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As a central tenet of falsificationism, Karl Popper holds that all possible scientific theories individually have a probability equal to zero. Popper’s position rests upon the Principle of Indifference, the equiprobability of mutually exclusive outcomes, to derive this zero probability. In this paper, I will illustrate that the Principle of Indifference fails to compute objective probabilities in cases in which an epistemic agent faces ignorance. Prior to experience, there is no sufficient reason to prefer any probability distribution to any other; yet, the Principle of Indifference implies a preference for a uniform probability distribution. Distribution preference is determined by the relevant experience and rational expectations of epistemic agents. Relevant experience is defined by observations and other sense experience regarding the relevant trial. Rational expectations represents the non-arbitrarity of distribution preference. Without rational expectations, the distribution preference is arbitrary even when informed by experience. If an agent lacks relevant experience, then any distribution preference is arbitrary; however, if an agent possesses relevant experience, then the Principle of Indifference does not apply. A rejection of the Principle of Indifference undermines the necessity of zero probabilities for scientific theories in which case Popper’s conclusions of falsificationism do not follow. Objective probability, then, understood within the logical interpretation, is a problematic notion.

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

In the main part of this thesis I study the relaxation mechanisms of charge carriers in silicon nanocrystals in SiO2 matrix. One of the potential applications of these structures lies in photovoltaics, specifically in construction of all-silicon tandem solar cells. I studied the dynamics of carriers in these structures by methods of ultrafast spectroscopy which helped to unravel the microscopic behaviour of carriers, their transport, localization etc. Furthermore I investigated the doping of such structures as the technology of doping is crucial for manufacture of pn- junctions which are the core component of solar cells. At the end I delve into the dissipative Jaynes-Cummings model by mathematical modeling and theoretical calculations which describes among others microlasers and as such comes under a field of cavity quantum electrodynamics.

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.