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Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera

Jedrkiewicz, O, Brambilla, Elena, Bache, M, Gatti, A, Lugiato, L A, Trapani, P D

Published Feb 8, 2005• 10 citations
OpenAlex

Abstract

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.

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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 center of the signal/idler pattern in the far-field plane.
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.
Using a 1 GW, 1 ps pump laser pulse in high-gain parametric down conversion allows us to detect sub-shot-noise spatial quantum correlation with up to 100 photoelectrons per mode by means of a high efficiency charge coupled device. The statistics is performed in single shot over independent spatial replica of the system. Evident quantum correlations were observed between symmetrical signal and idler spatial areas in the far field. In accordance with the predictions of numerical calculations, the observed transition from the quantum to the classical regime is interpreted as a consequence of the narrowing of the down-converted beams in the very high-gain regime.
We review and compare the results of quantum spatial correlation measurements in parametric down-conversion in the high-gain pulsed regime, with preliminary measurements performed in the low-gain cw-pumped regime. The diagnostics is based on a high quantum efficiency CCD camera, and in the second case the radiation pattern is recorded after temporal integration of the "single-photon" spatial distribution. The effect of the detected number of temporal modes on the accessibility of the sub-shot noise regime is discussed, together with the identification of suitable regimes for weak image detection.
Spontaneous down conversion (SPDC) occurs in a nonlinear crystal when a pump photon splits in a pair of signal and idler photons. This paper demonstrates detection of single photons in low light level images with an electron multiplying CCD camera (EMCCD). The opposite spatial fluctuations of SPDC radiation are correlated in the quantum regime. Here, correlations between pixels are presented for collinear phase matching. The far field image of the parametric fluorescence is formed in the focal plane of a lens on a back-illuminated EMCCD. A thresholding procedure is applied on each image, in order to decide whether there is one or zero photo-electron on each pixel. We have experimentally demonstrated that spatial SPDC fluctuations between opposite pixels are quantum correlated in the far field.
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.
We study the spatial correlations of quantum fluctuations that can be observed in multimode parametric down-conversion in the regime of high gain. We investigate both a type-I and a type-II phase-matching configuration: in the latter case spatial correlations at the quantum level are shown to exist both in the near-field and in the far-field zones of the down-converted light. In the stationary and plane-wave approximation we treat the problem analytically. A stochastic model is solved numerically to obtain quantitative results beyond this approximation. The finite transverse size and pulse duration of the pump beam and other features of the system, such as spatial walk-off and diffraction are taken into account, and we show that correlations beyond the standard quantum limit exist for values of parameters consistent with realistic experiments.