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Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 339-359). Also available via the Internet

by Ng Pak Hong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 111-112). / Text in English; abstract also in Chinese. / by Ng Pak Hong. / Acknowledgments --- p.i / Abstract --- p.ii / Table of contents --- p.iv / Chapter Chapter 1 --- INTRODUCTION --- p.1 / Chapter 1.1 --- History --- p.2 / Chapter 1.2 --- Airy Theory --- p.4 / Chapter 1.2.1 --- Rainbow angle --- p.4 / Chapter 1.2.2 --- Airy's cubic wave front --- p.4 / Chapter 1.3 --- High-order rainbows --- p.7 / Chapter 1.4 --- Glare points --- p.8 / Chapter 1.5 --- Interference between overlapping rainbows --- p.10 / Chapter Chapter 2 --- HIGH-ORDER RAINBOWS --- p.17 / Chapter 2.1 --- Experiment --- p.17 / Chapter 2.2 --- Results and discussions --- p.19 / Chapter 2.2.1 --- General features --- p.19 / Chapter 2.2.2 --- Angular positions and angular widths of rainbows --- p.21 / Chapter 2.2.3 --- Rainbow intensities as functions of order number --- p.22 / Chapter 2.3 --- Vertical positions of rainbows --- p.24 / Chapter 2.4 --- Vertical spreads of rainbows --- p.26 / Chapter 2.5 --- Rainbow patterns at different values of the refractive index ..… --- p.28 / Chapter 2.6 --- Effect of eccentricity of a droplet's circumference in the equatorial plane on the rainbow angles --- p.30 / Chapter CHAPTER 3 --- GLARE POINTS --- p.56 / Chapter 3.1 --- Experiment --- p.56 / Chapter 3.2 --- Results and discussions --- p.57 / Chapter 3.2.1 --- General features --- p.57 / Chapter 3.2.2 --- Glare point position and intensity --- p.58 / Chapter A. --- Glare point position --- p.58 / Chapter B. --- Glare point intensity --- p.61 / Chapter C. --- Summary of results of glare points --- p.62 / Chapter 3.2.3 --- Fourier transform of rainbow patterns --- p.63 / Chapter Chapter 4 --- INTERFERENCE BETWEEN OVERLAPPING RAINBOWS --- p.90 / Chapter 4.1 --- Experiment --- p.90 / Chapter 4.2 --- Results and discussions --- p.91 / Chapter 4.2.1 --- General features --- p.91 / Chapter 4.2.2 --- Simulation of the interference --- p.91 / Chapter 4.2.3 --- Estimation of the droplet vibration amplitude and frequency --- p.95 / Chapter 4.3 --- Comparison with results of Lock and Woodruff --- p.96 / Chapter Chapter 5 --- CONCLUSION --- p.107 / APPENDIX A --- p.109 / References --- p.111

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A new wave-kinetic numerical method for the propagation of optical waves in weakly inhomogeneous media is discussed, and it is applied to several canonical problems: the propagation of beam and plane waves through a weak 3-D ( or 2-D ) Gaussian eddy. The numerical results are also compared to those from a Monte-Carlo simulation and the first Born approximation. Within the validity of the Liouville approximation, the Wigner distribution function ( WDF ) is conserved along the conventional ray trajectories, and, thus, by discretizing the input WDF with Gaussian beamlets, we can represent the output WDF as a sum of Gaussians, from which irradiance can be obtained by analytical integration of each Gaussian with respect to wavevector. Although each Gaussian beamlet propagates along a geometrical optics ray trajectory, it can correctly describe diffraction effects, and the propagation of optical waves through caustics or ray crossings. The numerical results agree well with either the Monte-Carlo method or the first Born approximation in regions where one or both of these are expected to be valid. / M.S.

Estudamos teoricamente a geração de estados emaranhados do campo eletromagnético através do processo de mistura de quatro ondas em uma nuvem de átomos frios em configuração duplo- trabalhando perto da ressonância. Mostra-se que neste caso é possível gerar emaranhamento com uma potência de bombeio muito menor do que na situação em que temos átomos quentes [17]. Baseando-se nos parâmetros da armadilha de átomos de rubídio de nosso laboratório, calcula-se uma violação de 46.5 % do limite imposto pela desigualdade DGCZ [59] para uma frequência de Rabi dos bombeios de =0.8 MHz (neste caso, equivalente a uma potência de 0.3 µW) e uma dessintonia de =20 MHz para uma transição enquanto a outra permanece ressonante. Também foi analisado o emaranhamento entre as bandas laterais dos feixes de prova e conjugado, estudando a estrutura do emaranhamento entre estes quatro modos através do critério positividade sobre transposição parcial em variáveis continuas. Nesta análise, se observaram correlações quânticas entre pares de campos (a banda superior do feixe de prova e a banda inferior do feixe conjugado, e a banda inferior do feixe de prova e a banda superior do feixe conjugado). Estas evidências, junto com as equações de evolução dos feixes, sugerem que a mistura de quatro ondas, dentro das considerações supostas neste trabalho, gera estados nos quais o emaranhamento é exclusivo entre as bandas laterais superior de um feixe com a inferior do outro. [17] Vincent Boyer et al. Science, 321-544 (2008). [59] Lu-Ming Duan et al. Phys. Rev. Lett 84-2722 (2000) / We have theoretically studied the generation of entangled states of the electromagnetic field through the four wave mixing (FWM) process in a cold atomic cloud in a double-, close to resonance configuration. It is shown that in this case it possible to generate entanglement with a pump power much weaker than in the situation which we have hot atoms [17]. Based in the parameters obtained in the magneto-optical trap (MOT) with rubidium at our laboratory, we calculated a violation of 46.5 % of the limit imposed by the DGCZ inequality [59] at a Rabi frequency of the pump fields of =0.8 MHz (in this case, this is equivalent to a pump power of 0.3 µW) and a detuning of =20 MHz in one of the transition, while the other one remains resonant. We also analysed the entanglement between the side bands of the probe and conjugate beams. Using the positive partial transpose criterion in continuous variables, we studied the structure of entanglement within these side bands. In this analysis we observed quantum correlations between pairs of fields (the upper side band of the probe beam with the lower side band of the conjugate beam, and the lower side band of the probe beam with the upper side band of the conjugate beam). These evidences, together with the evolution equations of the beams, suggest that the 4WM process, within the considerations made in this work, generates states where the entanglement is exclusive between the upper side band of one beam and the lower side band of the other. [17] Vincent Boyer et al. Science, 321-544 (2008). [59] Lu-Ming Duan et al. Phys. Rev. Lett 84-2722 (2000).

Estudamos teoricamente a geração de estados emaranhados do campo eletromagnético através do processo de mistura de quatro ondas em uma nuvem de átomos frios em configuração duplo- trabalhando perto da ressonância. Mostra-se que neste caso é possível gerar emaranhamento com uma potência de bombeio muito menor do que na situação em que temos átomos quentes [17]. Baseando-se nos parâmetros da armadilha de átomos de rubídio de nosso laboratório, calcula-se uma violação de 46.5 % do limite imposto pela desigualdade DGCZ [59] para uma frequência de Rabi dos bombeios de =0.8 MHz (neste caso, equivalente a uma potência de 0.3 µW) e uma dessintonia de =20 MHz para uma transição enquanto a outra permanece ressonante. Também foi analisado o emaranhamento entre as bandas laterais dos feixes de prova e conjugado, estudando a estrutura do emaranhamento entre estes quatro modos através do critério positividade sobre transposição parcial em variáveis continuas. Nesta análise, se observaram correlações quânticas entre pares de campos (a banda superior do feixe de prova e a banda inferior do feixe conjugado, e a banda inferior do feixe de prova e a banda superior do feixe conjugado). Estas evidências, junto com as equações de evolução dos feixes, sugerem que a mistura de quatro ondas, dentro das considerações supostas neste trabalho, gera estados nos quais o emaranhamento é exclusivo entre as bandas laterais superior de um feixe com a inferior do outro. [17] Vincent Boyer et al. Science, 321-544 (2008). [59] Lu-Ming Duan et al. Phys. Rev. Lett 84-2722 (2000) / We have theoretically studied the generation of entangled states of the electromagnetic field through the four wave mixing (FWM) process in a cold atomic cloud in a double-, close to resonance configuration. It is shown that in this case it possible to generate entanglement with a pump power much weaker than in the situation which we have hot atoms [17]. Based in the parameters obtained in the magneto-optical trap (MOT) with rubidium at our laboratory, we calculated a violation of 46.5 % of the limit imposed by the DGCZ inequality [59] at a Rabi frequency of the pump fields of =0.8 MHz (in this case, this is equivalent to a pump power of 0.3 µW) and a detuning of =20 MHz in one of the transition, while the other one remains resonant. We also analysed the entanglement between the side bands of the probe and conjugate beams. Using the positive partial transpose criterion in continuous variables, we studied the structure of entanglement within these side bands. In this analysis we observed quantum correlations between pairs of fields (the upper side band of the probe beam with the lower side band of the conjugate beam, and the lower side band of the probe beam with the upper side band of the conjugate beam). These evidences, together with the evolution equations of the beams, suggest that the 4WM process, within the considerations made in this work, generates states where the entanglement is exclusive between the upper side band of one beam and the lower side band of the other. [17] Vincent Boyer et al. Science, 321-544 (2008). [59] Lu-Ming Duan et al. Phys. Rev. Lett 84-2722 (2000).

Dans cette dissertation nous présentons une étude expérimentale et théorique sur les propriétés optiques de nanotubes de carbone mono-parois (SWNTs) semi-conducteurs. Nous nous concentrons sur les aspects et phénomènes typiquement quantiques dont la description nécessite de sortir du cadre de la physique classique et des équations de Maxwell. Notre résultat experimental le plus important est l'observation du dégroupement des photons dans la photoluminescence (FL) émise par les SWNTs. Tenant compte des particularités de notre échantillon qui consiste de SWNTs enrobés dans un surfactant et déposés sur un substrat fonctionalisé, nous montrons que l'absence d'émission simultanée de plusieurs photons est dûe à la localisation des excitons dans des pièges de quelques nanomètres de long sur nanotube. L'annihilation exciton-¬exciton rapide et efficace résultant de la dimension réduite des nanotubes de carbone joue un role déterminant pour éviter l'émission de paires de photons. La fidèle reproduction des larges lignes asymétriques en FL par un model physique reposant sur le confinement des excitons supporte cette vision. Nous calculons le spectre d'une boîte quantique (QD) formée sur un SWNT et démontrons que le couplage de l'exciton avec les phonons acoustiques de faible énergie du nanotube cause un déphasage ultra-rapide et non-markovien de l'état optiquement excité. Dans le domaine spectral, la force d'oscillateur est transférée de la transition sans phonon (ZFL) vers des ailes associées aux phonons et présentant une forte asymétrie aux températures cryogéniques. Nous prouvons que nos données sont des preuves directes de la réalisation expérimentale du modèle spin-boson dans le régime (sous-)ohmique. Ceci est une conséquence de l'uni-dimensionnalité du bain de phonons se réfléchissant dans la densité spectrale gouvernant les dissipations. Nous soulignons les différences qua-litatives par rapport aux boîtes quantiques traditionnels dans une matrice à trois dimensions, et discutons brièvement les conséquences pour l'utilisation des SWNT¬QDs dans le traitement d'information quantique. Une possibilité passionnante ouverte par le fort couplage exciton-phonon dans les nanotubes de carbone est leur utilisation comme résonateurs mécaniques pour le refroidissement assisté par laser. Nous proposons un dispositif basé sur un SWNT suspendu où le confinement de l'exciton est contrôlé par de fines pointes servant de grilles. Le potentiel appliqué aux pointes peut en outre être utilisé pour induire le couplage de l'exciton au mode de flexion du SWNT et pour régler sa force. La diffusion inélastique d'un faible laser désaccordé vers le rouge permet alors de réduire le nombre d'occupation du mode fondamental de flexion jusqu'àl'état fondamental quantique. Dans une tentative de donner une image unifiée pour l'ensemble de nos obser-vations expérimentales, nous proposons aussi une origine physique à la formation de SWNT-QDs dans notre échantillon. Nous considérons la présence d'une impureté h chargée dans les environs du nanotube et démontrons que le champ électrique qui en résulte piège les excitons du SWNT. Les caractéristiques particulières de ce potentiel confinant pourraient expliquer la plupart des caractéristiques expérimentales. Enfin, nous montrons comment le couplage spin-orbite non-nul récemment me-surédans des expériences de transport permet la manipulation purement optique du spin dans des nanotubes de carbone. Nous effectuons des simulations numériques basées sur les équations de Bloch pour démontrer que la préparation du spin avec haute fidélitéest réalisable. La manipulation optique cohérente du spin et de pos¬sibles utilisations du spin des nanotubes de carbone dans le traitement quantique de l'information sont également discutées. Alliant de nouveaux résultats expérimentaux surprenants et de diverses études théoriques et numériques, ce travail met l'accent sur le potentiel fascinant des nano-tubes de carbone dans l'étude de la physique quantique des matériaux de dimension réduite.