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Journal of Experimental and Theoretical Physics Letters

Multiplication of a ghost image by means of multimode entangled quantum states

A. S. Chirkin

Published Sep 1, 2015• 10 citations
Publisher

Abstract

It has been shown that multimode (multifrequency) entangled quantum states of light fields make it possible to simultaneously reconstruct several ghost images of an object from the measurement of the spatial correlation function between photons of the object channel and reconstruction channels, where radiation of a single frequency propagates. The detection of radiation in the object channel does not give information on the object. Calculations have been performed for four-frequency entangled quantum light fields.

DOI
10.1134/s0021364015180046

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It has been shown that multimode (multifrequency) entangled quantum states of light fields make it possible to simultaneously reconstruct several ghost images of an object from the measurement of the spatial correlation function between photons of the object channel and reconstruction channels, where radiation of a single frequency propagates. The detection of radiation in the object channel does not give information on the object. Calculations have been performed for four-frequency entangled quantum light fields.
Ghost imaging allows one to obtain information on an object from the spatial correlation function between photons propagating through or reflected from the object and photons of the reference arm. In this case, detection in the object arm is performed over the entire aperture of the beam and, therefore, it does not give information on the object. The reference beam does not interact with the object, but is recorded with a scanning point detector or a CCD array permitting the measurement of the spatial correlation function of photons in two arms. The use of multimode entangled quantum light beams by illuminating the object by one beam and orienting other beams to reference arms makes it possible to obtain simultaneously several ghost images (GIs). Cross correlations of multiplexed GIs (MGIs) are determined by eighth-order field correlation functions. A special algorithm is developed for calculating higher-order correlations of Bose operators. The presence of GI cross correlations is used for improving the quality of the reconstructed object’s image by their processing using the measurement reduction method. An example of the computer simulation of the image reconstruction by MGIs formed in the field of four-frequency entangled quantum states is considered. It is found that in this case the reduced GI has a signal-to-noise ratio several times higher than that of GIs.
When observing a ghost image, information on an object is obtained by measuring the spatial correlation between photons propagating in the object and reconstruction channels. In the traditional schemes involving two-mode entangled quantum states or quasithermal light sources, the correlation function of photons has a background associated with the average number of photons in the channels. It has been shown in this work that the use of polarization-entangled states, e.g., Bell states, allows removing this background and, thereby, obtaining a higher quality reconstructed image.
Ghost imaging allows extracting information about an object from the spatial correlation function between the photons that interacted with an object and the photons in the reference arm(s). The reference beam does not interact with the object; however, it is measured by a CCD matrix. The mathematical method of measurement reduction allows using both the mutual correlations of multiplexed ghost images and prior information about how the image of the research object can look in order to improve the quality of the reconstructed image. The information about the object is the sparsity of its transparency distribution under a given transform. Computer modelling of image reconstruction using multiplexed ghost images formed by four-mode entangled quantum light states confirms the efficiency of the proposed algorithm even with a small number of photons that illuminate the research object.
Ghost imaging can be performed using either quantum or classical states of light that possess strong spatial correlations. In both cases, the image is formed by averaging over many optical events. Here we show that it is possible to distinguish an object from a preestablished basis set of objects by using a small number of position-correlated photon pairs produced by spontaneous parametric down-conversion. The signal photon is incident on one member of a set of spatially nonoverlapping objects. The "ghost" image information is impressed upon the spatially separated idler photon and is extracted by means of holographic filtering and coincidence detection. We were able to distinguish among sets of two and four spatially nonoverlapping objects with confidence levels higher than 87% and 81%, respectively. This method of ghost imaging can be performed in situations requiring extremely low light levels.
The theory of the formation of polarization ghost images in biphoton light of spontaneous parametric scattering is developed. On the basis of the developed theory, the quantum ghost polarimetry concept has been suggested, which makes it possible to obtain two-dimensional maps of the polarization properties of objects by measuring a set of correlation functions obtained in various polarization states of photons. For objects with linear dichroism, a complete set of measurement states is found, which allows for obtaining the maps of the distributions of absorption, value, and azimuth of anisotropy.