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Physical Review A

Theoretical scheme of thermal-light many-ghost imaging by N th-order intensity correlation

Ying-Chuan Liu, Le‐Man Kuang

Published May 6, 2011• 17 citations
Publisher

Abstract

In this paper, we propose a theoretical scheme of many-ghost imaging in terms of $N$th-order correlated thermal light. We obtain the Gaussian thin lens equations in the many-ghost imaging protocol. We show that it is possible to produce $N\ensuremath{-}1$ ghost images of an object at different places in a nonlocal fashion by means of a higher order correlated imaging process with an $N$th-order correlated thermal source and correlation measurements. We investigate the visibility of the ghost images in the scheme and obtain the upper bounds of the visibility for the $N$th-order correlated thermal-light ghost imaging. It is found that the visibility of the ghost images can be dramatically enhanced when the order of correlation becomes larger. It is pointed out that the many-ghost imaging phenomenon is an observable physical effect induced by higher order coherence or higher order correlations of optical fields.

DOI
10.1103/physreva.83.053808

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In this paper, we propose a theoretical scheme of many-ghost imaging in terms of NNNth-order correlated thermal light. We obtain the Gaussian thin lens equations in the many-ghost imaging protocol. We show that it is possible to produce N\ensuremath−1N\ensuremath{-}1N\ensuremath−1 ghost images of an object at different places in a nonlocal fashion by means of a higher order correlated imaging process with an NNNth-order correlated thermal source and correlation measurements. We investigate the visibility of the ghost images in the scheme and obtain the upper bounds of the visibility for the NNNth-order correlated thermal-light ghost imaging. It is found that the visibility of the ghost images can be dramatically enhanced when the order of correlation becomes larger. It is pointed out that the many-ghost imaging phenomenon is an observable physical effect induced by higher order coherence or higher order correlations of optical fields.
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In a near-field three-photon correlation measurement, we observed the third-order temporal and spatial correlation functions of chaotic thermal light in the single-photon counting regime. In the study, we found that the probability of jointly detecting three randomly radiated photons from a chaotic thermal source by three individual detectors is 666 times greater if the photodetection events fall in the coherence time and coherence area of the radiation field than if they do not. From the viewpoint of quantum mechanics, the observed phenomenon is the result of three-photon interference. By making use of this property, we measured the three-photon thermal light lensless ghost image of a double spot and achieved higher visibility compared with the two-photon thermal light ghost image.
Thermal light, such as sunlight, is usually considered classical light. In a macroscopic picture, classical theory successfully explained the first-order coherence phenomena of thermal light. The macroscopic theory, based on the statistical behavior of light intensity fluctuations, however, can only phenomenologically explain the second- or higher-order coherence phenomena of thermal light. This thesis introduces a microscopic quantum picture, based on the interferences of a large number of randomly distributed and randomly radiated subfields, wavepackets or photons, to the study of high-order coherence of thermal light. This thesis concludes that the second-order intensity fluctuation correlation is caused by nonlocal interference: a pair of wavepackets, which are randomly paired together, interferes with the pair itself at two distant space-time coordinates. This study has the following practical motivations: (1) to simulate N-qbits. Practical quantum computing requires quantum bits(qubits) of N-digit to represent all possible integers from 0 to 2 N -1 simultaneously. A large number of independent particles can be prepared to represent a large set of N orthogonal |0> and |1> bits. In fact, based on our recent experiments of simulating the high-order correlation of entangled photons, thermal radiation is suggested as a promising source for quantum information processing. (2) to achieve sunlight ghost imaging. Ghost imaging has three attractive non-classical features: (a) the ghost camera can see targets that can never be seen by a classic camera; (2) it is turbulence-free; and (3) its spatial resolution is mainly determined by the angular diameter of the light source. For example, a sunlight ghost image of an object on earth may achieve a spatial resolution of 200 micrometer because the angular diameter of sun is 0.53 degree with respect to Earth. Although ghost imaging has been experimental demonstrated by using entangled photon pairs and pseudo-thermal light, we still have difficulties to make sunlight ghost image. From the picture of macroscopic local statistics of intensity fluctuations, we may never find the problem that causes sunlight ghost imaging so difficult comparing with that of pseudo-thermal light. To achieve the goals in both fundamental understanding of physics and practical engineering applications, this thesis aims at studying the high-order quantum coherence of thermal light. The first successful attempt of this study is to invent a novel measurement scheme — Positive-Negative Intensity Fluctation Correlation(PNFC) protocol, to measure the intensity fluctuation correlation(or photon number fluctuation correlation) of thermal light. This new photodetection measurement protocol distinguishes positive and negative intensity fluctuations(or photon number fluctuations) of two or more photodetectors within a sequence of short time windows, and then calculates the statistical correlation between these individual fluctuations. With the help of this invention, an anti-correlation of thermal light in a typical Hanbury Brown and Twiss(HBT) interferometry was discovered, which cannot be understood from the view point of traditional macroscopic classical theory. In the microscopic quantum coherence picture, the observation is successfully explained as a nonlocal two-photon interference phenomenon. We also successfully simulated the behavior of Bell-state with thermal light. By manipulating polarization, a thermal Bell-like state was built from two incoherent and orthogonally polarized thermal radiations. With intensity fluctuation correlation measurement, a sinusoidal function with 100% visibility, which suggests thermal light as a feasible source for preparing qubits. Besides the fundamental significance, PNFC protocol also brings incredibly high contrast for quantum imaging, such as 100% visibility for ghost imaging. Above all, we invented a 100% Intensity Fluctuation Correlation of Chaotic-thermal Light and Turbulence-free Imaging System, which provides high contrast as well as high resolution. Based on the experiments of the simulations of quantum interference in thermal light and the dramatically improvement of the contrast in quantum imaging, this study of the high-order coherence of thermal light has a great significance both for fundamental physics and applications.
Multiparticle interference is one of the most surprising consequences of quantum mechanics. In quantum theory, a interference happens between different, yet indistinguishable probability amplitudes. Probability amplitudes can be nonlocal when they are connected with systems including several particles. The interference between these nonlcoal probability amplitudes sometimes can only be understood by quantum theory. In this dissertation, the multiphoton coherence of thermal light is studied, theoretically and experimentally, as the consequences of interference between nonlcoal probability amplitudes. The study showed that the higher order correlation functions of thermal light had higher contrast compared with the lower order correlation functions. For example, the contrast of the Nth order correlation function of thermal light can reach N!:1. This is because in higher order correlation functions there are more cross terms from interference contribute to the correlation peak. In this dissertation, the high contrast property is employed to increase the contrast of thermal light ghost imaging. An experiment showed that the contrast of the third order ghost image is significantly improved compared with that of the second order ghost image.
The arbitrary Nth-order intensity correlation measurement with thermal light is both theoretically and experimentally investigated. In a double-slit interference scheme with thermal light, we compare the results for higher- and lower-order intensity correlation and demonstrate that the visibility of the interference pattern can be dramatically enhanced while the resolution can also be improved when the order N becomes larger. The experimental results are in agreement with our theoretical analysis.
A scheme for fourth-order double-slit ghost interference with a pseudo-thermal light source is proposed. It is shown that not only can the visibility be dramatically enhanced compared to the third-order case, but also higher resolution is demonstrated if we scan two of three reference detectors in opposite directions with the same speed, meanwhile another two in identical directions where the speed of one reference detector is twice the other. The results show that the visibility and resolution improvement of the fourth-order ghost interference fringe can be applied to the N th-order ghost imaging.