Abstract

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 substancially. In this paper, we consider the field generated through the process of frequency down-conversion in a travelling wave optical parametric amplifier. In [1] we demonstrated that such a system, when coupled with an appropriate classical imaging device, is able to generate two amplified copies of an injected input image, symmetrical with respect to the system axis, that are strongly correlated to each other: they indeed display synchronized local intensity fluctuations at the level of quantum noise, and for this reason they may be referred to as twin images. Here 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 consider a homodyne detection scheme which allows to measure the quadrature components of the field, ${\text{X}}_{\text{1}}^{\varphi }$ and ${\text{X}}_{\text{2}}^{\varphi }$ from two corresponding portions of the output images (encircled regions in the figure), those selected by the phase of the local oscillator field ϕ. We find that the difference between two quadratures ${\text{X}}_1^{\varphi }-{\text{X}}_2^{\varphi }$ display exactly the same fluctuation spectrum as the sum of the corresponding orthogonal quadratures, ${\text{X}}_1^{\varphi +\pi /2}{\text{+X}}_2^{\varphi +\pi /2}$. The common uncertainty of those observables can be reduced well below the shot noise level, provided the amplification is strong enough and the phase of the local oscillator field is correctly adjusted. This adjustment is best perfomed by fitting the spatial quadratic dependence of the phase of the local oscillator field in the area of maximal amplification. In these particular conditions, the system exhibits a spatialrealization of the Einstein-Podolsky-Rosen paradox for the two orthogonal quadrature components of the output field under examination.

© 2000 IEEE