O objetivo desta dissertação é a utilização de metodologias de RMN para caracterizar a separação de fases e, em algum grau, a dinâmica de segmentos moleculares em copolímeros em bloco. Na primeira parte do trabalho, técnicas de RMN de Difusão de Spins, cujo fenômeno envolvido traz informações sobre a formação de domínios de segmentos moleculares, foram exploradas no sentido de avaliar seu desempenho assim como as principais dificuldades experimentais. Para isso, foi usado como referência o copolímero tri-bloco SEBS (Estireno-EtilenoButileno-Estireno), cuja morfologia é bem conhecida. Os testes experimentais foram realizados em equipamentos de RMN com campo magnético de 0.5 T e 9.4 T, sendo que em baixo campo uma proposta alternativa de tratamento dos dados foi utilizada. Como já apontado na literatura, os resultados indicaram que embora seja possível realizar tais experimentos em baixo campo a análise dos dados se torna mais complexa devido aos tempos de relaxação T1 mais curtos, tornando necessário o uso de simulações numéricas, que fazem a análise mais dependente de modelos específicos. A segunda parte do trabalho foi dedicada ao estudo de copolímeros em bloco compostos por polióxidoetileno (POE) ou Polietileno Glicol (PEG - POE de baixo peso molecular) e poliestireno (PS) e atambém copolimeros a base de PS e acrilatos ramificados com POE (PMAPEG - do inglês Poly Methyl Acrilate Polyethylene Glicol). Nesses estudos, técnicas de RMN de 1H e 13C como função da temperatura foram usadas para estudar as principais transições dinâmicas das cadeias de POE. Foi demonstrado que, embora o comportamento dinâmico das cadeias de POE seja similar em todos os copolímeros estudados, nas amostras de copolímeros com PMAPEG o grau de heterogeneidade dos movimentos das cadeias de POE é consideravelmente menor, o que foi atribuído ao empacotamento local semelhante e mais regular nos segmentos PMAPEG. Experimentos de RMN de Difusão de Spins foram utilizados nos estudos de morfologia, sendo demonstrada a separação de fases com formação de domínios em todas as amostras, com a regularidade desses domínios dependendo da composição. As dimensões médias dos domínios foram estimadas e os resultados correlacionados com os aspectos dinâmicos. / The main objective of this dissertation is the use of NMR methods to characterize the phase separation and, to some extent, the dynamics of the molecular segments in block copolymers. In the first part, NMR Spin Diffusion methods were explored in order to evaluate their performance as well as the main experimental difficulties. For that, a reference tri-block polymer SEBS (styrene-block-butadiene-block-styrene), which had a well known morphology, was used. The experimental tests were carried out in NMR equipments with magnetic field of 0.47 T and 9.4 T and at low filed an alternative proposal for data analysis was used. A already shown in the literature, the results indicated that , despite being possible to accomplish these experiments in low field, the data analysis become more intricate due to the shorter T1 values at this magnetic field, requiring the use of numerical simulations, which make the method more model dependent. The second part was dedicated to the study of copolymers consisting of Polyoxyethylene (PEO) or Polyethylene Glycol (PEG-low molecular weight PEO) and polystyrene (PS) as well as copolymers based on PS and Poly acrylates with PEO branches (PMAPEG -Poly Methyl Acrylate Polyethylene Glicol). In these studies, 1H and 13C NMR methods as function of temperature were used to characterize the main dynamic transitions in the PEO chains. It was shown that, despite similar dynamic behavior was observed in all samples, the PS-PMAPEG copolymers present a smaller degree of motional heterogeneity, which was attributed to the similar local packing of the PMAPEG chains. Using Spin diffusion NMR information about the morphology of the samples were obtained, showing evidences of phase separation and domain formation in all samples, being the regularity of the domain related with the sample composition. The average domain sizes were estimated.

Nesta tese desenvolvemos um método numérico para diagonalizar o Hamiltoniano de Heisenberg iterativamente. O método consiste basicamente em diagonalizar cadeias de spins, cada vez maiores, em que cada passo da diagonalização corresponde à adição de um novo spin à cadeia. A base de vetores para calcular o Hamiltoniano de uma cadeia de N spins, HN, é construída por meio do produto direto dos autovetores do Hamiltoniano Hn-1 da rede diagonalizada no passo anterior, pelos autoestados correspondentes ao N-ésimo spin adicionado. Além de usar a comutação do Hamiltoniano com a componente azimutal do spin total, Sz, prática comum em outros métodos, usufruímos da conservação com o quadrado do spin total, S2. Para uma classe específica de redes também implementamos a simetria de reflexão. Obtemos o espectro completo de energia de cadeias de spins 1/2 com até 20 sítios, para as quais mostramos resultados da dependência com a temperatura da susceptibilidade magnética e do calor específico, para redes com impurezas tipo spin substitucionais, com defeitos nas ligações ou com efeitos de bordas, isto é, para sistemas sem invariância translacional. Usualmente essa restrição impõe enormes dificuldades em métodos tradicionais. Para diagonalizar cadeias com um número maior de sítios, implementamos um procedimento que seleciona os estados de mais baixa energia para serem usados na base de vetores do passo seguinte. Com esse tipo de truncamento de estados, fomos capazes de obter o estado fundamental e alguns estados de baixa energia de cadeias com mais de uma centena de sítios, com precisão de até cinco algarismos significativos. Nossos resultados reproduzem os da literatura para os casos conhecidos, em geral sistemas homogêneos. As aproximações desenvolvidas recentemente no contexto da Teoria do Funcional da Densidade, aplicada ao modelo de Heisenberg, e que também se aplicam a sistemas inomogêneos, estão em conformidade com nossos resultados numericamente exatos. Generalizamos o método para diagonalizar escadas de spins 1/2. Calculamos o estado fundamental e o gap de energia desse sistema, onde variamos a razão entre os acoplamentos ao longo das pernas da escada e ao longo dos degraus da mesma; nossos resultados são comparados com os da literatura. Apresentamos também a implementação do método iterativo no modelo de Hubbard, que descreve um sistema de spins itinerantes. Sabe-se que no regime de alta repulsão Coulombiana entre os spins e densidade um (número de spins igual ao número de sítios da cadeia), esse modelo é mapeado no modelo de Heisenberg, resultado que é verificado numericamente em nosso procedimento por meio do cálculo de energias de ambos os modelos em um regime paramétrico apropriado. / In this Thesis we develop a numerical method to diagonalize the Heisenberg model iteratively. In essence, we diagonalize spin chains in steps, each one corresponding to an addition of a spin to a smaller chain. The basis vectors to calculate the Hamiltonian of a N-spin chain, HN, is built by means of the direct product of the eigenvectors of the (N-1)-spin Hamiltonian, diagonalized on the previous step, by the eigenstates of the N-th added spin. Besides the common use of the conservation of the z-component of the total spin, Sz, we also exploit the conservation of the squared total spin, S2. For a specific class of spin systems we also implemented the reflection symmetry. We obtain the entire energy spectrum of spin-1/2 chains up to 20 sites, for which we show the temperature dependence of the magnetic susceptibility and specific heat, for systems with substitutional impurity spins, bond defects, border effects, i.e., for systems without translational invariance. This normally imposes enormous restrictions in many traditional methods. In order to diagonalize chains with a larger number of sites we implemented a procedure that selects lower energy states to be used in the basis vector on the next step. Using this truncation scheme, we are able to obtain low-lying energy states for chains with more than a hundred sites, up to five significant figures of accuracy. Our results reproduce those of the literature for the known cases, in general homogeneous systems. The approaches recently developed in the context of Density Functional Theory to the Heisenberg model, which also apply to inhomogeneous systems, are consistent with our numerical results. We generalize the method to diagonalize spin-1/2 ladders. We calculate the ground-state and the energy gap of this system, for arbitrary ratio of the couplings along the lags or over the rungs of the ladder. We also present the implementation of our iterative method to the Hubbard model, which describes a system of itinerant spins. It is known that in the regime of high Coulomb repulsion between the spins and unitary density (number of spins equal to the number of sites in the chain), this model is mapped onto Heisenberg one, a result which is verified numerically in our procedure by calculating the energy spectrum of both models in na appropriated parametric regime.

Submitted by Danielle Karla Martins Silva (danielle.martins@ufpe.br) on 2015-03-06T13:36:10Z No. of bitstreams: 2 Dissertação_Pedro_Avelino.pdf: 1323463 bytes, checksum: e318ba395aedcf401b84f9051875d9eb (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Made available in DSpace on 2015-03-06T13:36:10Z (GMT). No. of bitstreams: 2 Dissertação_Pedro_Avelino.pdf: 1323463 bytes, checksum: e318ba395aedcf401b84f9051875d9eb (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2012 / O estudo das intera¸c˜oes entre os spins em materiais magn´eticos ´e um tema de grande importˆancia em mecˆanica estat´ıstica. A investiga¸c˜ao das grandezas termodinˆamicas e estat´ısticas de modelos de spins, tal como o modelo de Potts, ajudam a entender melhor a dinˆamica de sistemas complexos, possibilitando uma grande variedade de aplica¸c˜oes em diversas ´areas. No caso do modelo de Potts, por exemplo, suas aplica¸c˜oes v˜ao desde a teoria de grafos em F´ısica Matem´atica, simula¸c˜oes de forma¸c˜ao de guetos ´etnicos em Sociologia at´e estudos sobre padr˜ao de crescimento de c´elulas malignas e sua influˆencia no crescimento de tumores de cˆancer. Nesta disserta¸c˜ao, investiga-se a transi¸c˜ao de fase do modelo de Potts com q estados, definido em uma rede fractal e com intera¸c˜oes aleat´orias (positivas e negativas) entre spins primeiros vizinhos. Os valores dessas intera¸c˜oes s˜ao escolhidos randomicamente a partir de uma fun¸c˜ao de densidade de probabilidades e distribu´ıdas em uma rede hier´arquica da fam´ılia diamante com fator de escala 3. Considerou-se as seguintes fun¸c˜oes sim´etricas: gaussiana (normal), delta-bimodal, uniforme e exponencial. Essa fam´ılia de redes ´e constru ´ıda de uma maneira iterativa em um processo que lhe assegura a propriedade de invariˆancia de escala, possibilitando assim que a t´ecnica do grupo de renormaliza¸c˜ao no espa¸co real de Migdal-Kadanoff seja apropriada para estudar os fenˆomenos cr´ıticos do modelo em tais redes. As equa¸c˜oes de renormaliza¸c˜ao para os acoplamentos e para suas correspondentes transmissividades t´ermicas foram obtidas de forma anal´ıtica exata. Utilizando o m´etodo conhecido como m´etodo dos reservat´orios foi poss´ıvel analisar numericamente a evolu¸c˜ao das distribui¸c˜oes dos acoplamentos renormalizados e verificar a existˆencia de uma transi¸c˜ao da fase paramagn´etica de altas temperaturas para a fase condensada em baixas temperaturas, determinando-se os respectivos pontos cr´ıticos para os casos particulares com o n´umero de estados de Potts q = 3, 4, 5 e 6, em redes com dimens˜ao fractal Df = 4, 5 e 6. Para cada modelo espec´ıfico com n´umero de estados de Potts q = 3, 4, 5 e 6, foi tamb´em calculada a correspondente dimens˜ao cr´ıtica inferior, abaixo da qual a transi¸c˜ao de fase n˜ao ´e observada

Nous avons investigué les propriétés des champs de jauge de spin élevé libres à travers une étude de divers aspects de leur dynamique hamiltonienne. Pour des champs se propageant sur un espace-temps plat, les contraintes issues de l'analyse hamiltonienne de ces théories de jauge ont été identifiées et résolues par l'introduction de prépotentiels, dont l'invariance de jauge comprend, de façon intrigante, à la fois des difféomorphismes linéarisés généralisés et des transformations d'échelle de Weyl généralisées et linéarisées. Cela a motivé notre étude systématique des invariants conformes pour les spins élevés. Les invariants correspondants ont été construits à l'aide du tenseur de Cotton, dont nous avons établi les propriétés essentielles (symétrie, conservation, trace nulle; invariance, complétude). Avec ces outils géométriques, l'analyse hamiltonienne a pu être complétée et une action du premier ordre écrite en termes des prépotentiels. Nous avons constaté que cette action possédait une invariance manifeste par dualité électromagnétique; cette invariance, combinée à l'invariance de jauge des prépotentiels, fixe d'ailleurs uniquement l'action. En outre, de façon générale, cette action s'est révélée être exactement celle obtenue à travers une réécriture des équations du mouvement des spins élevés comme des conditions d'auto-dualité tordue (non manifestement covariantes).Avec un intérêt pour les extensions supersymétriques, nous avons amorcé la généralisation de cette étude aux champs fermioniques. Le champ de masse nulle libre de spin 5/2 a été soumis à la même analyse, et son prépotentiel s'est révélé partager l'invariance de jauge conforme déjà observée dans le cas bosonique général. Le supermultiplet incorporant les spins 2 et 5/2 a ensuite été considéré, et une symétrie rigide de son action, combinant une transformation de dualité électromagnétique du spin 2 avec une transformation de chiralité du spin 5/2 a été construite pour commuter avec la supersymétrie. Dans une autre direction, nous avons étudié les propriétés d'un champ tensoriel chiral de symétrie mixte dans un espace-temps plat à six dimensions: une (2,2)-forme. Son analyse hamiltonienne a été réalisée, des prépotentiels introduits et l'action de premier ordre obtenue s'est encore une fois révélée être la même que celle obtenue à travers une réécriture des équations du mouvement comme des conditions d'auto-chiralité (non manifestement covariante).Finalement, nous nous sommes penchés sur les charges de surface des champs fermioniques et bosoniques de spin élevé se propageant sur un espace-temps à courbure constante. Cela a été réalisé par une analyse hamiltonienne de ces systèmes, les contraintes étant identifiées aux générateurs des transformations de jauge. Injectant dans ces générateurs des valeurs des paramètres des transformations de jauge correspondant à des transformations impropres de jauge (imposant une réelle variation physique sur les champs) a ensuite permis d'évaluer la valeur de ces générateurs pour des champs résolvant les équations du mouvement: elle s'est bien révélée finie et non-nulle, constituant les charges de surface de ces théories. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Le mode d’excitation collective exotique appelé chiralité a été étudié et des isomères de longue durée de vie ont été recherchés dans les noyaux ¹³⁶Nd et ¹³⁵Nd. Cinq paires de bandes Δ I=1 presque dégénérées et de même parité ont été identifiées à des spins élevés dans ¹³⁶Nd Les bandes observées ont été étudiées en utilisant la théorie de la fonctionnelle de densité covariante contrainte et rotation autour d'une axe incliné, et par un nouveau modèle de rotor plus particules développé pour décrire le couplage de particules dans quatre couches j à un rotor triaxial. Les propriétés de ces bandes doublet sont en bon accord avec les résultats des calculs théoriques. Par conséquent, l'existence de bandes chirales multiples (MχD) dans le noyau ¹³⁶Nd a été établie. Il s'agit de la première preuve expérimentale de l'existence de bandes chirales dans des noyaux pairs. Les cinq paires de bandes chirales constituent le plus grand ensablé de bandes chirales observé jusqu'à présent dans un seul noyau. De plus, le schéma de niveaux de ¹³⁶Nd a été considérablement étendu aux spins bas, moyens et très élevés. Les configurations possibles de toutes les bandes rotationnelles ont été attribuées á l'aide du modèle Nilsson-Strutinsky en rotation. La structure de ¹³⁶Nd a été clarifiée et les divers types d'excitations uni-particule et collectives ont été bien compris. Une nouvelle paire de bandes chirales á parité positive a été identifiée dans. Les caractéristiques des bandes soutiennent leur interprétation en termes de bandes chirales. Des bandes chirales à parité négative ayant été identifiées précédemment, la présence de multiple bandes chirales dans ¹³⁵Nd est ainsi établie. Les bandes chirales observées ont été étudiées en utilisant la théorie avec fonctionnelle de densité covariante contrainte et avec le modèle rotor plus particules; elles reproduisent fidèlement les données expérimentales, confirmant ainsi le phénomène MχD dans ce noyau. Les bandes chirales nouvellement observées dans ¹³⁵Nd représentent une étape importante dans la confirmation de l'existence du phénomène MχD dans les noyaux. La recherche d'états isométriques à longue durée de vie dans ¹³⁵Nd et ¹³⁶Nd a été aussi effectuée, mais n'a pas permis d'identifier de nouveaux isomères. Cependant, nous avons pu confirmer la présence des isomères déjà identifiés dans les noyaux ¹³⁸Nd, ¹³⁴Ce, ¹³⁶Pr, et ¹³⁷Pr dans nos données. / The exotic collective excitation mode called chirality has been investigated and long-lived isomers have been searched for in the ¹³⁶Nd and ¹³⁵Nd nuclei. Five pairs of nearly degenerate Δ I=1 bands with the same parity have been identified at high spins in ¹³⁶Nd. The observed bands were investigated by the constrained and tilted axis cranking covariant density functional theory and a new developed four single-j shells particle-rotor model. It was found that the properties of these doublet bands are in good agreement with results of the model calculations. Therefore, the multiple chiral doublets (MχD) phenomenon in the nucleus ¹³⁶Nd was confirmed. This was the first experimental evidence for the MχD bands in even-even nuclei. The five pairs of chiral doublet bands is the largest observed in a single nucleus until now. In addition, the level scheme of the ¹³⁶Nd has been extended significantly at low, medium, and very high spins. Possible configurations of all rotational bands have been assigned by using the cranked Nilsson-Strutinsky model. The band structure of ¹³⁶Nd was clarified and the various types of single-particle and collective excitations were well understood. A new pair of positive-parity chiral doublet bands has been identified in ¹³⁵Nd. The characteristics of the doublet bands support the chiral interpretation. Together with the previously reported negative-parity chiral doublet bands show the presence of MχD bands in ¹³⁵Nd. The observed doublet bands were compared with constrained covariant density functional theory and particle-rotor model calculations which nicely reproduce the experimental data, confirming the MχD phenomenon in this nucleus. The newly observed MχD bands in ¹³⁵Nd represent an important milestone in supporting the existence of MχD in nuclei. The search for long-lived isomeric states in ¹³⁵Nd and ¹³⁶Nd has also been performed. This did not lead to the identification of new isomers, but we could confirm the existence of the previously reported isomers in the nuclei ¹³⁸Nd, ¹³⁴Ce, ¹³⁶Pr, and ¹³⁷Pr in our data.

L’étude de l’état fondamental liquide de spins est un des domaines très actif de la recherche en matière condensée. Le réseau le plus à même de stabiliser un tel état fondamental semble être, à deux dimensions, le réseau kagomé de spins antiferromagnétiques 1/2. Il y a à présent un consensus théorique sur le fait que ce modèle stabilise un état fondamental liquide de spin. Cependant, la nature de cet état est encore inconnue, notamment la nature des corrélations. Nous ne savons toujours pas si ces dernières sont à courte portée avec un gap dans le spectre d’excitations, ou si elles sont à plus longue portée avec un spectre d’excitations sans gap. D’un point de vue expérimental il n’existe que très peu de matériaux et seul l’Herbertsmithite présente un réseau kagomé de spins 1/2 géométriquement parfait. Les différentes études réalisées sur ce composé pointent toutes vers un état liquide de spin sans gap mais révèlent aussi des déviations à l’hamiltonien de Heisenberg qui pourraient être responsables de la fermeture de ce gap.Cette thèse traite de l’étude expérimentale principalement par RMN et µSR de nouveaux composés kagomé à base de vanadium faisant partie d’une famille récemment synthétisée, les vanadates fluorés à géométrie kagomé. Le matériau que nous avons le plus étudié est un composé à réseau kagomé de spins 1/2 à base de V4+, (NH4)2[C7H14N][V7O6F18] (DQVOF). Le modèle magnétique de ce composé peut être décomposé en deux sous systèmes presque indépendants, des plans kagomé trimérisés isolés et des ions V3+ quasi paramagnétiques. Les études de µSR démontrent une absence de gel magnétique jusqu’à 20 mK donc un état liquide de spins dans DQVOF. Les études de chaleur spécifique et de RMN dévoilent un comportement liquide de spin sans gap malgré la trimérisation du réseau et la faible valeur supposée de l’interaction Dzyaloshinskii Moriya. Nos résultats montrent finalement que l’absence de gap, intrinsèque ou due à des déviations à l’hamiltonien idéal, est une caractéristique robuste des matériaux kagomé. Nous avons de plus étudié un second matériau de cette famille, (NH4)2[C2H8N][V3F12] (DDVF), dont le réseau magnétique est formé par des plans kagomé découplés entre eux à base de V3+ (S = 1). Ce réseau présente de fortes distorsions par rapport au réseau idéal et les expériences thermodynamiques et de µSR mettent en évidence une transition magnétique vers un état gelé à 10 K avec une mise en ordre à longue distance qui s’effectue à 6 K uniquement. / The search for quantum liquid state is a very active field in condensed matter research. In two dimensions, the antiferromagnetic spin 1/2 kagome lattice seems to be the most able to stabilize such a ground state. Indeed, from recent theoretical investigations, we are now quite sure that this model has a quantum spin liquid ground state. However, we still do not know its nature, in particular the nature of its correlations. They could be short ranged with a gap in the excitation spectrum, or long ranged with a gapless excitation spectrum. On the experimental side, only few materials exist and only one possesses a geometrically perfect lattice, the Herbertsmithite. All the experiments that have been done on this compound reveal a gapless spin liquid state along with deviations to the spin 1/2 Heisenberg hamiltonian which could be responsible of the gap closure.This thesis deals with the experimental study, mainly by NMR and µSR, of new vanadium based kagomé compounds which are part of a newly synthesized family, the kagome fluoride vanadates. The material that we studied the most is a spin 1/2 kagomé compound based on V4+, (NH4)2[C7H14N][V7O6F18] (DQVOF). The magnetic model of this compound can be decomposed in two rather independent parts, trimerized kagome planes and quasi paramagnetic V3+ ions. The µSR studies, showing the absence of frozen moment down to 20 mK, reveal a spin liquid ground state in DQVOF. The heat capacity and the NMR experiments point out a gapless behavior despite trimerization and likely weak Dzyaloshinskii Moriya interactions. Our results demonstrate that the gapless ground state, whether intrinsic or due to deviation to the ideal hamiltonian, is a rather robust characteristic of kagome materials.Furthermore, we studied another compound of this family, (NH4)2[C2H8N][V3F12] (DDVF), which magnetic lattice is made of uncoupled kagomé planes based on V3+ (S = 1). The lattice shows large deviations to the ideal kagomé and the thermodynamic experiments and the µSR studies reveal a magnetic transition to a frozen state at 10 K with a long distance order which is effective only below 6 K.

In this thesis we study various aspects of integrable methods in AdS3/CFT2 holog- raphy. These techniques come from exploiting special form of gauge compatible with asymptotic boundary conditions on the bulk fields in Chern Simons formulation of 3d gravity and higher spin theories. The integrable systems emerging are so called Toda field theories. The rigid structure of these theories allows us to learn more about certain gravitational solutions - multi centered solutions. One of the most interesting applications of the formalism developed is in the problem of black hole deconstruction and information paradox where we can read of the information about the temperature from the Toda field theory charges and. Aside of the gravitational applications we also study a vast generalization of the WZW to Toda field theory reduction and its connection to the Closed Toda systems. 1

Quantum communication protocols require maximally entangled state of pair of qubits (spin-1/2 states in this context) to be shared between sender and the receiver. The entangled qubits lose entanglement because of random magnetic field disturbances. The dynamics in the form of joint density matrix of random pure entangled state provide the steady (joint) state and the associated timescales (time taken by the pair to reach the steady state) providing a scope in future to quantify the effective utilization of quantum communication protocols. / The dynamics of an identical pair of entangled spin-1/2 particles, both subjected to the identical, independent, correlated random magnetic fields is studied. The dynamics of the pure joint state of the pair is derived using stochastic calculus. In case of identical fields, an ensemble of such pure states are combined using the modified spin joint density matrix and the joint relaxation time is obtained for the pair of spin-1/2 particles. These dynamics can be interpreted as special kind of correlations involving the spatial components of the Bloch polarization vectors of the constituent entangled spin-1/2 particles. In case of independent random magnetic fields, the dynamics are obtained by considering a pure joint state of entangled spin-1/2 particles. The disentanglement time defined as the time taken for the particles to become disentangled, is obtained. In case of correlated random magnetic fields, the dynamics of a maximally entangled pair of spin-1/2 particles are derived in terms of the joint density matrix of the entangled pair from which the steady state density matrix and the associated timescale for it to be reached are obtained. The asymptotic density matrix in this case represents a state of (partial) disentanglement. In other words, there is a persistent entanglement in case of correlated field disturbances. / Thesis / Doctor of Philosophy (PhD) / Maximally entangled pair of quantum bits (in the form of spin-1/2 states) lose entanglement either partially or completely depending upon the nature of random magnetic field disturbances around them (correlated/independent/identical fields). The dynamics of entangled states (in the form of density matrix of a random pure state) in the presence of random magnetic fields are obtained using the ideas of stochastic calculus to understand the steady state of the pair and the associated timescales to be reached.

Quantum networks play an indispensable role in quantum information tasks such as secure communications, enhanced quantum sensing, and distributed computing. In recent years several platforms are being developed for such tasks, witnessing breakthrough technological advancement in terms of fabrication techniques, precise control methods, and information transfer. Among the most mature and promising platforms are color centers in solids. These systems provide an optically active electronic spin and long-lived nuclear spins for information storage. The first part of this dissertation is concerned with error mechanisms in the control of electronic and nuclear spins. First, I will focus on control protocols for improved electron-spin rotations tailored to specific color centers in diamond. I will then discuss how to manipulate the entanglement between the electron and the always-coupled nuclear spin register. I will describe a general formalism to quantify and control the generation of en- tanglement in an arbitrarily large nuclear spin register. This formalism incorporates exactly the dynamics with unwanted nuclei, and quantifies the performance of entangling gates in the presence of unwanted residual entanglement links. Using experimental parameters from a well-characterized multinuclear spin register, I will show that preparation of multipartite entanglement in a single-shot is possible, which drastically reduces the total gate time of conventional protocols. Then, I will present a new formalism for describing all-way entanglement and show how to design gates that prepare GHZM states. I will show how to incorporate errors such as unwanted correlations, electronic dephasing errors or pulse control errors. The second part of this thesis focuses on the preparation of all-photonic graph states from a few quantum emitters. I will introduce heuristic algorithms that exploit graph theory concepts in order to reduce the entangling gate counts, and also discuss the role of locally equivalent graphs in the optimization of the generation circuits. / Doctor of Philosophy / Quantum information science emerged by combining ideas and principles of information theory, nanoscale engineering, photonics, atomic and solid-state physics in a unified effort to realize and fabricate efficient quantum-based architectures. Spin-based solid-state quantum computers are one of the leading candidates for quantum architectures. For these types of devices, the quantum bit of information can be encoded in the spin states of electron/nuclear memories, while the logical operations are performed by driving transitions between a multi- level spin structure. In this thesis, I will describe the role of color centers for quantum computations and networking. I will explain the error sources and dynamics of SiV− and SnV− color centers in diamond and show how to drive with high fidelity optical rotations of their spin states. Additionally, I will explain how periodic driving of the electronic spin can serve as a method to control the nuclear spin memories and show how to precisely prepare multipartite entangled states within an arbitrarily large electron-nuclear spin register. Lastly, I will focus on the preparation of all-photonic graph states and show how to prepare them with optimal resources.

L’imagerie par résonance magnétique (IRM) est un outil important pour l’investigation qualitative et quantitative de la physiologie du cerveau. L’investigation de l’activité neuronale à l’aide de cette modalité est possible grâce à la détection de changements hémodynamiques qui surviennent de manière concomitante aux activités de signalisation des neurones, tels l’augmentation régionale du débit sanguin cérébral (CBF) ou encore la variation de la concentration de désoxyhémoglobine dans les vaisseaux veineux. Pour étudier la formation de contrastes fonctionnels qui découlent de ces phénomènes, deux séquences de pulses ont été développées en vue d’expériences en IRM fonctionnelle (IRMf) visant l’imagerie du signal oxygéno-dépendant BOLD ainsi que de la perfusion. Le premier objectif de cette thèse fut le développement d’une séquence de type écho-planar (EPI) permettant l’acquisition entrelacée d’images en mode échos de gradient (GRE-EPI) ainsi qu’en mode échos de spins (SE-EPI) pour l’évaluation de la performance de ces deux méthodes d’imagerie au cours d’une expérience en IRMf BOLD impliquant l’utilisation d’un stimulus visuel chez 4 sujets adultes sains. Le deuxième objectif principal de cette thèse fut le développement d’une séquence de marquage de spins artériels employant un module de marquage fonctionnant en mode pseudo-continu (pCASL) pour la quantification du CBF au repos. Cette séquence fut testée chez 3 sujets adultes en bonne santé et sa performance fut comparée à celle d’une séquence similaire développée par un groupe de recherche extérieur. Les résultats de l’expérience portant sur le contraste BOLD indiquent une supériorité de la performance du mode GRE-EPI vis-à-vis celle du mode SE-EPI en termes des valeurs moyennes du pourcentage de l’ampleur d’effet et du score t associés à l’activité neuronale en réponse au stimulus. L’expérience visant la quantification du CBF démontra la capacité de la séquence pCASL développée au cours de ce projet de calculer des valeurs de la perfusion de la matière grise ainsi que du cerveau entier se retrouvant dans une plage de valeurs qui sont physiologiquement acceptables, mais qui demeurent inférieures à celles obtenues par la séquence pCASL développée par le groupe de recherche extérieur. Des expériences futures seront effectuées pour optimiser le fonctionnement des séquences présentées dans ce mémoire en plus de quantifier l’efficacité d’inversion de la séquence pCASL. / Magnetic resonance imaging (MRI) is an important tool for the qualitative and quantitative investigation of brain physiology. The investigation of neuronal activation using this modality is made possible by the detection of concomitantly-arising hemodynamic changes in the brain’s vasculature, such as localized increases of the cerebral blood flow (CBF) or the variation of the concentration of paramagnetic deoxyhemoglobin in venous vessels. To study the formation of functional contrasts that stem from these changes in MRI, two pulse sequences were developed in this thesis to carry out experiments in blood oxygenation level dependent (BOLD) and perfusion functional MRI (fMRI). The first objective laid out in this work was the development of an echo planar imaging (EPI) sequence permitting the interleaved acquisition of images using gradient-echo EPI and spin-echo EPI to assess the performances of these imaging techniques in a BOLD fMRI experiment involving a visual stimulation paradigm in 4 healthy adult subjects. The second main objective of this thesis was the development of a pseudo-continuous arterial spin labelling (pCASL) sequence for the quantification of cerebral blood flow (CBF) at rest. This sequence was tested on 3 healthy adult subjects and compared to an externally-developed pCASL sequence to assess its performance. The results of the BOLD fMRI experiment indicated that the performance of GRE-EPI was superior to that of SE-EPI in terms of the average percent effect size and t-score associated with stimulus-driven neuronal activation. The CBF quantification experiment demonstrated the ability of the in-house pCASL sequence to compute values of CBF that are within a range of physiologically-acceptable values while remaining inferior to those computed using the externally-developed pCASL sequence. Future experiments will focus on the optimization of the sequences presented in this thesis as well as on the quantification of the pCASL sequence’s labelling efficiency.