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Physical Review A

Generation and detection of magnified images via illumination by entangled photon pairs

Ivan F. Santos, Leonardo Neves, G. Lima, Carlos Henrique Monken, Sebastião Pádua

Published Sep 8, 2005• 13 citations
Publisher

Abstract

We show experimentally that quantum coincidence imaging with photon pairs generated by spontaneous parametric down conversion, in certain conditions, differs from the classical imaging in two aspects: the magnified image is produced by an ``apodized'' effective lens and its effective wavelength is the De Broglie wavelength of the photon pair $\ensuremath{\lambda}∕2$, where $\ensuremath{\lambda}$ is the central wavelength of the single photon wave packet. Better resolution and apodization effects (reduced intensity of the diffraction fringes around the image) are observed in the detected images.

DOI
10.1103/physreva.72.033802

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We show experimentally that quantum coincidence imaging with photon pairs generated by spontaneous parametric down conversion, in certain conditions, differs from the classical imaging in two aspects: the magnified image is produced by an ``apodized'' effective lens and its effective wavelength is the De Broglie wavelength of the photon pair \ensuremathλ∕2\ensuremath{\lambda}∕2\ensuremathλ∕2, where \ensuremathλ\ensuremath{\lambda}\ensuremathλ is the central wavelength of the single photon wave packet. Better resolution and apodization effects (reduced intensity of the diffraction fringes around the image) are observed in the detected images.
We show that an image of an object is obtained when at least one of the photons of a parametric down-converted pair illuminates the object and the two photons are detected in coincidence after they have been transmitted by two lenses. The image is mathematically described by a quantum fourth-order correlation function that differs from the classical image description in two aspects. The quantum image is produced by a nonlocal effective lens whose aperture is described by a compressed convolution of the magnitude of lens transmission functions. The image is generated by the entangled state two-photon light source in which the effective wavelength is equal to the de Broglie wavelength $\ensuremath{\lambda}/2,$ where $\ensuremath{\lambda}$ is the wavelength associated to the individual photons. Images can be obtained with a resolution better than the obtained with coherent classical light sources. Better resolution and strong apodization effects are observed.
We demonstrate one- and two-photon diffraction and interference experiments utilizing parametric down-converted photon pairs (biphotons) and a transmission grating. With two-photon detection, the biphoton exhibits a diffraction-interference pattern equivalent to that of an effective single particle that is associated with half the wavelength of the constituent photons. With one-photon detection, however, no diffraction-interference pattern is observed. We show that these phenomena originate from the spatial quantum correlation between the down-converted photons.
We report the experimental observation of quantum holographic imaging of one-dimensional object with entangled photon pairs, generated in a spontaneous parametric down-conversion process. The signal photons play both roles of “object wave” and “reference wave” in holography but are recorded by a point detector providing only encoding information, while the idler photons travel freely and are locally manipulated with spatial resolution. The holographic image is formed by the two-photon correlation measurement, although both the signal and idler beams are incoherent. Three types of quantum holography schemes are analyzed according to the detection regime of the signal photons.
We examine the resolution of a ghost imaging system for the case in which the entangled photons are nondegenerate in frequency. The signal photon illuminates the object and is detected by a bucket detector. The idler photon is detected by a point detector. We consider the two cases in which the imaging lens is in the same arm as the object and when it is in the other arm. In the first case, the Airy disk is shown to depend on the wavelength of the idler photon; however, because the magnification depends on the two wavelengths, the resolution of a pair of point scatters on the object depends on the wavelength of both photons. In cases in which the position of the object can be controlled, the minimum resolvable distance can be optimized. In the case in which the object is in the far field, the resolution depends only on the signal wavelength. In the second case, the Airy disk depends on the wavelength of both photons but the resolution depends on the signal photon. While the ghost imaging system has flexibility for certain applications, the resolution of the nondegenerate ghost imaging system does not offer improvement over the classical illumination of the object.