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Acta Sinica Quantum Optica

Coincidence imaging and interference with Coherent Gaussian beams

Shi‐Yao Zhu

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

We present a theoretical study of coincidence imaging and interference with coherent Gaussian beams. The equations for the coincidence image formation and interference fringes are derived, from which it is clear that the imaging is due to the corresponding focusing in the two paths. The quality and visibility of the images and fringes can be high simultaneously. The nature of the coincidence imaging and interference between with quantum entangled photon pairs and with coherent Gaussian beams are different. The coincidence image with coherent Gaussian beams is due to intensity-intensity correspondence, a classical nature, while that with entangled photon pairs is due to the amplitude correlation, a quantum nature.

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We present a theoretical study of coincidence imaging and interference with coherent Gaussian beams. The equations for the coincidence image formation and interference fringes are derived, from which it is clear that the imaging is due to the corresponding focusing in the two paths. The quality and visibility of the images and fringes can be high simultaneously. The nature of the coincidence imaging and interference between with quantum entangled photon pairs and with coherent Gaussian beams are different. The coincidence image with coherent Gaussian beams is due to intensity-intensity correspondence, a classical nature, while that with entangled photon pairs is due to the amplitude correlation, a quantum nature.
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.
The spatial correlation between down-converted photons allows for non-local spatial filtering when two-photon coincidences are registered. This allows one to non-locally control the visibility of interference fringes, to observe ghost images and interference patterns, and to "retrieve" a coherent quantum image from an incoherent field distribution. We show theoretically that non-local spatial filtering can lead to counter-intuitive effects when the pump beam is no longer given by a Gaussian profile. Namely, increased non-local filtering can actually decrease the visibility of interference fringes, contrary to what has been observed so far. We explain this behavior through the transverse spatial parity entanglement of the down-converted photons.
We present a theoretical framework for super-resolution imaging based on quantum coincidence detection. By comparing the classical Airy point spread function with the two-photon wavefunction of entangled photon pairs, we derive that coincidence detection yields an effective narrowing of the point spread function by a factor of two or the square root of two, depending on the maintenance of correlation. This model highlights the role of transverse phase accumulation in the image plane and predicts a quantum resolution limit that is half of the classical diffraction limit when correlation is maintained. The results offer clear insight into recent experimental demonstrations of quantum imaging beyond the classical diffraction limit.
The transverse correlation of triphoton entanglement generated within a single crystal is analyzed. Among many interesting features of the transverse correlation, they arise from the spectral function FFF of the triphoton state produced in the parametric processes. One consequence of transverse effects of entangled states is quantum imaging, which is theoretically studied in photon counting measurements. Klyshko's two-photon advanced-wave picture is found to be applicable to the multiphoton entanglement with some modifications. We found that in the two-photon coincidence counting measurement by using triphoton entanglement, although the Gaussian thin lens equation (GTLE) holds, the imaging shown in coincidences is obscure and has a poor quality. This is because of tracing the remaining transverse modes in the untouched beam. In the triphoton imaging experiments, two kinds of cases have been examined. For the case that only one object with one thin lens is placed in the system, we found that the GTLE holds as expected in the triphoton coincidences and the effective distance between the lens and imaging plane is the parallel combination of two distances between the lens and two detectors weighted by wavelengths, which behaves as the parallel combination of resistors in the electromagnetism theory. Only in this case, a point-point correspondence for forming an image is well-accomplished. However, when two objects or two lenses are inserted in the system, though the GTLEs are well-satisfied, in general a point-point correspondence for imaging cannot be established. Under certain conditions, two blurred images may be observed in the coincidence counts. We have also studied the ghost interference-diffraction experiments by using double slits as apertures in triphoton entanglement. It was found that when two double slits are used in two optical beams, the interference-diffraction patterns show unusual features compared with the two-photon case. This unusual behavior is a destructive interference between two amplitudes for two photons crossing two double slits.
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.
Moiré patterns are produced when two periodic structures with different spatial frequencies are superposed. The transmission of the resulting structure gives rise to spatial beatings which are called moiré fringes. In classical optics, the interest in moiré fringes comes from the fact that the spatial beating given by the frequency difference gives information about details (high spatial frequency) of a given spatial structure. We show that moiré fringes can also arise in the spatial distribution of the coincidence count rate of twin photons from the parametric down-conversion, when spatial structures with different frequencies are placed in the path of each one of the twin beams. In other words, we demonstrate how moiré fringes can arise from quantum images.