Les systèmes quantiques ouverts décrivent l'évolution d'un système de référence S en interaction avec un ou plusieurs autres systèmes appelés environnements. Pour les étudier on rencontre deux approches dans la littérature: l'approche hamiltonienne, où on décrit complètement les systèmes et leurs interactions, et l'approche markovienne, où on abandonne l'idée de décrire l'environnement et on considère une dynamique, dite effective, du système S seul mais prenant en compte les effets de l'interaction avec l'environnement.Nous nous intéresserons dans cette thèse à une classe particulière de tels systèmes: les système quantiques avec interactions répétées. Le système S interagit successivement avec une suite de sous-systèmes indépendants. L'approche de ces systèmes est à la fois hamiltonienne et markovienne. Leur étude joue un rôle fondamental dans la compréhension pratique et théorique des processus d'interaction matière-lumière ainsi qu'en optique quantique (expérience du maser à un atome).Cette thèse porte sur l'étude d'un système de type maser à un atome. Le modèle considéré décrit un champ électromagnétique dans une cavité et traversé par un faisceau d'atomes mais auquel on ajoute un réservoir supplémentaire interagissant de façon continue avec le champ électromagnétique. L'idée est que la cavité n'est pas parfaitement isolée et le réservoir permet de modéliser les fuites dans la cavité. Ainsi l'interaction entre le champ électromagnétique et les atomes est décrit par un système quantique avec interactions répétées et l'interaction entre le champ électromagnétique et le réservoir est décrit par une approche hamiltonienne des systèmes quantiques ouverts.Le système "cavité+réservoir" à été étudié par Könenberg en se basant sur des travaux de Arai. Via une diagonalisation du Hamiltonien du système couplé il montre des propriétés de retour à l'équilibre. Dans une première partie nous donnerons une nouvelle approche de ces travaux en utilisant des résultats récents de Nam, Napiórkowki et Solovej sur la diagonalisation des hamiltoniens bosoniques quadratiques.Dans un premier temps, nous étudierons l'auto-adjonction des Hamiltoniens du système et on s'intéressera notamment à la diagonalisation de l'un d'eux. Dans un second temps, nous étudierons le comportement en temps long du système, nous obtenons entre-autres des formules explicites pour l'évolution à un temps donné des observables de Weyl. Ces résultats nous permettent d'étudier la variation d'énergie totale ainsi que les échanges d'énergies dans le système. Enfin on terminera en étudiant la production d'entropie dans le système que l'on reliera aux formules de variation d'énergie. Pour cela on généralisera au préalable la formule dite de production d'entropie de Jaksic et Pillet. / Open quantum systems describe the evolution of a system S in interaction with one or more other systems called environments. Two approaches in the literature to study such systems: the hamiltonian approach in which the entire system is considered, and the markovian approach in which one gives up the idea of describing the environment and only considers a so called effective dynamics of the system S which takes into account the effect of the environment.A particular class of such systems will interest us: the quantum systems with repeated interactions. The system S interacts successively with a series of independent subsystems. The approach of these systems is both Hamiltonian and Markovian. Their study plays a fundamental role in the understanding of light-matter interactions as well as in quantum optics (like one-atom maser experiment).In this thesis we study a repeated interaction system of the one-atom maser type. The model describes an electromagnetic field trapped in a cavity and a beam of atoms passing through it but with an additional reservoir interacting continuously with the electromagnetic field. The idea is that the cavity is not perfectly isolated and we describe the leaks in the cavity via the interaction with this reservoir. Thus the interaction between the electromagnetic field and the atoms is described by a quantum system with repeated interactions and the interaction between the electromagnetic field and the reservoir is described by a Hamiltonian approach of open quantum systems.The system "cavity+reservoir" has been studied by Konenberg, based on previous works by Arai. Usingan explicit diagonalization of the hamiltonian he proved some properties of return to equilibrium. In a first part we will give a new approach to it using recent results by Nam, Napiorkowski and Solovej about the diagonalization of quadratic bosonic hamiltonians.First we study the self-adjointness of some Hamiltonians which will play an important role in this thesis and we consider the diagonalization of one of them. In a second time, we study the long time behavior of the system, we obtain an explicit formula for the evolution at a given time of Weyl observables. These results will also allow us to study the total energy variation as well as the energy exchanges in the system. Finally we study the entropy production in the system and relate it to the energy variation. To do so we will need to slightly generalize the Jaksic-Pillet entropy production formula.

The limits of the current micro-scale electronics technology have been approaching rapidly. At nano-scale, however, the physical phenomena involved are fundamentally different than in micro-scale. Classical and semi-classical physical principles are no longer powerful enough or even valid to describe the phenomena involved. The rich and powerful concepts in quantum mechanics have become indispensable. There are several commercial software packages already available for modeling and simulation of the electrical, magnetic, and mechanical characteristics and properties of the nano-scale devices. However, our objective here is to go one step further and create a physics-based problem-adapted solution methodology. We carry out computation for eigenfunctions of canonical and the associated perturbed quantum systems and utilize them as co-ordinate functions for solving more complex problems. We have profoundly worked with the infinite quantum potential-well problem, since they have closed-form solutions and therefore are analytically known eigenfunctions. Perturbation of the infinite quantum potential-well was done through a single box function, multiple box functions, and with a triangular function. The proposed solution concept utilizes the notion of

Foundational problems of quantum theory, regarding the appearance of classicality and the measurement problem are stated and their link to studies of open quantum systems is discussed. This study&#039 / s main aim is to analyze the main approaches that are employed in the context of open quantum systems. The general form of Markovian master equations are derived by a constructive approach. The Quantum State Diffusion (QSD) formalism is stressed upon as an alternative method to the master equations. Using the Caldeira-Leggett model in the context of QSD, stationary solutions of a charged particle exposed to a uniform magnetic field are found. The important points are summarized and the results are discussed.

One consequence of a quantum theory in which resonances are mathematically unified with decaying states is an asymmetry in time evolution, even for closed quantum mechanical systems. This time asymmetry is different from the environmentally induced, dynamical irreversibility that is experienced only by open quantum systems and that is quantified by an increase in entropy. To investigate the connection between time asymmetry and dynamical irreversibility, we study open systems within a time asymmetric theory. We find that, when using a time asymmetric theory for open systems, one must relax the assumption that measurements are perfectly repeatable. To treat this problem, we develop a framework in which one can incorporate the interference from multiple environmental systems affecting a single experiment. We also study a kinematic effect of indistinguishability that affects only open systems, and we show how it leads to a monotonic increase in entropy without requiring an active measurement. Finally, within our framework we develop two models that reproduce for open systems the expected and observed phenomena. One is a model of photons scattering inefficiently from a beam splitter. The other is a model of systems undergoing Rabi oscillations and suffering environmental interference. We find that the kinematic effect of indistinguishability can explain for such systems the generally measured Excitation Induced Dephasing, which has previously been treated dynamically. / text

Mutually unbiased bases is an important topic in the recent quantum system researches. Although there is much work in this area, many problems related to mutually unbiased bases are still open. For example, constructing a complete set of mutually unbiased bases in the Hilbert spaces with composite dimensions has not been achieved yet. This thesis defines a weaker concept than mutually unbiased bases in the Hilbert spaces with composite dimensions. We call this concept, weak mutually unbiased bases. There is a duality between such bases and the geometry of the phase space Zd × Zd, where d is the phase space dimension. To show this duality we study the properties of lines through the origin in Zd × Zd, then we explain the correspondence between the properties of these lines and the properties of the weak mutually unbiased bases. We give an explicit construction of a complete set of weak mutually unbiased bases in the Hilbert space Hd, where d is odd and d = p1p2; p1, p2 are prime numbers. We apply the concept of weak mutually unbiased bases in the context of quantum tomography and quantum cryptography.

Recent experiments show evidence for long-lived electronic coherence in several photosynthetic complexes, for example in the Fenna-Matthews-Olson complex of green sulfur bacteria. The experiments raise questions about the microscopic reasons for this quantum coherence and its role to the functioning of these highly evolved biological systems. The present thesis addresses both questions. We find that an interplay of electronic coherence and the fluctuating phonon environment is responsible for the high exciton transport efficiency in these complexes and generalize this idea to the concept of environment-assisted quantum transport (ENAQT). In addition, we quantify the contribution of coherent dynamics to the efficiency and thus to the biological functioning. We determine the effect of temporal (non-Markovian) and spatial correlations and develop an ab initio propagation method based on atomistic detail which predicts the long-lived coherence. The research in photosynthetic energy transfer can inspire new designs for the control of excitons in engineered systems. We develop a method for computing the Forster coupling between semiconductor nanoparticle quantum dots. The focus is on the size and shape dependence and the presence of a spatially varying dielectric environment and metallic gates. A separation of the wavefunction into slowly and fast varying part provides the basis for an efficient computation on a real-space grid. Finally, the simulation of structured models of photosynthetic energy transfer is a challenging task using conventional computing resources. To this end, we propose a special-purpose superconducting device based on flux quantum bits and quantum LC resonators and show that parameters can be engineered such that this simulation becomes possible. / Chemistry and Chemical Biology

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-17T18:35:17Z No. of bitstreams: 1 JOÃO GUSTAVO DA SILVA SANTOS Ó – DISSERTAÇÃO (PPGFísica) 2016.pdf: 3276092 bytes, checksum: f4b6dd7217e33af856588a93c1291306 (MD5) / Made available in DSpace on 2018-10-17T18:35:17Z (GMT). No. of bitstreams: 1 JOÃO GUSTAVO DA SILVA SANTOS Ó – DISSERTAÇÃO (PPGFísica) 2016.pdf: 3276092 bytes, checksum: f4b6dd7217e33af856588a93c1291306 (MD5) Previous issue date: 2016-07 / Capes / Desenvolvemos neste trabalho um estudo teórico da aplicação da dinâmica de campo térmico sobre o modelo de Jaynes-Cummings. De acordo com a abordagem feita por Hashizume no artigo, A new perspective to formulate a dissipative ther mo eld dynamics aplicamos os mesmos conceitos para investigar o processo de relaxação envolvido no modelo de Jaynes-Cummings. Num primeiro momento, fi zemos uma revisão de alguns elementos primordiais para a compreensão de toda a discussão envolvida nessa dissertação. Em seguida, estudamos processos de relaxação em sistemas quânticos simples, para podermos, mais tarde, traçar um paralelo entre os resultados e estabelecer alguma relação com o que foi encontrado. Diante da dinâmica de campo térmico, mas conhecida como TFD (ThermoFieldDynamics), usamos uma abordagem feita por Hashiz um e colaboradores, e investigamos como o processo de relaxação se desenvolve mediante a representação via TFD. / We develop in this work, a the or etical study of the application of theThermo eld dynamics on the model of Jaynes-Cummings. According to the approach taken by Hashizu me in the article, A new perspective to formulate a dissipative thermo eld dynamics", we use the same concepts to investigate the relaxation process involved in model Jaynes-Cummings. In the rst moment, we did are view of some key elements to comprenção all the discussion involved in this dissertation. Then, we study relaxation processes in simple quantum systems, for we could later draw a parallel between the results and establish some relationship to what was found. Front the thermal eld dynamics, butknownas TFD, we use an approach made by Hashizu me and colaborators, and we investigated how the relaxation process it developed through there presentation via TFD.

Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all mutually unbiased bases for higher (non-prime) dimension is still open. We derive an alternate approach to mutually unbiased bases by studying a weaker concept which we call weak mutually unbiased bases. We then compare three rather different structures. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1/√k (where k∣d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. We give an explicit breakdown of this triality.

On commence dans le chapitre d'introduction par rappeler les résultats majeurs sur l'intrication et les systèmes quantiques ouverts. Puis en particulier on prouve la désintrication en temps fini pour deux qubits (systèmes quantiques à deux niveaux d'énergie) en interaction avec des bains thermiques distincts à température positive. On propose dans le premier chapitre de cette thèse une méthode pour empêcher la désintrication en temps fini basée sur des mesures continues sur les bains et utilisant la théorie des sauts quantiques et celle des équations différentielles stochastiques. Dans le deuxième chapitre on étudie un sous-ensemble des états de deux qubits : celui des états qu'on peut représenter dans la base canonique pour une matrice ayant une forme de X. Cela nous permet d'obtenir des formules explicites pour la décomposition d'un état X séparable en au plus cinq états purs produits. On généralise ensuite cette étude à l'ensemble des états obtenus à partir d'états X par conjugaison avec des unitaires locaux. Puis on donne un algorithme pour décomposer tout état séparable de cet ensemble en une combinaison convexe de cinq états purs produits. Le troisième chapitre de cette thèse propose l'étude de l'évolution de l'intrication de deux qubits dans un modèle d'interactions répétées avec la même chaîne de spins dans les limites de van Hove et de couplage singulier. En particulier on observe une intrication asymptotique non nulle quand la chaîne est à température infinie et des phénomènes de création d'intrication quand la chaîne est à température nulle. / In the introductory chapter we first give the major results about entanglement and open quantum systems. In particular we give the proof of entanglement sudden death (ESD) for two qubits (two level quantum systems) interacting with their own heat bath at positive temperature. We propose in the first chapter a method to protect qubits against ESD, based on continuous measurements of the baths and using the theory of quantum jumps and stochastic differential equations. In the second chapter, we study a subset of two qubits states : the set of states that we can represent in the canonical basis by an X-form matrix. We also give explicit formulas for decompositions of a separable X-state in a convex sum of five pure product states. We generalize this study to the set of states obtained from X-states by a conjugation with local unitary operators. Furthermore, we give an algorithm to decompose a separable state of this set in a convex sum of five pure product states. Finally, in the third chapter we study entanglement of two qubits in a model of repeated interactions with the same spin chain in the van Hove and singular coupling limits. In particular we observe non zero asymptotic entanglement when the chain is at infinite temperature and phenomenons of entanglement sudden birth when the chain is at zero temperature.

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No. of bitstreams: 1 cervatineto_a_me_sjrp.pdf: 2223044 bytes, checksum: 7fd8ad5a2c1a98b7bf95f401b2c2b358 (MD5) Previous issue date: 2018-01-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A teoria de informação e computação quântica é uma área de pesquisa que vem crescendo de maneira acentuada nos últimos anos devido aos inúmeros avanços tecnológicos que a acompanham. Neste mestrado começamos nossos estudos nesta área de pesquisa onde nos introduzimos e aprofundamos em seus aspectos intrigantes e peculiares. Dada nossa formação inicial na área de ciências da computação, inicialmente nos dedicamos a entender os aspectos fundamentais da mecânica quântica, assim como da teoria de informação e computação quântica. Focamos principalmente nos sistemas quânticos abertos, visto que o maior obstáculo a ser superado para o desenvolvimento destes computadores é o efeito deletério do meio ambiente. A princípio, concentramos nossos estudos nos ditos processos não-Markovianos, que apresentam efeitos de memória. Aprendemos sobre as novas medidas de não-Markovianidade, principalmente as medidas baseadas na dinâmica do emaranhamento e na dinâmica da informação mútua. Conseguimos publicar nosso primeiro resultado, onde provamos a inequivalência destas duas medidas de não-Markovianidade. De fato, mostramos que tais medidas, em geral, podem discordar sobre o tipo de processo dissipativo, sendo que uma pode reconhecê-lo como Markoviano enquanto outra pode reconhecê-lo como não-Markoviano. Como mostramos, esta inequivalência está diretamente relacionada com o refluxo de informação do meio ambiente para o sistema, e como mensuramos tal informação nestas duas medidas distintas de não-Markovianidade. Finalmente, na fase final de nossos estudos, tivemos como objetivo encontrar um meio de otimizar o controle das operações lógicas. Especificamente, trabalhamos com um método numérico utilizado em sistemas fechados para otimizar sistemas abertos Markovianos. Observamos que a eficácia deste método depende do tipo e intensidade da interferência do ambiente e das condições iniciais do sistema, obtendo melhores resultados em casos específicos. / Quantum information theory and computation is a field of research that has been growing acutely in the past few years due to the many technological improvements it follows. In this masters’ course, we began our studies in this area of research where we were introduced and immersed in its intriguing and peculiar aspects. Given our initial formation in computer science, we initially dedicated ourselves to understanding the fundamentals of quantum mechanics, as well as of information theory and quantum computation. Our main focus were open quantum systems, since the greatest obstacle to the development of these computers is the harmful effect of the environment. At first, we concentrated our studies in the so called non-Markovian processes, that show memory effects. We learned about the new non-Markovianity measurements, mainly those based on the dynamics of entanglement and mutual information. We managed to publish our first result, where we proved the inequivalence of these two measurements of non-Markovianity. Indeed, we showed that such measurements, in general, can disagree about the dissipative process, so that one can regard it as Markovian and the other as non-Markovian. As we demonstrated, this inequivalence is directly related to the information back-flow from the environment to the system, and how this information is measured by each of the two distinct measurements. Finally, in the last stage of our studies, our goal was to find a way to optimize the control of the logical operations. Specifically, we worked with a numeric method used in closed systems to optimize Markovian open systems. We have observed that the effectiveness of this method depends on the type and intensity of the interference of the environment and of its initial conditions, attaining better results for specific cases.