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THE HIGH-ORDER QUANTUM COHERENCE OF THERMAL LIGHT

Hui Chen

Published Jan 1, 2014• 1 citation
Publisher

Abstract

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.

DOI
10.13016/m2p064

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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.
In this thesis we discuss an extension of the historical Hanbury Brown and Twiss experiment and investigate spatial intensity correlations of higher-orders in the radiation field of statistically independent light sources. The light sources can be non-classical like single-photon emitters or classical, obeying thermal or coherent statistics. Although the light sources are assumed to emit the photons in an incoherent manner, we find spatial photon correlations in the far field which can be explained by the quantum mechanical concept of multi-photon interferences. We demonstrate that spatial correlation measurements between indistinguishable photons based on linear optical detection techniques can be used to overcome the resolution limit of classical optics (Abbe/Rayleigh limit) and also to manipulate the spatial radiation characteristic of the light sources. Both remarkable properties of higher-order intensity correlations have been experimentally verified using statistically independent pseudothermal light sources. Due to the fact that the reported correlation measurements require neither special quantum tailoring of light nor N-photon absorbing media, they are of particular interest for the field of quantum imaging and quantum information processing. The thesis is divided into three main parts: In the first part (Chapter 2 and 3) we introduce a quantum path formalism which allows to describe multi-photon interferences arising in both classical and nonclassical light fields. This quantum path approach explains the origin of the underlying interference mechanism of the higher-order spatial intensity correlation functions in a transparent and simple manner. Moreover, it enables us to compare the multi-photon interferences obtained by nonclassical single-photon emitters with those generated by classical light sources. In the course of this discussion it appears that Dirac's famous statement “Each photon interferes only with itself. Interference between two different photons never occurs.” should better read “A multi-photon state of independent photons only interferes with itself. Interference between different multi-photon states never occurs.” This general statement summarizes the physics behind all multi-photon interference phenomena investigated in this thesis. In the second part of the thesis (Chapter 4) we investigate particular multi-photon interference measurements of independent light sources in the context of quantum imaging. We demonstrate that the Nth-order spatial intensity correlation functions display at specific ‘magic’ detector positions the ability to filter sub-wavelength information out of the light fields arising from N incoherently radiating light sources. These multi-photon interference patterns achieve a higher resolution for N>2 than the classical Abbe/Rayleigh limit for imaging the light source. In case of N single-photon emitters we theoretically show that the super-resolving interference patterns obtained for the ‘magic’ detector positions are identical to the ones generated by NOON states with N-1 photons. Quite unexpected, the same is true for N thermal light sources, except for a reduced visibility. Experimental results with up to eight independent thermal light sources confirm this approach to improve the spatial resolution in imaging. In the last part of this thesis (Chapter 5) we finally demonstrate that multi-photon detections can lead to a strong angular focussing of incoherent photons emitted again by either uncorrelated single-photon sources or statistically independent classical light sources. For this effect the sources can be far away from each other and do not interact. The mth-order intensity correlation measurement causes source correlations which produce a heralded peaked emission pattern for the initially uncorrelated light sources. In particular, we show that if m-1 photons have been detected in a particular direction, the conditional probability to detect the mth photon in the same direction can be as high as 100 %. Owing to the great flexibility of detector positions for the correlation measurement, a wide variety of additional detection schemes exists which produces similar directional photon emission patterns. This theoretically predicted measurement-induced focussing was experimentally confirmed with up to eight pseudothermal light sources for three particular detection schemes.
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.
Spatial anti-bunching, in contrast to the well-known bunching behavior observed in classical light sources, describes a situation where photons tend to avoid each other in space, resulting in a reduced probability of detecting two or more photons in proximity. This anti-bunching effect, a hallmark of nonclassical light, signifies a deviation from classical intensity fluctuations and has been observed not only in free electrons and entangled photon pairs but also in chaotic-thermal light. This work investigates the generation mechanism of spatial anti-bunching correlation in random light fields, leveraging the wandering of light centers to induce a second-order coherence degree below unity. Unlike traditional Gaussian Schell-model partially coherent light, this work predicts the emergence of two fundamentally distinct orbital angular momentum states, arising from the inherent differences between rigid body rotation and fluid-like rotation in the wandering light. These predictions are supported by experimental evidence. Based on these findings, we propose a resolution-enhanced lensless ghost imaging system as an application example. Experimental results indicate that the adoption of the anti-bunching correlated light field as the illumination source enables the imaging system to attain super-resolution imaging capabilities. Our findings provide new insights into the utilization of anti-correlated light fields for precision imaging and detection applications.
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 $N\ensuremath{-}1$ 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.
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.
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.