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arXiv:quant-ph/0502028 · Journal of Modern Optics

Theoretical investigation of moiré patterns in quantum images

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

Published Feb 21, 2006• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1080/09500340500217720

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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.
Classically, the spatial resolution of the image of an object is usually determined by the Rayleigh criterion. However, quantum properties of light have been exploited to form images with resolutions exceeding this criterion and beating the standard quantum limit, which allow high measurement sensitivity. We found that it is possible to super-resolve a distributed object made of two parts that are spatially separated but when superposed over each other form an object. A coincidence interference pattern of a nonlocal two-photon system with periodicity proportional to $\ensuremath{\lambda}/2$ was measured even when each photon, with wavelength of $\ensuremath{\lambda}$, has been scattered by different parts of an object, none of them being the object itself.
Using the unique detection properties offered by metastable helium atoms we have produced high resolution images of the transverse spatial profiles of an atom laser beam. We observe transverse fringes on the beam, resulting from quantum mechanical interference between atoms that start from rest at different transverse locations within the outcoupling surface and end up at a later time with different velocities at the same transverse position. Further, for high outcoupling rates we see the emergence of structure on the beam profile, which is not predicted by the usual Gross-Pitaevskii equation.
We present a theoretical study of coincidence imaging and interference with coherent Gaussian beams. The equations for the coincidence image formation and interference fringes are derived, from which it is clear that the imaging is due to the corresponding focusing in the two paths. The quality and visibility of the images and fringes can be high simultaneously. The nature of the coincidence imaging and interference between with quantum entangled photon pairs and with coherent Gaussian beams are different. The coincidence image with coherent Gaussian beams is due to intensity-intensity correspondence, a classical nature, while that with entangled photon pairs is due to the amplitude correlation, a quantum nature.
This dissertation contains scientific research within the realm of quantum optics, which is a branch of physics. An experimental and theoretical study is made of two-photon interference phenomena in various optical systems. Spatially entangled photon pairs are produced via the nonlinear optical process of spontaneous parametric down-conversion. These entangled photons are then passed through different optical systems to study various aspects of two-photon interference. Firstly, an experimental analysis is made of the high-dimensional entanglement that is present in the orbital angular momentum of the photons. Secondly, we present a comprehensive description of two-photon quantum interference behind a double slit. We demonstrate how to control the quantum correlations and present the first observations of complete two-photon diffraction patterns behind a double slit. Finally, we present pioneering experiments on spatially entangled two-photon states that are scattered of random media. We have observed and theoretically analyzed the structure in the random two-photon interference patterns called two-photon speckle patterns. Spatial entanglement gives two-photon speckle a much richer structure than ordinary one-photon speckle. Our experiments also demonstrate a two-photon interference phenomenon that survives averaging over different realizations of disorder. The latter results are closely related to bosonic, fermionic, and anyonic particle exchange symmetries.