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Photonics Research

Theory of ghost scattering with biphoton states

Jing Cheng

Published Jan 4, 2017• 7 citations
Publisher

Abstract

We show how quantum entangled biphoton states can be used to realize ghost scattering, a nonlocal scheme to obtain scattering information of an unknown object through the correlation measurement of the scattering photons in two different optical paths. We present a framework to describe the biphoton ghost scattering process from the T-matrix formula of the scattering theory. We find the scattering information of a test object can be retrieved from either the test arm or the reference arm. By adjusting the biphoton states, the ghost scattering patterns may be varied from the scattering pattern of the object in the test arm to the object in the reference arm.

DOI
10.1364/prj.5.000041

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We show how quantum entangled biphoton states can be used to realize ghost scattering, a nonlocal scheme to obtain scattering information of an unknown object through the correlation measurement of the scattering photons in two different optical paths. We present a framework to describe the biphoton ghost scattering process from the T-matrix formula of the scattering theory. We find the scattering information of a test object can be retrieved from either the test arm or the reference arm. By adjusting the biphoton states, the ghost scattering patterns may be varied from the scattering pattern of the object in the test arm to the object in the reference arm.
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.
Quantum ghost imaging (GI) has significantly advanced the research and application of spatially entangled photon pairs over the past three decades. Nevertheless, existing works predominantly concentrate on qualitative analyses of GI results. The absence of rigorous theoretical models limits the capability of GI to address quantitative problems, which is essential in complex scenarios. Here, we present a comprehensive theoretical model that describes the evolution of the biphoton state throughout the GI process. Based on this model, we can explicitly analyze how the biphoton state evolves, and how object information is encoded into two-photon correlation measurements. We further introduce a virtual single-arm (VSA) operator, which maps the effects of two-arm optical elements into an equivalent single-arm representation, enabling a more intuitive analysis of biphoton-state evolution. Experimental validation is performed using a GI system based on an intensified charge-coupled device (ICCD) camera with multiple objects placed at different longitudinal positions. The excellent agreement between experimental and simulation results confirms the validity of the theoretical framework. This work clarifies the evolution of the biphoton states in quantum GI and opens new avenues for its applications in GI and broader quantum information tasks.
Ghost imaging was first demonstrated with entangled photon pairs and well-known for its peculiar properties. The signal beam that illuminates the object possesses no spatial resolution, whereas the reference beam, which never interacts with the object, is spatially resolved. Either beam alone cannot retrieve the image, which can only be obtained when the signal and reference beams are correlated. Here we will report a ghost imaging experiment with even more peculiar properties, in which the image can be reconstructed when no photon interacts with the object or even no photon in neither signal nor reference beam. All the photons interacted with the object are discarded. Only the time bins with zero photon are employed to retrieve the image, a process referred to as "ghost imaging with zero photons" hereafter. The reason why ghost image can be retrieved with zero photons is jointly determined by photon-number projection measurement and photon statistics of thermal light. The results are helpful to resolve the debate on the physics of ghost imaging and understand the relation between quantum and classical correlations.
Quantum ghost imaging is a nonlocal imaging technique in which the image or diffraction pattern of an object illuminated by photon pairs can be observed through the correlation measurement. This study theoretically demonstrates the cloaking effect of such a quantum imaging. Quantum ghost imaging completely offsets two objects that are placed at proper positions in the interferometer. Furthermore, illusion of quantum imaging, where an object transforms into another object, has also been observed. This phenomenon can be understood by quantum interferences in the correlation measurement.
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.
One of the most surprising consequences of quantum mechanics is the nonlocal multi-particle interference observable in joint-detection of distant particle-detectors. Ghost imaging is one of such phenomena. Two types of ghost imaging have been experimentally demonstrated since 1995. Type-one ghost imaging uses entangled photon pairs as the light source. The nonlocal point-to-point image-forming correlation is the result of a constructive-destructive superposition among a large number of biphoton amplitudes, a nonclassical entity corresponding to different yet indistinguishable alternative ways of producing a joint-detction event between distant photodetectors. Type-two ghost imaging uses chaotic-thermal light. The type-two image-forming correlation is the result of interferences between paired two-photon amplitudes, corresponding to two different yet indistinguishable alternative ways of triggering a join-detection event by two independent photons. A great deal of confusion about ghost imaging comes from "ghost shadow". Similar to x-ray photography, a ghost shadow can be made in coincidences by "blocking-partial blocking-unblocking" of either co-rotating laser beams or classically correlated "speckles". "Ghost shadow" is indeed a classical phenomenon. The physics of ghost imaging, however, is fundamentally different. This article is aimed at exploring the nonlocal two-photon interference nature of ghost imaging.