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Physical Review A

Resolution of quantum and classical ghost imaging

Milena D’Angelo, Alejandra Valencia, Morton H. Rubin, Yanhua H. Shih

Published Jul 14, 2005• 103 citations
Publisher

Abstract

The quantum ghost imaging phenomena, experimentally demonstrated a decade ago, exploited the apparent spooky action at a distance of entangled photon pairs and offered a novel approach toward imaging. Can ghost imaging effects be produced by ``classical'' light sources, such as separable systems of photon pairs or thermal light? If so, can these sources achieve the same accuracy achieved by entangled states? In order to answer these questions, we formulate the different physics behind entangled and separable systems in terms of a set of inequalities derived from the historical argument of Einstein, Podolsky, and Rosen. We show that the ghost images produced by separable sources are subject to the standard statistical limitations. However, entangled states offer the possibility of overcoming such limitations. Imaging can, therefore, achieve its fundamental limit through the high spatial resolution and nonlocal behavior of entangled systems.

DOI
10.1103/physreva.72.013810

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The quantum ghost imaging phenomena, experimentally demonstrated a decade ago, exploited the apparent spooky action at a distance of entangled photon pairs and offered a novel approach toward imaging. Can ghost imaging effects be produced by ``classical'' light sources, such as separable systems of photon pairs or thermal light? If so, can these sources achieve the same accuracy achieved by entangled states? In order to answer these questions, we formulate the different physics behind entangled and separable systems in terms of a set of inequalities derived from the historical argument of Einstein, Podolsky, and Rosen. We show that the ghost images produced by separable sources are subject to the standard statistical limitations. However, entangled states offer the possibility of overcoming such limitations. Imaging can, therefore, achieve its fundamental limit through the high spatial resolution and nonlocal behavior of entangled systems.
Since the early days of quantum mechanics, physicists have been puzzled by the counterintuitive consequences of entanglement. Quantum imaging is one of the most intriguing effects exhibiting the typical nonlocal behavior of entangled states and has in fact stimulated an intense debate regarding fundamental issues of quantum theory. Recently, particular attention has been given to the possibility of simulating quantum imaging classically, that is, without entanglement. The study of quantum imaging has also lead to useful practical applications such as high precision nonlocal timing-positioning and quantum lithography, in which measurements may achieve resolution even beyond the classical limits. In this paper, we first introduce the concept of quantum imaging and emphasize its peculiar quantum nature through a set of inequalities derived from the historical argument of Einstein, Podolsky and Rosen (EPR). The EPR inequalities are the quantitative formulation of the very different physics governing entangled and separable systems. We show that two-photon imaging may achieve its fundamental limit only through nonlocal measurements realized on entangled photon pairs. Furthermore, we show that quantum imaging may be exploited to overcome the Rayleigh diffraction limit; this is the basic idea behind quantum lithography. Finally, we discuss the possibility of extending the coherent two-photon imaging typical of entangled photon pairs to incoherent coincidence imaging, by employing chaotic light. From an applicative viewpoint, chaotic radiation may represent the ideal candidate for mimicking quantum ghost imaging, provided adequate detection schemes are developed.
The process of image recording is arguably one of the most prevalent technology in modern society and continues to inspire vast swathes of research due to its widespread applications spanning military, medical and consumer spheres. The danger present in a field so broad is that separate niches of research can become isolated with critical advancements struggling to traverse the gulfs between. Unifying the field is the omnipresent drive to acquire an ever increasing quality of images at the lowest possible cost, a goal which warrants continual fundamental research. Quantum entanglement exhibits many intriguing characteristics which make it a suitable tool for such fundamental investigations. The process of spontaneous parametric down- conversion has offered a yet unbeaten strength of photon correlations with the quantum nature of their production providing a reliable and controllable source of single-photons. Arising from these attributes is the technique known as ghost imaging. Though now known to be classically possible, the strength of entanglement generated correlations is yet to be surpassed. This thesis implemented this technique in tandem with the cutting edge detector technology in order to probe the fundamentals of image formation. This form of imaging allowed us to subject an object to a known number of photons whilst acquiring structural information from spatially separate, correlated photons which never interact with the object. The strength of the produced correlations allow us to acquire low background, high resolution images with far less light than traditional techniques and affords many novel benefits. The possibility of incorporating this technique with pre-existent regimes allowed me to draw from advancements made across the landscape of imaging research. Although referred to as “quantum ghost imaging” throughout this work, it should be noted that the intrinsic quantum nature of the correlations was not directly relied upon but provided an ideal source of strongly correlated photons. In order to determine the limits of a traditional imaging system this thesis first sought to answer the question: “can an image of an object be reconstructed from fewer photons than ii pixels in the image?” In chapter 3 I approached this from the perspective of compression, which minimises redundant information within a signal. This lead to the development of an imaging regime capable of imaging with far fewer photons than pixels in the image. By employing assumptions about the sparsity of natural images I was able to reconstruct an image of a biological sample containing an average of less than one photon per image pixel. Having reduced the number of photons necessary to form an image I then considered alternative methods for reducing the optical energy impinging on a sample. I sought to answer the question: “can non-degenerate ghost imaging reduce the optical energy impinged upon an object during imaging”. The photons produced in SPDC need not be of similar wavelengths, however may be chosen far from degeneracy, i.e. non-degenerate. In Chapter 4 I presented a ghost imaging system which illuminated the object with infrared light whilst recording the structural information via entangled visible photons. This allowed for objects opaque to visible light to be imaged in high quality without the need for a spatially resolving infrared detector, the state of the art of which lags behind their silicon based visible counterparts. I presented the systems capabilities by imaging objects which were etched into a gold substrate layered on to silicon, both of which are opaque to visible light. Not only did a reduction in energy deposition arise from the lower energy probe wavelength but applying the reconstruction techniques from the previous chapter brought that down to as low as ≈16 nJcm−2s−1. Seeking to expand the repertoire of applications, the low-light capabilities of my ghost imaging were applied to the technique of phase-contrast microscopy in chapter 5. Typically applied to translucent objects, phase-contrast imaging transfers phase information, i.e. the refractive index changed within the object, into an intensity distribution through the use of a phase-filter. In many of these applications the objects tend to be biological in nature, where high optical exposure can result in bleaching or damage. By applying the phase-filter non- locally, i.e. to the photons correlated to those probing the object, I acquired edge-enhanced images of a phase object whilst illuminating with significantly fewer photons than standard phase-contrast techniques. Having displayed the broad applicability of our low-light ghost imaging system, I then sought to determine the optical resolution in chapter 6. The resolution limits of ghost imaging are not clear at first glance owing to the resolutions dependence upon the strength of spatial correlations. As the length over which the spatial correlations are produced can be brought below the standard diffraction limit, it would seem the resolution of the system could be brought similarly low. To clarify this I artificially restricted the number of spatial modes in each of the correlated beams to uncover the physically realisable resolution. I show that although the resolution of a ghost imaging system to be fundamentally determined by the strength of the correlations, this can never be reached due to the inherent limitations of the intervening imaging system.
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.
There has been an intense debate on the quantum versus classical origin of ghost imaging with a thermal light source over the last two decades. A lot of distinguished work has contributed to this topic, both theoretically and experimentally, however, to this day this quantum-classical dilemma still persists. Here we formulate for the first time a density matrix in the photon orbital angular momentum (OAM) Hilbert space to fully characterize the two-arm ghost imaging system with the basic definition of thermal light sources. Our formulation offers a mathematically precise method to describe the formation of a ghost image in a nonlocal fashion. More importantly, it provides a more physically intuitive picture to reveal the quantumness hidden in the thermal ghost imaging, and therefore, presenting a sound resolution to the ongoing quantum-classical dilemma, which distinguishes the quantum correlations beyond entanglement in terms of geometric measure of discord. Our work also suggests further studies of using thermal multi-photon OAM states directly to implement some quantum information tasks.
Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has started to play important roles in practical engineering applications. Quantum imaging is one of these exciting areas. Quantum imaging has so far demonstrated three peculiar features: enhancing the spatial resolution of imaging beyond the diffraction limit; reproducing ghost images in a “nonlocal” manner; and dispersion-cancelation or turbulence-free imaging. The enhanced spatial resolution apparently “violates” the uncertainty principle. The ghost imaging is considered as a “nonlocal” phenomenon due to a point-to-point correlation of two interaction-free photons at distance. All the peculiar features are the results of two-photon interference, which involves the superposition of two-photon amplitudes, a nonclassical entity corresponding to different yet indistinguishable alternative ways of creating a joint-detection event. The effect of turbulence on a classic image can be easily seen from the blurring of the images.