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Spatial Resolution Enhancement in Quantum Imaging beyond the Diraction Limit Using Entangled Photon-Number State

Jianming Wen, Morton H. Rubin, Yanhua H. Shih

Published Dec 10, 2008• 1 citation
OpenAlex

Abstract

In this paper we study the resolution of images illuminated by sources composed of $N+1$ photons in which one non-degenerate photon is entangled with $N$ degenerate photons. The $N$ degenerate photons illuminate an object and are collected by an $N$ photon detector. The signal from the $N$ 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 $N+1$. Using the Rayleigh criterion, we find that the system may give an improvement in resolution by a factor of $N$ compared to using a classical source. For the case that the $N$-photon number detector is a point detector, a coherent image is obtained. If the $N$-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 $N$-photon point detector may reduce the Airy disk by a factor of $N$.

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arXiv:2101.05849•npj Quantum Information•Aug 9, 2021•8 citations
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.
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.
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.
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.
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.
Abstract Quantum imaging can beat classical resolution limits, imposed by the diffraction of light. In particular, it is known that one can reduce the image blurring and increase the achievable resolution by illuminating an object by entangled light and measuring coincidences of photons. If an n-photon entangled state is used and the nth-order correlation function is measured, the point-spread function (PSF) effectively becomes n\sqrt{n}n​ n times narrower relatively to classical coherent imaging. Quite surprisingly, measuring n-photon correlations is not the best choice if an n-photon entangled state is available. We show that for measuring (n − 1)-photon coincidences (thus, ignoring one of the available photons), PSF can be made even narrower. This observation paves a way for a strong conditional resolution enhancement by registering one of the photons outside the imaging area. We analyze the conditions necessary for the resolution increase and propose a practical scheme, suitable for observation and exploitation of the effect.