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Physical Review Letters

Quantum Entangled Images

A. Gatti, E. Brambilla, Luigi A. Lugiato, Mikhail I. Kolobov

Published Aug 30, 1999• 92 citations
Publisher

Abstract

We analyze a scheme consisting of an optical parametric amplifier and two imaging lenses. From an off-axis input image such a system creates two quantum entangled output images, signal and idler, symmetrical with respect to the optical axis of the scheme. In the limit of large amplification the idler image is a quantum twin of the signal one in the sense that they display identical intensity fluctuations in space-time.

DOI
10.1103/physrevlett.83.1763

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We analyze a scheme consisting of an optical parametric amplifier and two imaging lenses. From an off-axis input image such a system creates two quantum entangled output images, signal and idler, symmetrical with respect to the optical axis of the scheme. In the limit of large amplification the idler image is a quantum twin of the signal one in the sense that they display identical intensity fluctuations in space-time.
Nonclassical spatial correlations are shown to arise in the cross section of transverse multimode optical beams as a consequence of nonlinear wave mixing phenomena. These correlations represent a macroscopic manifestation of quantum entanglement. As an applicative perspective, we discuss some quantum aspects of parametric amplification of images. A broadband parametric amplifier, enclosed in a telescopic system, is able to amplify and duplicate a faint coherent image. We show that the two output images are quantum twins of each other, in the sense that intensity fluctuations in corresponding pixels are correlated with a conditional variance well beyond the standard quantum limit. In a phase-sensitive amplification scheme we demonstrate an efficient transfer of information from the input image to each of the two output images.
Summary form only given. Optical system which display quantum entanglement properties in the spatial domain are of great interest for applications, since the amount of information that can be manipulated and processed in parallel exploiting quantum correlation effects increase substantially. In this paper, we consider the field generated through the process of frequency down-conversion in a travelling wave optical parametric amplifier. We present new results showing that the two images are locally correlated, not only with respect to intensity fluctuations, but also to phase fluctuations.
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We show that the spatial entanglement of two twin images obtained by parametric down conversion is complete, i.e., concerns both amplitude and phase. By considering a homodyne detection scheme, which allows comparison of field quadrature components of the two images pixel by pixel, Einstein-Podolsky-Rosen correlations are shown to exist between symmetrical pixels of the two images. The best possible correlation is obtained by adjusting the phase profile of the local oscillator in the amplification area. The results for quadrature components hold even in the absence of any input image, i.e., for pure parametric fluorescence. In this case, they are not related to intensity and phase fluctuations.
The signal and idler beams from a non-degenerate, above threshold, optical parametric oscillator have a strong quantum correlation, which are called twin beams. This correlation arises from the simultaneous generation of the signal and idler photons in the form of twin pairs of photons through the parametric down conversion, and the generated twin beams have exactly the same photon statistics. As a result, the fluctuations on the difference between the intensities of the twin beams are reduced with respect to the shot noise limit, that is, intensity-difference squeezing. We give a comprehensive overview of the generation of twin beams using the optical parametric oscillator, and the applications exploiting the quantum correlation of twin beams are presented.