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Conference on Lasers and Electro-Optics

Spatial entanglement of twin quantum images

Patrick Navez, E. Brambilla, A. Gatti, L. A. Lugiato

Published Aug 29, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iqec.2000.907755

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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.
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.
We show that spatial entanglement of two twin images obtained by parametric down-conversion is complete, i.e. concerns both amplitude and phase. This is realised through a homodyne detection of these images which allows for measurement of the field quadrature components. EPR correlations are shown to exist between symmetrical pixels of the two images. The best possible correlation is obtained by adjusting the phase of the local oscillator field (LO) in the area of maximal amplification. The results for quadrature components hold unchanged even in absence of any input image i.e. for pure parametric fluorescence. In this case they are not related to intensity and phase fluctuations.
Two beams of light can be quantum mechanically entangled through correlations of their phase and intensity fluctuations. For a pair of spatially extended image-carrying light fields, the concept of entanglement can be applied not only to the entire images but also to their smaller details. We used a spatially multimode amplifier based on four-wave mixing in a hot vapor to produce twin images that exhibit localized entanglement. The images can be bright fields that display position-dependent quantum noise reduction in their intensity difference or vacuum twin beams that are strongly entangled when projected onto a large range of different spatial modes. The high degree of spatial entanglement demonstrates that the system is an ideal source for parallel continuous-variable quantum information protocols.
A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.
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.