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En optique quantique, la nature quantique de la lumière se manifeste dans des effets d’ordonnement d’opérateurs, inexistants en optique classique. Cette thèse est consacrée à une étude détaillée de ce type d’effets d’ordonnement dus à la dynamique des systèmes physiques. Nous considérons deux systèmes en particulier, 1) la conversion paramétrique descendante dans un milieu χ (2), et 2) un ion dans un piège de Paul entraı̂né par un champ classique; décrit par un modèle de Jaynes-Cummings non linéaire. Les effets d’ordonnement dans ces systèmes dynamiques sont étudiés via le développement et l’approximation de Magnus. Dans le scénario de conversion paramétrique descendante, nous considérons deux cas, (i) une pompe monochromatique (où une solution exacte de la dynamique est connue) et (ii) une pompe spectralement large. Pour la pompe monochromatique, nous écrivons explicitement la décomposition de Bloch-Messiah et obtenons les modes propres et les paramètres de compression. Nous comparons ces résultats exacts avec les approximations de Magnus en incluant certains ou aucun effets d’ordonnement. Nous effectuons une analyse similaire pour la pompe spectralement large lorsque la décomposition de Bloch-Messiah ne peut être évaluée que numériquement. Pour le modèle dynamique de Jaynes-Cummings non linéaire, nous analysons, à nouveau, les effets d’ordonnement via des approximations de Magnus et obtenons la solution exacte, qui n’avait pas été publiée dans la littérature auparavant. Enfin, nous évaluons pour la première fois les limites supérieures exactes (qui dépassent les limites suffisantes) de la convergence du développement de Magnus pour les deux modèles dynamiques à solutions exactes. / In quantum optics, the quantum nature of light manifests itself in operator ordering effects, nonexistent in classical optics. This thesis is devoted to a detailed study of such ordering effects that are due to the dynamics of physical systems. We consider two systems in particular, 1) parametric down-conversion in a χ(2) medium, and 2) an ion in a Paul trap driven by a classical field; described by a nonlinear Jaynes-Cummings model. Ordering effects in these dynamical systems are studied via the Magnus expansion and approximation. In the parametric down-conversion scenario we consider two cases, (i) a monochromatic pump (where an exact solution of the dynamics is known), and (ii) a spectrally broad pump. For the monochromatic pump, we write explicitly the Bloch-Messiah decomposition and obtain the squeezing eigenmodes and parameters. We compare these exact results with the Magnus approximations that contain some or no ordering effects. We perform similar analysis for the spectrally broad pump, where the Bloch-Messiah decomposition can only be evaluated numerically. For the dynamics in the nonlinear Jaynes-Cummings model we again analyze ordering effects via Magnus approximations and obtain the exact solution, which has not been published in the literature before. Lastly, we evaluate the exact upper bounds (which exceed sufficient bounds) of convergence of the Magnus expansion for the two models with exact solutions, for the first time.

Orientador: Antonio Vidiella-Barranco / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-03T15:39:51Z (GMT). No. of bitstreams: 1 Gomes_AlvaroFernandez_D.pdf: 1463180 bytes, checksum: e7afc315eaab1eeb818ae16a2027e1de (MD5) Previous issue date: 2003 / Resumo: A construção de estados puros do campo eletromagnético é importante não só para o estudo dos fundamentos da mecânica quântica, como a questão do estado gato de Schrõdinger, mas também possui um grande potencial de aplicação, como por exemplo, na computação quântica, na criptografia quântica e nas medidas de alta precisão. Nesta tese, apresentamos três propostas onde o ponto central é o estudo da transferência progressiva de coerência dos átomos para o campo eletromagnético, visando gerar um estado com um alto grau de purificação a partir de um estado de mistura estatística. Para isso utilizamos o micromaser com a interação átomo-campo dado pelo modelo Jaynes-Cummings de dois fótons. No primeiro trabalho consideramos os átomos inicialmente preparados em uma superposição coerente de dois estados (condição necessária para a transferência de coerência átomo-campo) e o campo na cavidade preparado em um estado mistura do. Primeiramente determinamos o melhor tempo de interação de cada átomo para que o estado do campo apresentasse o maior grau de purificação possível. Fixamos esse tempo para todos os átomos e determinamos o grau de pureza do estado final do campo, após N -átomos terem passado pela cavidade. Em nosso segundo trabalho acrescentamos à cavidade um meio não-Iinear tipo Kerr. Utilizando o mesmo procedimento do primeiro caso, obtivemos um menor tempo de interação átomo-campo e um grau de purificação maior para o estado do campo gerado na cavidade, em relação ao primeiro trabalho. Por último, acrescentamos um campo clássico externo interagindo com o átomo dentro da cavidade sem o meio Kerr. Novamente, com o mesmo procedimento dos trabalhos anteriores, verificamos que esse campo, além de influenciar na transferência de coerência átomo-campo, torna desnecessária a preparação dos átomos em uma superposição coerente de dois estados. Visando a caracterização do estado do campo final gerado, foram calculadas a função de coerência de segunda ordem e a quasiprobabilidade conhecida como a função de Husimi (ou função Q) / Abstract: The construction of pure states of the electromagnetic field is important not only for the study of the foundations of the quantum mechanics, such as the question of the Schrõdinger cat states, but also for its potential applications, for example, in quantum computation, quantum criptography and in higher precision measurements. In this thesis, we present three proposals where the central point is the study of the progressive transfer of coherence of atoms to the electromagnetic field, aiming the generation of a state with a higher degree of purity from a mixed state. For this we use the micromaser with the atom-field interaction given by the two-photon Jaynes-Cummings model. In our first work we initially consider atoms prepared in a coherent superposition of two states (necessary condition for the atom-field transfer of coherence) and the field in the cavity prepared in a mixed state. We determine the best interaction time for each atom so that the state of the field presents the highest possible degree of purification. We fix that time for all atoms and determine the degree of purity of the final state of the field, after N -atoms have crossed the cavity. In our second work we add to the cavity a nonlinear Kerr-like medium. Using the same procedure as in the first case, we obtain smaller atom-field interaction times as well as a higher degree of purification for the state of the field generated in the cavity, compared to the first work. Finally, we add an external classical field interacting with the atom inside the cavity without the Kerr medium. Again, with the same procedure of the previous works, we verify that the external field, besides influencing in the atom-field transfer of coherence turns unnecessary the preparation of atoms in a coherent superposition of two states. In order to characterize the state of the generated ( final) field, we have calculated the second order correlation function as well as the quasiprobàbility known as the Husimi function (or Q function) / Doutorado / Física / Doutor em Ciências

Orientador: Antonio Vidiella Barranco / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-31T02:56:15Z (GMT). No. of bitstreams: 1 Decordi_GustavoLazero_D.pdf: 2456755 bytes, checksum: 42a17eacb2e1a86e81888e48272ed08e (MD5) Previous issue date: 2016 / Resumo: Estudamos nesta tese, sistemas quânticos compostos sob a influência de ambientes externos. Na primeira parte do trabalho, investigamos um sistema de dois qubits interagentes, estando um deles isolado e o outro acoplado a um banho térmico. Analisamos os efeitos da temperatura do banho sobre a dinâmica do sistema de dois qubits. Com essa finalidade, empregamos dois modelos distintos da interação sistema-ambiente: i) um modelo microscópico, no qual a equação mestra é obtida levando-se em conta o acoplamento entre os qubits na dedução do termo dissipativo, ii) um modelo fenomenológico, no qual o termo dissipativo é simplesmente adicionado ao termo unitário da equação de evolução do operador densidade. Obtemos soluções analíticas para os modelos, o que permitiu estudá-los em um intervalo considerável do acoplamento entre os qubits. Dedicamos a segunda parte do trabalho ao estudo de um sistema quântico em particular acoplado a um pequeno ambiente. Neste contexto, resolvemos exatamente o modelo da interação radiação-matéria conhecido como modelo de Tavis-Cummings a dois átomos. De posse das soluções, obtidas em circunstâncias bastante gerais e até então não encontradas na literatura, investigamos os efeitos oriundos da interação de um pequeno ambiente (átomo em estado de mistura estatística) sobre a dinâmica do subsistema composto pelo outro átomo acoplado ao modo do campo eletromagnético. Nós mostramos que propriedades não-clássicas associadas ao sistema principal podem ser significativamente degradadas pela ação do ambiente quando o átomo 2 está acoplado de maneira resonante ao campo. Encontramos que o comportamento não-clássico do sistema pode ser restaurado a medida que dessintonizamos o campo da frequência de transição do átomo 2, o ambiente / Abstract: We study in this thesis composite quantum systems under the influence of external environments. In the first part of this work, we investigate a two qubit interacting system having one of them isolated and the other coupled to a thermal bath. We analyze the effect of the temperature of the bath on the dynamics of the two qubit system. In order to do that, we consider two different models of system-reservoir interaction: i) a "microscopic" model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a "phenomenological" approach, in which the master equation consists of a dissipative term added to the unitary evolution term. We show that in the strong coupling regime between the subsystems (qubits), the expected thermal equilibrium steady state for the two-qubit system naturally arises in the framework of the microscopic model, while in the phenomenological approach it is obtained a steady state density operator which is not correct. Furthermore, the differences are even more profound in the weak coupling regime, when the models give rise to opposite behaviors with regard to the linear entropy of qubit 1. At the context of quantum systems coupled to environments with few degrees of freedom, we solve analytically the matter-radiation interaction model known as two atom Tavis-Cummings Model. With the solutions at hand, achieved in general circumstances until the present not found in literature, in which the constituent atoms may be coupled with different strengths to the field and also have different frequency detunings, we study the effects that arise from the interaction of a small environment (atom in a statistical mixture state) with the other atom coupled to an oscillator (cavity mode). We show that nonclassical features associated to the main system may be significantly degraded by the action of the small environment, if atom 2 is resonantly coupled to the field. We also demonstrate that the nonclassical behaviour of the system may be restored if we detune the field from the transition frequency of atom 2, the environment / Doutorado / Física / Doutor em Ciências / 899872/2011 / CAPES

Made available in DSpace on 2014-07-29T15:07:09Z (GMT). No. of bitstreams: 1 dissertacao_Alexandre Divino.pdf: 736654 bytes, checksum: 2b8069070ebe78eef1b634051df5d432 (MD5) Previous issue date: 2009-02-20 / In this work we have studied the two photon Jaynes-Cummings model to describe the interaction of a three-level atom in the configuration with a single-mode of a cativy-field. We have used the effetive and full microscopic Jamiltonian approach to compare the results obtained in these tow descriptions. We employed the two-photon Jaynes-Cummings model int the full microscopic Hamiltonian context to implement schemes to quantuam entanglement swapping, for approximate and conditional quantuam teleportation for an unknown atomic state, for a superposition of zero- and two photon states. Both schemes were implemented using no measurement in the Bell base states. / Neste trabalho estudamos o modelo Jaynes-Cummings de dois fótons para descrever a interação de um átomo de Rydberg na configuração (ladeira) de três níveis com único modo do campo eletromagnético. A descrição deste sistema foi obtida usando o hamiltoniano efetivo e também o hamiltoniano microscópico completo, com o objetivo de compararmos resultados obtidos nas suas descrições. No modelo de Jaynes-Cummings de dois fótons descrito pleo hamiltoniano microscópico completo propusemos esquemas para realização de troca de emaranhamento quântico e teletransporte quântico aproximado e condicional de estados atômicos desconhecidos bem como estados de superposição de zeros e dois fótons do campo. Esses dois esquemas foram realizados sem uso de medida na base dos estados de Bell.

Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.

Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.

Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.

Die vorliegende Arbeit behandelt die Modellierung einer Quantenpunkt-LED und die Berechnung des elektrischen Stromes und der Lichtproduktion im Landauer-Büttiker-Formalismus. Die Elektron-Photon-Wechselwirkung kann im Landauer-Büttiker-Formalismus behandelt werden, indem wir annehmen, dass jedes Elektron mit einem separaten Photonenfeld interagiert. Dies erlaubt es uns, ein Elektron zusammen mit seinem Photonenfeld als „einzelnes, nicht wechselwirkendes Teilchen“ im Sinne des Landauer-Büttiker-Formalismusses zu betrachten. Wir entwickeln ein Modell einer QP-LED, dessen Elektron-Photon-Wechselwirkung auf dem Jaynes-Cummings-Modell basiert, das die Interaktion eines Quantenpunkts mit einer Mode des elektromagnetischen Feldes beschreibt. Um auch die Energieverteilung der emittierten Photonen analysieren zu können, schlagen wir ein auf einem Pauli-Fierz-Modell basiertes Modell vor. Anstelle einer einzelnen Mode modelliert es Photonen beliebiger Energie, allerdings beschränken wir uns auf den Unterraum mit maximal einem Photon. Wir beweisen eine abstrakte Landauer-Büttiker-Formel, die für alle relativ nuklearen Streusysteme gilt. Sie ist ähnlich zu dem Ergebnis von Aschbacher et al. (2007), unterscheidet sich aber in der Regularisierung des Stroms. Wir wenden das abstrakte Ergebnis auf die Jaynes-Cummings-QP-LED an. Als Startpunkt für die Berechnung der Streumatrix verallgemeinern wir die Darstellung der Streumatrix durch die Weyl-Funktion eines Randwert-Triplets von Behrndt et al. (2010) vom Fall für Störungen endlichen Ranges auf den Fall relativ nuklearer Störungen. Dies deckt insbesondere den Fall der Jaynes-Cummings-QP-LED ab. Die Resolventendifferenz der Pauli-Fierz-QP-LED ist nicht nuklear, weshalb wir eine verallgemeinerte Landauer-Büttiker-Formel für eine gewisse Klasse von Multiplikationsoperatoren beweisen, die in der Faser nuklear sind. Dieses abstrakte Resultat liefert uns auch für die Pauli-Fierz-QP-LED eine Landauer-Büttiker-Formel. / This thesis treats the modeling of a quantum dot LED and the calculation of the electric current and the light production in the Landauer-Büttiker framework. The electron-photon interaction is fitted into the Landauer-Büttiker framework by assuming that every electron interacts with a separate photon field. It allows us to consider an electron together with its photon field as a ''single non-interacting particle'' in the sense of the Landauer-Büttiker formalism. We develop a model of a QD-LED with an electron-photon interaction that is based on the Jaynes-Cummings model, which describes the interaction of a quantum dot with a single mode of the electromagnetic field. To be able to analyze the energy distribution of the emitted photons, we propose a second model of a QD-LED that is based on a one-dimensional Pauli-Fierz model. It models photons of arbitrary positive energy instead of just a single mode, but we restrict it to the subspace of at most one photon. We prove an abstract Landauer-Büttiker formula that applies to all relatively trace class interactions. It is similar to the result by Aschbacher et al. (2007), but differs in the regularization of the flux. We apply this formula to the Jaynes-Cummings QD-LED. Since knowing of the scattering matrix is essential for explicit calculations with the Landauer-Büttiker formula, we generalize a result by Behrndt et al. (2010) on a representation of the scattering matrix in terms of the Weyl function of a boundary triplet from the finite rank case to relatively trace class perturbations, which covers the case of the Jaynes-Cummings QD-LED. The resolvent difference of the Pauli-Fierz QD-LED is not trace class, whence we prove a generalized Landauer-Büttiker formula for a certain multiplication operators that are trace class in the fiber. This abstract result gives us a Landauer-Büttiker formula also for the Pauli-Fierz QD-LED.

We study the phase transition super uid-Mott insulator in optical lattices through model Jaynes-Cummings-Hubbard using the fermion approximation. Initially we did a review of the Jaynes-Cummings model that is a model that describes the interaction between an atom with two levels and a quantized electromagnetic eld. Then we stu- died the properties of the phase transition super uid-Mott insulator (SF-MI) through the model Bose-Hubbard and we discuss the characteristics of the two quantum phases and the conditions for phase transition. Apply the model Jaynes-Cummings-Hubbard in order to study the in uence of topology of network Bravais linear, square, single cubic (SC), body-centered cubic (BCC) and face-centered cubic (FCC) in the phase transi- tion SF-MI to different numbers of excitation and different detuning values between the atom and the eld and we found that the Mott lobes and the critical hopping terms are not renormalizable only for the FCC network. But the regime from many excitations, the critical hopping is renormalizable to all networks and is independent of detuning. Then we study the Jaynes-Cummings-Hubbard model for a chain with the addition of the Kerr effect (nonlinear optical effect) through the approximation of fermions (FA). We observed that the Kerr effect does not cause large changes in the energy spectrum. However, the properties of the phase transition SF-MI undergoes signicant changes due to the Kerr effect. Another important feature which has been observed is that the Kerr effect favors the phase MI. / Estudamos a transi¸c ao de fase superfluido-isolante de Mott (SF-MI) em redes ´opticas via modelo Jaynes-Cummings-Hubbard utilizando a aproxima¸c ao de f´ermions. Inicialmente fazemos uma revis ao do modelo Jaynes-Cummings que descreve a intera¸c ao de um ´atomo de dois n´ıveis com um campo eletromagn´etico quantizado. Em seguida estudamos as propriedades da transi¸c ao de fase SF-MI no modelo Bose-Hubbard e discutimos as caracter´ısticas das duas fase qu anticas e as condi¸c oes para a transi¸c ao de fase. Aplicamos o modelo Jaynes-Cummings-Hubbard com a finalidade de estudarmos a influ encia da topologia das redes de Bravais linear, quadrada, c´ubica simples (SC), c´ubica de corpo centrado (BCC) e c´ubica de faces centradas (FCC) na transi¸c ao de fase SF-MI para diferentes n´umeros de excita¸c ao e diferentes valores de dessintonia entre o ´atomo e o campo e encontramos que os l´obulos de Mott n ao s ao renormaliz ´aveis apenas para a rede FCC. Mas no regime de muitas excita¸c oes, as redes BCC e FCC passam a ter o mesmo comportamento enquanto que as demais continuam com sua depend encia no n´umero de vizinhos. Em seguida, estudamos o modelo de Jaynes-Cummings-Hubbard para uma cadeia com a adi¸c ao do efeito tipo Kerr (efeito ´optico n ao-linear) atrav´es da aproxima¸c ao de f´ermions (FA). Observamos que o efeito tipo Kerr n ao provoca grandes altera¸c oes no espectro de energia. No entanto, as propriedades de transi¸c ao de fase SF-MI passam por mudan¸cas significativas devido ao efeito tipo Kerr. Outra caracter´ıstica importante que foi observada ´e que o efeito tipo Kerr favorece a fase MI.