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arXiv:quant-ph/0412127 · Physical Review A

Moiré fringe patterns in spatial quantum correlations of twin photons

J. A. O. Huguenin, Marcelo Pereira de Almeida, P. H. Souto Ribeiro, Antonio Zelaquett Khoury

Published Apr 21, 2005• 8 citations
arXivHTMLPDF

Abstract

We observed Moir\'e fringes in spatial quantum correlations between twin photons generated by parametric down-conversion. Spatially periodic structures were nonlocally superposed giving rise to beat frequencies typical of Moir\'e patterns. This result brings interesting perspectives regarding metrological applications of such a quantum optical setup.

DOI
10.1103/physreva.71.043818

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We observed Moir'e fringes in spatial quantum correlations between twin photons generated by parametric down-conversion. Spatially periodic structures were nonlocally superposed giving rise to beat frequencies typical of Moir'e patterns. This result brings interesting perspectives regarding metrological applications of such a quantum optical setup.
Moiré patterns are produced when two periodic structures with different spatial frequencies are superposed. The transmission of the resulting structure gives rise to spatial beatings which are called moiré fringes. In classical optics, the interest in moiré fringes comes from the fact that the spatial beating given by the frequency difference gives information about details (high spatial frequency) of a given spatial structure. We show that moiré fringes can also arise in the spatial distribution of the coincidence count rate of twin photons from the parametric down-conversion, when spatial structures with different frequencies are placed in the path of each one of the twin beams. In other words, we demonstrate how moiré fringes can arise from quantum 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.
The measurement of the correlation between two quantum systems or particles has a broad significance in physics and also plays a central role in the fields of quantum optics and quantum information science. We propose a method of measuring the correlation between the transverse momenta of two photons, in which one only needs to detect one of the photons. We show that it is possible to generate a single-photon fringe pattern by using two spatially separated identical biphoton sources. The fringes are similar to the ones observed in a Michelson interferometer and possess certain remarkable properties. A striking feature of the fringes is that although the pattern is obtained by detecting one photon only of each photon pair, the fringes shift due to a change in the optical path traversed by the undetected photon; the shift is characterized by a combination of wavelengths of both photons. Using this method one can, therefore, measure the wavelength of a photon without detecting it. The visibility of the fringes diminishes as the correlation between the transverse momenta of twin photons decreases: visibility is unity for maximum momentum correlation and zero for no momentum correlation. This dependence allows us to determine the momentum correlation between both photons from the visibility of the fringe pattern obtained by detecting one of the photons only. Our method can potentially be generalized to other quantum entities.
Diffraction-interference patterns of parametric down-converted photons through a transmission grating by both one- and two-photon detection schemes are presented. The measured patterns are explained by the Fourier analysis of the two-photon wave packet, considering the quantum spatial correlation between the constituent photons. Spatial diffraction-interference patterns were recorded by a two-photon detector consisting of two avalanche photodiodes. For comparison, diffraction-interference patterns of Ti:sapphire laser are also observed using the same apparatus (a uncorrelated case).
We present one- and two-photon diffraction and interference experiments involving parametric down-converted photon pairs. By controlling the divergence of the pump beam in parametric down-conversion, the diffraction-interference pattern produced by an object changes from a quantum (perfectly correlated) case to a classical (uncorrelated) one. The observed diffraction and interference patterns are accurately reproduced by Fourier-optical analysis taking into account the quantum spatial correlation. We show that the relation between the spatial correlation and the object size plays a crucial role in the formation of both one- and two-photon diffraction-interference patterns.