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Journal of Modern Optics

Improving the observation of spatial quantum correlation of twin beams by means of a sub-pixel symmetry centre retrieval algorithm

Lucia Caspani, Ottavia Jedrkiewicz, E. Brambilla, A. Gatti

Published Jul 18, 2008• 3 citations
Publisher

Abstract

We propose a method to improve the observation of spatial quantum correlation of twin beams produced by parametric down-conversion in a non-linear crystal. By applying our post-acquisition algorithm to experimental data we are able to reduce the uncertainty in the determination of the symmetry centre of the signal-idler pattern in the far-field plane, by searching it with sub-pixel accuracy. Reducing the uncertainty leads to an improvement of the observation of spatial quantum correlation of the twin beams. We perform theoretical and numerical investigation in order to test potentialities and limits of our algorithm, and we identify a proper experimental configuration that minimises the problem of symmetry centre uncertainty.

DOI
10.1080/09500340801961513

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We propose a method to improve the observation of spatial quantum correlation of twin beams produced by parametric down-conversion in a non-linear crystal. By applying our post-acquisition algorithm to experimental data we are able to reduce the uncertainty in the determination of the symmetry centre of the signal-idler pattern in the far-field plane, by searching it with sub-pixel accuracy. Reducing the uncertainty leads to an improvement of the observation of spatial quantum correlation of the twin beams. We perform theoretical and numerical investigation in order to test potentialities and limits of our algorithm, and we identify a proper experimental configuration that minimises the problem of symmetry centre uncertainty.
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We consider travelling-wave parametric down-conversion in the high-gain regime and present the experimental demonstration of the quantum character of the spatial fluctuations in the system. In addition to showing the presence of sub-shot noise fluctuations in the intensity difference, we demonstrate that the peak value of the normalized spatial correlations between signal and idler lies well above the line marking the boundary between the classical and the quantum domain. This effect is equivalent to the apparent violation of the Cauchy–Schwartz inequality, predicted by some of us years ago, which represents a spatial analogue of photon antibunching in time. Finally, we analyse numerically the transition from the quantum to the classical regime when the gain is increased and we emphasize the role of the inaccuracy in the determination of the symmetry centre of the signal–idler pattern in the far-field plane.
We have measured sub-shot-noise quantum correlations of spatial fluctuations in the far-field image of the parametric fluorescence created in a type I $\ensuremath{\beta}$-barium-borate nonlinear crystal, either between opposite angular sectors (nondegenerate configuration) or between opposite pixels (degenerate configuration). Imaging is performed at a very low light level (0.20.20.2 photons per pixel) with an electron-multiplying CCD camera, resulting in purely spatial coincidences between single photons when detecting on pixels. Experimental results overcome the standard quantum-limit-shot-noise level without subtraction of the variance of the detection noise. We compare these experimental results with numerical results given by the quantum Green's function method, which is proved to have strong advantages over stochastic simulations.
Twin entangled beams produced by single-pass parametric down-conversion (PDC) offer the opportunity to detect weak amount of absorption with an improved sensitivity with respect to standard techniques which make use of classical light sources. We propose a differential measurement scheme which exploits the spatial quantum correlation of type-II PDC to image a weak amplitude object with a sensitivity beyond the standard quantum limit imposed by shot noise. By applying a quantitative numerical model to a specific PDC system (a type-II beta-barium borate crystal), we are able to identify conditions in parameter space suitable for a substantial enhancement of the imaging sensitivity, and we investigate the robustness of this enhancement against experimental imperfections.
We consider travelling-wave parametric down-conversion in the high-gain regime and present the experimental demonstration of the quantum character of the spatial fluctuations in the system. In addition to showing the presence of sub-shot noise fluctuations in the intensity difference, we demonstrate that the peak value of the normalized spatial correlations between signal and idler lies well above the line marking the boundary between the classical and the quantum domain. This effect is equivalent to the apparent violation of the Cauchy-Schwartz inequality, predicted by some of us years ago, which represents a spatial analogue of photon antibunching in time. Finally, we analyse numerically the transition from the quantum to the classical regime when the gain is increased and we emphasize the role of the inaccuracy in the determination of the symmetry center of the signal/idler pattern in the far-field plane.
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.