京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19479号 / 理博第4139号 / 新制||理||1595(附属図書館) / 32515 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 戸塚 圭介, 教授 川上 則雄, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The quantum mechanical phenomenon of entanglement plays a key role in areas such as quantum computing and quantum information. Entangled half spin particles, often called qubits, are used to realize quantum based logic which means that studying systems of qubits and their properties is of vital importance to the development of the fields. In this paper we simulate the time evolution of a three-qubit system for varying Hamiltonians and initial states. We look at the revival structure of the classically treated survival probability and compare its structure to that of the quantum mechanical concept of residual entanglement, which is a measure of the system's total entanglement. We do this for three different types of initial states: Uniform, GHZ and W, as well as varying the contributions of certain types of spin-spin interaction models in the Hamiltonian. The spin-spin interaction models that are examined are the DM model and the Heisenberg model. Further we also examine the effect of an added magnetic field in the zdirection, in the form of a Zeeman term. In general, the Zeeman term only affects the behavior of the survival probability, unless the DM term is rotated to not be in a parallel direction, the Heisenberg term generally affects the survival probability and the residual entanglement in the same way. We also note that for the Uniform initial state a dominant Heisenberg seems to remove some of the rapid oscillations in the residual entanglement and survival probability that naturally occur in the DM model, the Zeeman term then reintroduces these high frequencies in the survival probability while not affecting the residual entanglement. For some Hamiltonians we do not see any connection between the revival structure of the survival probability and the residual entanglement, while for some there is a clear connection.

No / A finite quantum system in which the position and momentum take values in the Galois field GF(p¿l) is constructed from a smaller quantum system in which the position and momentum take values in Zp , using field extension. The Galois trace is used in the definition of the Fourier transform. The Heisenberg¿Weyl group of displacements and the Sp(2, GF(p¿l)) group of symplectic transformations are studied. A class of transformations inspired by the Frobenius maps in Galois fields is introduced. The relationship of this 'Galois quantum system' with its subsystems in which the position and momentum take values in subfields of GF(p¿l) is discussed.

We define the affinization of an arbitrary monoidal category C, corresponding to the category of C-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to C. The affinization formalizes and unifies many constructions appearing in the literature. In particular, we describe a large number of examples coming from Hecke-type algebras, braids, tangles, and knot invariants. When C is rigid, its affinization is isomorphic to its horizontal trace, although the two definitions look quite different. In general, the affinization and the horizontal trace are not isomorphic. We then use the affinization to show our main result, which is an explicit isomorphism between the central charge k reduction of the universal central extension of the elliptic Hall algebra and the trace, or zeroth Hochschild homology, of the quantum Heisenberg category of central charge k. We use this isomorphism to construct large families of representations of the universal extension of the elliptic Hall algebra.

Este trabalho apresenta uma contribuição ao estudo das flutuações quânticas dos feixes sonda e de bombeio na condição de transparência induzida por laser. Com esse estudo conseguimos observar nas flutuações dos campos uma manifestação do caráter coerente da interação dos átomos com os feixes. Para alcançar nosso objetivo, derivamos a teoria do fenômeno da transparência induzida tratando ambos feixes dentro do formalismo quântico. Com tal formulação, encontramos que a condição de transparência induzida corresponde a um estado de equilíbrio dinâmico do sistema átomo - campo de bombeio - campo sonda onde, os átomos redistribuem os fótons entre os campos, correlacionando os mesmos e alterando, ao mesmo tempo, as propriedades estatísticas desses feixes. Utilizando dois critérios diferentes, mostrando que a correlação entre os feixes sonda e de bombeio é de natureza quântica, o que possibilita a aplicação desse sistema, por exemplo, na informação e computação quânticas. Os resultados experimentais obtidos confirmaram as previsões teóricas em relação às flutuações quânticas dos campos, e a existência de uma correlação entre eles. Trata-se da primeira investigação experimental de propriedades estatísticas dos campos em transparência induzida. A correlação de intensidade medida é o primeiro passo para a observação de emaranhamento entre feixes sonda e de bombeio na condiçào de transparência induzida. / In this work we presente a contribution to the study of quantum fluctuations of pump and probe filds in the Electromagnetically Induced Transparency (EIT) condition. We observed in the fields fluctuations evidence of the coherent character of the interaction between the atoms and the fields. To reach our purpose, the fields were treated quantum-mechanically in deriving the theory of the EIT phenomenon. Using this formulation, we concluded that the EIT condition corresponds to a state of dynamical equilibrium of the system atom pump field probe field, where the atoms redistribute the photons between both fields, correlating them and, at the same time, affecting their statistical properties. By means of two different criteria we showed that such a correlation is of quantum nature, making possible the application of this system in, for example, quantum information and quantum computation. The theoretical predictions were corroborated by our experimental results regarding the quantum fluctuations and the existence of a correlation between the pump and probe fields. This is the first experiment to investigate statistical properties of the fields in EIT. The intensity correlation measured is the first step towards the observation of entanglement between the fields.

Les propriétés magnétiques des matériaux sont fortement connectées à leur structure cristallographique. Nous proposons un modèle atomique de la dynamique d'aimantation capable de rendre compte de cette magnétoélasticité. Bien que ce travail s'inscrive dans une thématique générale de l'étude des matériaux magnétiques en température, nous la particularisons à un seul élément, le Cobalt. Dans ce modèle effectif, les atomes sont décrits par 3 vecteurs classiques qui sont position, impulsion et spin. Ils interagissent entre eux via un potentiel magnéto-mécanique ad hoc. On s'intéresse tout d'abord à la dynamique de spin atomique. Cette méthode permet d'aborder simplement l'écriture des équations d'évolution d'un système atomique de spins dans lequel la position et l'impulsion des atomes sont gelées. Il est toutefois possible de définir une température de spin permettant de développer naturellement une connexion avec un bain thermique. Montrant les limites d'une approche stochastique, nous développons une nouvelle formulation déterministe du contrôle de la température d'un système à spins.Dans un second temps, nous développons et analysons les intégrateurs géométriques nécessaires au couplage temporel de la dynamique moléculaire avec cette dynamique de spin atomique. La liaison des spins avec le réseau est assurée par un potentiel magnétique dépendant des positions des atomes. La nouveauté de ce potentiel réside dans la manière de paramétrer l'anisotropie magnétique qui est la manifestation d'un couplage spin-orbite. L'écriture d'un modèle de paires étendu de l'anisotropie permet de restituer les constantes de magnétostriction expérimentales du hcp-Co. En considérant un système canonique, où pression et température sont contrôlées, nous avons mis en évidence la transition de retournement de spin si particulière au Co vers 695K.Nous finissons par l'étude des retournements d'aimantation super-paramagnétiques de nanoplots de Co permettant de comparer ce couplage spin-réseau aux mesures récentes. / The magnetic properties of materials are strongly connected to their crystallographic structure. An atomistic model of the magnetization dynamics is developed which takes into account magneto-elasticity. Although this study is valid for all magnetic materials under temperatures, this study focuses only on Cobalt. In our effective model, atoms are described by three classical vectors as position, momentum and spin, which interact via an ad hoc magneto-mechanical potential.The atomistic spin dynamics is first considered. This method allows us to write the evolution equations of an atomic system of spins in which positions and impulsions are first frozen. However, a spin temperature is introduced to develop a natural connection with a thermal bath. Showing the limits of the stochastic approach, a genuine deterministic approach is followed to control the canonical temperature in this spin system.In a second step, several geometrical integrators are developed and analyzed to couple together both the molecular dynamics and atomic spin dynamics schemes. The connection between the spins and the lattice is provided by the atomic positions dependence of the magnetic potential. The novelty of this potential lies in the parameterization of the magnetic anisotropy which originates in the spin-orbit coupling. Using a dedicated pair model of anisotropy, the magnetostrictive constants of hcp-Co are restored. In a canonical system where pressure and temperature are controlled simultaneously, the transition of rotational magnetization of Co is found.Finally the magnetization reversals of super-paramagnetic Co nanodots is studied to quantify the impact of spin-lattice coupling respectively to recent measurements.

Made available in DSpace on 2016-06-02T20:15:29Z (GMT). No. of bitstreams: 1 5202.pdf: 3904832 bytes, checksum: c623a581c3cdb03d9cc81fc16ecef935 (MD5) Previous issue date: 2013-04-08 / Universidade Federal de Minas Gerais / This thesis presents a study of the magnetization plateau and the phenomenon of geometrical frustration in spin systems applied to lattices with triangular structure, as well as the results achieved by applying the differential operator technique of the Ising and Heisenberg models with external magnetic field applied to the easy magnetization axis z, their phase diagrams, behavior plateaus observed and analyzed according to the Haldane conjecture and appearance of plateaus presented by Oshikawa, Yamanaka and Affleck, and also to study the behavior of the magnetic susceptibility in order to verify the behavior of frustrated systems using the frustration factor f= θWC/TN to verify frustration encountered at various stages of the study models / Este trabalho apresenta um estudo da magnetização de platô e do fenômeno de frustração geométrica em sistemas de spins, aplicados às redes com estrutura triangular, bem como os resultados alcançados aplicando-se a técnica do operador diferencial a modelos de Ising e Heisenberg com campo magnético externo aplicado sobre o eixo fácil de magnetização z, seus diagramas de fases e comportamento de platôs observados e analisados segundo a conjectura de Haldane e a condição de aparecimento de platôs apresentada por Oshikawa, Yamanaka e Affleck, e ainda, o estudo do comportamento da susceptibilidade magnética com o objetivo de verificar o comportamento dos sistemas frustrados utilizando-se o fator de frustração f= θWC/TN para verificar a frustração nas diversas fases encontradas ao longo do estudo dos modelos.

Made available in DSpace on 2015-05-15T11:45:59Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 323962 bytes, checksum: b1f72af0670744659eabe72c7c444dc3 (MD5) Previous issue date: 2008-08-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The Weierstrass representation of minimal surfaces in R3 and its generalization to Rn shows is a very useful tool in the study of minimal surfaces in these spaces. In this work we want to describe a type Weierstrass representation for immersions simply connected in the group of Heisenberg H3. Using applications harmonics is possible obtain a formula for general representation, type Weierstrass for minimal immersions in manifolds Riemannian simply connected general, is that, useful of point view theoretical, however it is very difficult find solutions explicit. The dimention 3 and the structure of group Lie of the group of Heisenberg H3 allow a description Geometric simple and we can get some classic examples. / A representação deWeierstrass para superfícies mínimas em R3 e sua generalização a Rn mostra-se uma ferramenta muito útil no estudo de superfícies mínimas nestes espaços. Neste trabalho pretendemos descrever uma representação tipo Weierstrass para imersões simplesmente conexas no grupo de Heisenberg H3. Usando aplicações harmónicas é possível obter uma fórmula de representação geral, tipo Weierstrass, para imersões mínimas simplesmente conexas em variedades Riemannianas gerais, isto é útil do ponto de vista teórico, entretanto é muito difícil encontrar soluções explicitas. A dimensão 3 e a estrutura de grupo de Lie do grupo de Heisenberg H3 permitem uma descrição geométrica simples e podemos obter alguns exemplos clássicos.

Este trabalho apresenta uma contribuição ao estudo das flutuações quânticas dos feixes sonda e de bombeio na condição de transparência induzida por laser. Com esse estudo conseguimos observar nas flutuações dos campos uma manifestação do caráter coerente da interação dos átomos com os feixes. Para alcançar nosso objetivo, derivamos a teoria do fenômeno da transparência induzida tratando ambos feixes dentro do formalismo quântico. Com tal formulação, encontramos que a condição de transparência induzida corresponde a um estado de equilíbrio dinâmico do sistema átomo - campo de bombeio - campo sonda onde, os átomos redistribuem os fótons entre os campos, correlacionando os mesmos e alterando, ao mesmo tempo, as propriedades estatísticas desses feixes. Utilizando dois critérios diferentes, mostrando que a correlação entre os feixes sonda e de bombeio é de natureza quântica, o que possibilita a aplicação desse sistema, por exemplo, na informação e computação quânticas. Os resultados experimentais obtidos confirmaram as previsões teóricas em relação às flutuações quânticas dos campos, e a existência de uma correlação entre eles. Trata-se da primeira investigação experimental de propriedades estatísticas dos campos em transparência induzida. A correlação de intensidade medida é o primeiro passo para a observação de emaranhamento entre feixes sonda e de bombeio na condiçào de transparência induzida. / In this work we presente a contribution to the study of quantum fluctuations of pump and probe filds in the Electromagnetically Induced Transparency (EIT) condition. We observed in the fields fluctuations evidence of the coherent character of the interaction between the atoms and the fields. To reach our purpose, the fields were treated quantum-mechanically in deriving the theory of the EIT phenomenon. Using this formulation, we concluded that the EIT condition corresponds to a state of dynamical equilibrium of the system atom pump field probe field, where the atoms redistribute the photons between both fields, correlating them and, at the same time, affecting their statistical properties. By means of two different criteria we showed that such a correlation is of quantum nature, making possible the application of this system in, for example, quantum information and quantum computation. The theoretical predictions were corroborated by our experimental results regarding the quantum fluctuations and the existence of a correlation between the pump and probe fields. This is the first experiment to investigate statistical properties of the fields in EIT. The intensity correlation measured is the first step towards the observation of entanglement between the fields.

Nesta tese estudamos as propriedades críticas dos modelos anisotrópicos (isotrópicos) de Heisenberg com spin s arbitrário. O espectro das Hamiltonianas, com condições periódicas de contorno, foi calculado para redes finitas, resolvendo-se as equações do Bethe ansatz associadas. Nossos resultados indicam que a anomalia conforme destes modelos tem o valor c=3s/(1+s), independente da anisotropia, e os expoentes críticos variam continuamente com a anisotropia assim como no modelo de 8-vértices. O conteúdo de operadores destes modelos indica que a teoria de campos que governa a criticalidade destes modelos de spin é descrita por operadores formados pelo produto de um operador Gaussiano por outro com simetria Z(2s). Estudando estes modelos, com certas condições especiais de contorno, mostramos que eles são relacionados com uma nova classe de teorias unitárias recentemente propostas / This thesis is concerned with the critical properties of anisotropic (isotropic) Heisenberg chain,with arbitrary spin-s. The eigenspectrum of these Hamiltoniana, with periodic boundaries, are calculated for finite chains by solving numerically their associated Bethe ansatz equations. The results indicate that the conformal anomaly hás the value c=3s/1+s, independently of the anisotropy, and the exponentes vary continuously with the anisotropy like in the 8-vertex model. The operator content of these models indicate that the underlying field theory governing these critical spin-s models are described by composite fields formed by the product of Gaussian and Z(2s) fields. Studying these models, with some special boundary conditions, we show that they are related with a large class of unitary conformal field theories recntly introduced