Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-04-01T12:13:47Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertação - Gabriel da Cruz Borba de Andrade.pdf: 8890407 bytes, checksum: 2c4e4b4737788baa1ca937189ea8e250 (MD5) / Made available in DSpace on 2016-04-01T12:13:47Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertação - Gabriel da Cruz Borba de Andrade.pdf: 8890407 bytes, checksum: 2c4e4b4737788baa1ca937189ea8e250 (MD5) Previous issue date: 2014-09-25 / CNPq / Nesta dissertação apresentamos uma investigação teórica e experimental do armazenamento e extração de diversas ordens de não linearidades na interação átomo-luz, utilizando grades de coerência de um ensemble de átomos frios de Césio aprisionados em uma armadilha magneto-ótica. As diversas ordens são exploradas na condição de casamento de fase, modificando apenas o ângulo do feixe leitura em relação ao eixo de definido por um dos feixes da escrita. Elaboramos um modelo teórico consistindo em um sistema atômico de quatro níveis interagindo com campos clássicos com polarizações lineares ortogonais. Ele nos fornece uma expressão analítica para o campo elétrico do feixe gerado na direção de deteção, nos permitindo comparar diversos aspectos experimentais e teóricos e fornecendo um entendimento mais claro acerca do problema. Abordamos particularmente as primeiras três ordens de não linearidade existentes no nosso sistema, a saber, χ(3), χ(5) e χ(7). Dentre os aspectos do sinal estudados estão as polarizações dos feixes gerados, que demonstram clara dependência com a ordem de não linearidade. Analisamos ainda formas de pulso e curvas de saturação com as intensidades dos feixes envolvidos, e os tempos de coerência do sistema, que determinariam até quando seria possível retirar a informação armazenada no meio. / In this dissertation we present a theoretical and experimental investigation of the storage and retrieval of several orders of non-linearity in the light-atom interaction, using coherence gratings of cold cesium atoms ensemble trapped with a magnetic-optical trap. The orders are explored in the phase match condition, modifying only the angle between the reading beam and the axis defined by one of the writing beams. We elaborated a theoretical model of four level system interacting with the classical fields with orthogonal linear polarizations. It provides us an analytical expression from the generated electrical field, allowing us to compare several theoretical and experimental features, clarifying the problem. Particularly, we investigated the first three orders of non-linearity existent in our system, namely χ(3), χ(5) and χ(7). We analyzed the pulses shapes, the saturation curves with the intensity of the beams involved, and the system coherence times which determine how long would be possible to recover the stored information in the atomic medium.

This dissertation is the collection of a progressive research on the topic of topological quantum computation and information with the focus on the error threshold of the well-known models such as the unpaired Majorana, the toric code, and the planar code. We study the basics of quantum computation and quantum information, and in particular quantum error correction. Quantum error correction provides a tool for enhancing the quantum computation fidelity in the noisy environment of a real world. We begin with a brief introduction to stabilizer codes. The stabilizer formalism of the theory of quantum error correction gives a well-defined description of quantum codes that is used throughout this dissertation. Then, we turn our attention to a quite new subject, namely, topological quantum codes. Topological quantum codes take advantage of the topological characteristics of a physical many-body system. The physical many-body systems studied in the context of topological quantum codes are of two essential natures: they either have intrinsic interaction that self-corrects errors, or are actively corrected to be maintained in a desired quantum state. Examples of the former are the toric code and the unpaired Majorana, while an example for the latter is the surface code. A brief introduction and history of topological phenomena in condensed matter is provided. The unpaired Majorana and the Kitaev toy model are briefly explained. Later we introduce a spin model that maps onto the Kitaev toy model through a sequence of transformations. We show how this model is robust and tolerates local perturbations. The research on this topic, at the time of writing this dissertation, is still incomplete and only preliminary results are represented. As another example of passive error correcting codes with intrinsic Hamiltonian, the toric code is introduced. We also analyze the dynamics of the errors in the toric code known as anyons. We show numerically how the addition of disorder to the physical system underlying the toric code slows down the dynamics of the anyons. We go further and numerically analyze the presence of time-dependent noise and the consequent delocalization of localized errors. The main portion of this dissertation is dedicated to the surface code. We study the surface code coupled to a non-interacting bosonic bath. We show how the interaction between the code and the bosonic bath can effectively induce correlated errors. These correlated errors may be corrected up to some extend. The extension beyond which quantum error correction seems impossible is the error threshold of the code. This threshold is analyzed by mapping the effective correlated error model onto a statistical model. We then study the phase transition in the statistical model. The analysis is in two parts. First, we carry out derivation of the effective correlated model, its mapping onto a statistical model, and perform an exact numerical analysis. Second, we employ a Monte Carlo method to extend the numerical analysis to large system size. We also tackle the problem of surface code with correlated and single-qubit errors by an exact mapping onto a two-dimensional Ising model with boundary fields. We show how the phase transition point in one model, the Ising model, coincides with the intrinsic error threshold of the other model, the surface code.

Le développement considérable des signaux dans les bandes hyperfréquences (communications sans fil, radars, etc.) rend leur traitement extrêmement difficile. Il est en effet nécessaire d'analyser de larges bandes spectrales avec une grande résolution, ce que ne permettent pas les dispositifs purement électroniques. Une solution très prometteuse consiste à transposer les signaux hyperfréquences (hf) sur un laser puis à utiliser un cristal dopé par des ions de terres rares comme processeur. Cette technique tire parti des propriétés optiques exceptionnelles des ces matériaux, qui présentent des transitions à la fois extrêmement fines pour un centre unique (largeur homogène donnant la résolution spectrale) et larges pour un ensemble d'ions (largeur inhomogène donnant la bande d'analyse). Grâce à des techniques de pompage optique, ceci permet d'obtenir des bandes d'analyse de 20 GHz avec une résolution de 100 kHz, soit un rapport de 105. Ces résultats, obtenus dans des cristaux de Tm3+:Y3Al5O12, font l'objet d'études industrielles avancées, notamment en France par Thales, et auxquelles participe l'IRCP-MPOE. Le but du projet est de développer des cristaux dopés Er3+ pour une nouvelle génération d'analyseurs fonctionnant à 1.5 μm dans le but d'exploiter pleinement les technologies télécom en terme de transmission longue distance et de composants opto-électroniques. Les meilleurs cristaux actuels ne possèdent pas une largeur inhomogène suffisante pour l'application visée. Notre approche consistera à introduire un désordre chimique contrôlé, par exemple en utilisant un co-dopant, dans des monocristaux dopés Er3+ de haute qualité. Ceci permettra d'augmenter la largeur inhomogène optique mais pourrait aussi influencer la largeur homogène, point crucial pour l'analyse des signaux hf. Il s'agira de déterminer la nature et le niveau de désordre optimaux permettant d'obtenir les meilleures performances. D'une façon plus générale, ce travail permettra une compréhension approfondie des phénomènes dynamiques contrôlant la largeur homogène optique et de leur relation avec les structures cristallines. Outre l'analyse de signaux hyperfréquences, ceci pourra déboucher sur des avancées dans le traitement quantique de l'information dans le domaine télécom. / Significant progresses have been made recently on radar communications. However it is still difficult to analyse radar communications both efficiently and on a large frequency span. This is due to the fact that pure electronic processors are not able to process rapidly signals with high bandwidths. A very promising solution consists in transposing radar signals on a optical carrier (laser) and process the signals via rare-earths-doped single-crystals, which are able to interact efficiently with light. Rare-earth-ion doped crystals can have very narrow optical transitions at liquid helium temperature, making them attractive for applications in quantum information processing and advanced RF signal processing. One key property of these materials is the potential for a high ratio between the optical inhomogeneous and homogeneous linewidths. This allows signals with high bandwidth to be stored in quantum memories for a long time, or alternatively, the high resolution spectral analysis of RF signals. Er3+ is particularly interesting because it has a transition at 1.5 mm that is directly compatible with telecommunication components in existing optical fiber networks. The aim of the project is to enhance the bandwidths of those atomic processors by introducing a chemical disorder in the single crystals doped with Er3+. This will lead to an inhomogeneous broadening of the optical transitions and could also reduce the optical homogeneous linewidths, and so, increase the processing bandwidth for radar signals. For that, a better understanding of the nature of the dynamical processes acting on the optical homogeneous linewidth is needed.