how after the generation of parametric down-conversion radiation (PDC) in the very high gain pulsed regime, we are able to reconstruct the pump via up-conversion of the twin beams originated from that PDC process. The peculiarity of the experiment is the ultra-broad spectral and angular bandwidth sent into the process of sum frequency mixing thanks to an achromatic imaging technique from the exit face of the PDC crystal using off-axis parabolic mirrors. The recorded spectra presented illustrate the high visibility recombination of the intense phase-conjugated signal and idler beams and pave the way for the investigation of both the spatial and temporal properties of the near field biphoton amplitude.
We investigate the spatio-temporal structure of the biphoton entanglement in Parametric Down Conversion (PDC). In particular we study the biphoton amplitude at the output face of the nonlinear crystal (near-field) and we demonstrate its X-shaped geometry in the space-time dimensions, i.e. the non-factorability of the state with respect to spatial and temporal variables. Our analysis provides a precise and quantitative characterization of this structure in various regimes and types of phase matching of PDC. The key elements of novelty emerging from our analysis are the non-factorability of the state with respect to spatial and temporal variables, and the extreme relative localization of the entangled photons, both in space (few microns) and time (few femtoseconds). 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.