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Applied Physics Letters

Experimental observation of sub-Rayleigh quantum imaging with a two-photon entangled source

De-Qin Xu, Xin-Bing Song, Hong-Guo Li, Dejian Zhang, Hai-Bo Wang, Jun Xiong, Kaige Wang

Published Apr 27, 2015• 38 citations
Publisher

Abstract

It has been theoretically predicted that N-photon quantum imaging can realize either an N-fold resolution improvement (Heisenberg-like scaling) or a N-fold resolution improvement (standard quantum limit) beyond the Rayleigh diffraction bound, over classical imaging. Here, we report the experimental study on spatial sub-Rayleigh quantum imaging using a two-photon entangled source. Two experimental schemes are proposed and performed. In a Fraunhofer diffraction scheme with a lens, two-photon Airy disk pattern is observed with subwavelength diffraction property. In a lens imaging apparatus, however, two-photon sub-Rayleigh imaging for an object is realized with super-resolution property. The experimental results agree with the theoretical prediction in the two-photon quantum imaging regime.

DOI
10.1063/1.4919131

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•Dec 10, 2008•1 citation
It has been theoretically predicted that N-photon quantum imaging can realize either an N-fold resolution improvement (Heisenberg-like scaling) or a N-fold resolution improvement (standard quantum limit) beyond the Rayleigh diffraction bound, over classical imaging. Here, we report the experimental study on spatial sub-Rayleigh quantum imaging using a two-photon entangled source. Two experimental schemes are proposed and performed. In a Fraunhofer diffraction scheme with a lens, two-photon Airy disk pattern is observed with subwavelength diffraction property. In a lens imaging apparatus, however, two-photon sub-Rayleigh imaging for an object is realized with super-resolution property. The experimental results agree with the theoretical prediction in the two-photon quantum imaging regime.
We report an experimental observation of quantum Airy disk diffraction pattern using an entangled two-photon source. In contrast to the previous quantum lithography experiments where the subwavelength diffraction patterns were observed in the far field limit, we perform the Fraunhofer diffraction experiment with a convex lens. The experimental result shows that the two-photon Airy disk is provided with the super-resolution spot, which surpasses the classical diffraction limit. In particular, the spot size can be well controlled by the focal length, which adapted to optical super-focusing. Our experiment can promote potential application of quantum lithography.
The spatial resolution of an imaging apparatus is limited by the Rayleigh diffraction bound, a consequence of the imager's finite spatial extent. We show some NNN-photon strategies that permit resolution of details that are smaller than this bound, attaining either a 1∕N1∕\sqrt{N}1∕N​ enhancement (standard quantum limit) or a 1∕N1∕N1∕N enhancement (Heisenberg-like scaling) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, since classical light sources suffice. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.
In this paper we study the resolution of images illuminated by sources composed of N+1N+1N+1 photons in which one non-degenerate photon is entangled with NNN degenerate photons. The NNN degenerate photons illuminate an object and are collected by an NNN photon detector. The signal from the NNN photon detector is measured in coincidence with the non-degenerate photon giving rise to a ghost image. We discuss the case of three photons in various configurations and generalize to N+1N+1N+1. Using the Rayleigh criterion, we find that the system may give an improvement in resolution by a factor of NNN compared to using a classical source. For the case that the NNN-photon number detector is a point detector, a coherent image is obtained. If the NNN-photon detector is a bucket detector, the image is incoherent. The visibility of the image in both cases is 1. In the opposite case in which the non-degenerate photon is scattered by the object, then, using an NNN-photon point detector may reduce the Airy disk by a factor of NNN.
Quantum imaging exploits the spatial correlations between photons to image object features with a higher resolution than a corresponding classical light source could achieve. Using a quantum correlated NNN-photon state, the method of optical centroid measurement (OCM) was shown to exhibit a resolution enhancement by improving the classical Rayleigh limit by a factor of 1/N1/N1/N. In this work, the theory of OCM is formulated within the framework of an imaging formalism and is implemented in an exemplary experiment by means of a conventional entangled photon pair source. The expected resolution enhancement of a factor of two is demonstrated. The here presented experiment allows for single-shot operation without scanning or iteration to reproduce the object in the image plane. Thereby, photon detection is performed with a newly developed integrated time-resolving detector array. Multi-photon interference effects responsible for the observed resolution enhancement are discussed and possible alternative implementation possibilities for higher photon number are proposed.
Quantum imaging exploits the spatial correlations between photons to image object features with a higher resolution than a corresponding classical light source could achieve. Using a quantum correlated N-photon state, the method of optical centroid measurement (OCM) was shown to exhibit a resolution enhancement by improving the classical Rayleigh limit by a factor of 1/N. In this work, the theory of OCM is formulated within the framework of an imaging formalism and is implemented in an exemplary experiment by means of a conventional entangled photon pair source. The expected resolution enhancement of a factor of two is demonstrated. The here presented experiment allows for single-shot operation without scanning or iteration to reproduce the object in the image plane. Thereby, photon detection is performed with a newly developed integrated time-resolving detector array. Multi-photon interference effects responsible for the observed resolution enhancement are discussed and possible alternative implementation possibilities for higher photon number are proposed.
In this paper we study the resolution of images illuminated by sources composed of N+1N+1N+1 photons in which one non-degenerate photon is entangled with NNN degenerate photons. The NNN degenerate photons illuminate an object and are collected by an NNN photon detector. The signal from the NNN photon detector is measured in coincidence with the non-degenerate photon giving rise to a ghost image. We discuss the case of three photons in various configurations and generalize to N+1N+1N+1. Using the Rayleigh criterion, we find that the system may give an improvement in resolution by a factor of NNN compared to using a classical source. For the case that the NNN-photon number detector is a point detector, a coherent image is obtained. If the NNN-photon detector is a bucket detector, the image is incoherent. The visibility of the image in both cases is 1. In the opposite case in which the non-degenerate photon is scattered by the object, then, using an NNN-photon point detector may reduce the Airy disk by a factor of NNN.