The experiment performed by Itano, Heinzen, Bollinger and Wineland on the quantum Zeno effect is analyzed in detail through a quantum map derived by conventional quantum mechanics based on the Schrodinger equation. The analysis shows that a slight modification of their experiment leads to a significantly different result from the one that is predicted through von Neumann's hypothesis of collapse of the wave function in the quantum measurement theory. This may offer a possibility of an experimental test of von Neumann's quantum measurement theory. / text

Decoherence is central to our understanding of the transition from the quantum to the classical world. It is also a way of probing the dynamics of interacting many-body systems. Photoexcited semiconductors are such systems in which the transient dynamics can be studied in considerable detail experimentally. Recent advances in spectroscopy of semiconductors provide powerful tools to explore many-body physics in new regimes. An appropriate theoretical framework is necessary to describe new physical effects now accessible for observation. We present a possible approach in this thesis, and discuss results of its application to an experimentally relevant scenario. The major portion of this thesis is devoted to a formalism for the multi-dimensional Fourier spectroscopy of semiconductors. A perturbative treatment of the electromagnetic field is used to derive a closed set of differential equations for the multi-particle correlation functions, which take into account the many-body effects up to third order in the field. A diagrammatic method is developed, in which we retain all features of the double-sided Feynman diagrams for bookkeeping the excitation scenario, and complement them by allowing for the description of interactions. We apply the formalism to study decoherence between the states of optically excited excitons embedded in an electron gas, and compare it with the decoherence between these states and the ground state. We derive a dynamical equation for the two-time correlation functions of excitons, and compare it with the corresponding equation for the interband polarization. It is argued, and verified by numerical calculation, that the decay of Raman coherence depends sensitively on how differently the superimposed exciton states interact with the electron gas, and that it can be much slower than the decay of interband polarization. We also present a new numerical approach based on the length gauge for modeling the time-dependent laser-semiconductor interaction. The interaction in the length gauge involves the position operator for electrons, as opposed to the momentum operator in the velocity gauge. The approach is free of the unphysical divergences that arise in the velocity gauge. It is invariant under local gauge symmetry of the Bloch functions, and can handle arbitrary electronic structure and temporal dependence of the fields.

Decoherence is central to our understanding of the transition from the quantum to the classical world. It is also a way of probing the dynamics of interacting many-body systems. Photoexcited semiconductors are such systems in which the transient dynamics can be studied in considerable detail experimentally. Recent advances in spectroscopy of semiconductors provide powerful tools to explore many-body physics in new regimes. An appropriate theoretical framework is necessary to describe new physical effects now accessible for observation. We present a possible approach in this thesis, and discuss results of its application to an experimentally relevant scenario. The major portion of this thesis is devoted to a formalism for the multi-dimensional Fourier spectroscopy of semiconductors. A perturbative treatment of the electromagnetic field is used to derive a closed set of differential equations for the multi-particle correlation functions, which take into account the many-body effects up to third order in the field. A diagrammatic method is developed, in which we retain all features of the double-sided Feynman diagrams for bookkeeping the excitation scenario, and complement them by allowing for the description of interactions. We apply the formalism to study decoherence between the states of optically excited excitons embedded in an electron gas, and compare it with the decoherence between these states and the ground state. We derive a dynamical equation for the two-time correlation functions of excitons, and compare it with the corresponding equation for the interband polarization. It is argued, and verified by numerical calculation, that the decay of Raman coherence depends sensitively on how differently the superimposed exciton states interact with the electron gas, and that it can be much slower than the decay of interband polarization. We also present a new numerical approach based on the length gauge for modeling the time-dependent laser-semiconductor interaction. The interaction in the length gauge involves the position operator for electrons, as opposed to the momentum operator in the velocity gauge. The approach is free of the unphysical divergences that arise in the velocity gauge. It is invariant under local gauge symmetry of the Bloch functions, and can handle arbitrary electronic structure and temporal dependence of the fields.

The construction of a high-resolution optical microscope system for micro-photoluminescence (µ-PL) spectroscopy is described, and a range of time-integrated and time-resolved experimental work on single InGaN quantum dots (QDs) is presented. Time-integrated measurements demonstrate the existence of InGaN QDs in three different samples via the presence of sharp exciton recombination lines in the µ-PL spectra. The narrowest peaks display a linewidth Γ of ~230 µeV, implying a decoherence time T2 ≥5.7 ps. Time-resolved measurements on exciton recombination lines from single self-assembled InGaN QDs reveal typical lifetimes of ~2.0 ns (which decrease with increasing temperature), while typical lifetimes for excitons in single selectively-grown micropyramidal InGaN QDs are found to be ~0.4 ns. The shorter exciton recombination lifetime in selectively-grown QDs is believed to be due to a stronger coupling of these QDs to the underlying quantum well. Temporal fluctuations (on a timescale of seconds) in the energy, intensity and FWHM of µ-PL peaks arising from the recombination of excitons in single self-assembled InGaN QDs are observed. These are attributed to transient Stark shifts induced by a fluctuating local charge distribution as carriers become trapped in defect states in the vicinity of the QDs. Time-integrated power-dependent measurements are used to demonstrate the presence of biexciton states in single self-assembled InGaN QDs. The exciton–biexciton energy splitting is found to be ~41 meV, in agreement with values predicted by theoretical calculations. Time-resolved studies of the biexciton and exciton decay curves reveal a coupling as the exciton population is refilled by biexciton decays. The biexciton lifetime is found to be ~1.4 ns, compared to an exciton lifetime of ~1.0 ns. Lateral electric fields are applied to a single self-assembled InGaN QD using aluminium electrodes lithographically defined on the sample surface. Application of fields of the order of ~0.17 MVcm-1 is found to cause both a red-shift and a reduction in the intensity of the exciton recombination peak in the µ-PL spectrum.

In this thesis quantum-classical dynamics is applied to the study of quantum condensed phase processes. This approach is based on the quantum-classical Liouville equation where the dynamics of a small subset of the degrees of freedom are treated quantum mechanically while the remaining degrees of freedom are treated by classical mechanics to a good approximation. We use this approach as it is computationally tractable, and the resulting equation of motion accurately accounts for the quantum and classical dynamics, as well as the coupling between these two components of the system. By recasting the quantum-classical Liouville equation into the form of a generalized master equation we investigate connections to surface-hopping. The link between these approaches is decoherence arising from interaction of the subsystem with the environment. We derive an evolution equation for the subsystem which contains terms accounting for the effects of the environment. One of these terms involves a memory kernel that accounts for the coherent dynamics. If this term decays rapidly, a Markovian approximation can be made. By lifting the resulting subsystem master equation into the full phase space, we obtain a Markovian master equation that prescribes surface-hopping-like dynamics. Our analysis outlines the conditions under which such a description is valid. Next, we consider the calculation of the rate constant for a quantum mechanical barrier crossing process. Starting from the reactive-flux autocorrelation function, we derive a quantum-classical expression for the rate kernel. This expression involves quantum-classical evolution of a species operator averaged over the initial quantum equilibrium structure of the system making it possible to compute the rate constant via computer simulation. Using a simple model for a proton transfer reaction we compare the results of the rate calculation obtained by quantum-classical Liouville dynamics with that of master equation dynamics. The master equation provides a good approximation to the full quantum-classical Liouville calculation for our model and a more stable algorithm results due to the elimination of oscillating phase factors in the simulation. Finally, we make use of the theoretical framework established in this thesis to analyze some aspects of decoherence used in popular surface-hopping techniques.

Orientador: Prof. Dr. Fernando Luis da Silva Semião / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017.

Made available in DSpace on 2016-06-02T20:15:18Z (GMT). No. of bitstreams: 1 2020.pdf: 852206 bytes, checksum: 2ecfc5be0d185b9d31d4198520c9d7cd (MD5) Previous issue date: 2008-07-03 / Universidade Federal de Sao Carlos / In this thesis we first demonstrate that the inevitable action of the environment can be substantially weakened when considering appropriate nonstationary quantum systems. Beyond protecting quantum states against decoherence, an oscillating frequency can be engineered to make the system-reservoir coupling almost negligible. Differently from the program for engineering reservoir and similarly to the schemes for dynamical decoupling of open quantum systems, our technique does not require a previous knowledge of the state to be protected. However, differently from the previously-reported schemes for dynamical decoupling, our technique does not rely on the availability of tailored external pulses acting faster than the shortest time scale accessible to the reservoir degree of freedom. We show, in the domain of cavity quantum electrodynamics, how to engineer such a nonstationary cavity mode through its dispersive interaction with a driven two-level atom. Next, we consider different aspects of the dynamical Casimir effect (DCE) through the derivation of effective Hamiltonians which exhibit the essential features of the phenomenon. We start by investigating the dynamical Casimir effect in a nonideal cavity at finite temperature. We first compute a general expression for the average number of particle creation, applicable for any law of motion of the cavity boundary. We also compute a general expression for the linear entropy of an arbitrary state prepared in a selected mode, also applicable for any law of motion of the cavity boundary. As an application of our results we have analyzed both the average number of particle creation and linear entropy within a particular oscillatory motion of the cavity boundary. On the basis of these expressions we develop a comprehensive analysis of the resonances in the number of particle creation in the nonideal dynamical Casimir effect. We also demonstrate the occurrence of resonances in the loss of purity of the initial state and estimate the decoherence times associated with these resonances. We also consider the dynamical Casimir effect for a massless scalar field, under Dirichlet boundary conditions, between two concentric spherical shells. We obtain a general expression for vii the average number of particle creation, for an arbitrary law of radial motion of the spherical shells, using two distinct methods: by computing the density operator of the system and by calculating the Bogoliubov coefficients. We apply our general expression to breathing modes: when only one of the shells oscillates and when both shells oscillate in or out of phase. We also analyze the number of particle production and compare it with the results for the case of plane geometry. Finally, we analyze the action of the gravitational field on the dynamical Casimir effect. We consider a massless scalar field confined in a cuboid cavity placed in a gravitational field described by a static and diagonal metric. With one of the plane mirrors of the cavity allowed to move, we compute the average number of particles created inside the cavity by means of the Bogoliubov coefficients computed through perturbative expansions. We apply our result to the case of an oscillatory motion of the mirror, considering a weak gravitational field described by the Schwarzschild metric. The regime of parametric amplification is detailed analyzed, demonstrating that our computed result, for the mean number of particles created, is in agreement with associated particular cases in literature. / Demonstramos nesta tese, primeiramente, que a ação inevitável do meio ambiente pode ser substancialmente enfraquecida quando consideramos sistemas quânticos não estacionários apropriados. Diferentemente do programa de engenharia de reservatórios e de forma similar aos protocolos para o desacoplamento dinâmico de sistemas quânticos abertos, nossa proposta não requer o conhecimento prévio do estado a ser protegido. Diferentemente mesmo dos esquemas de desacoplamento dinâmico, a proteção de estados de modos não estacionários prescinde da disponibilidade de pulsos externos ultra rápidos que atuem sobre o sistema de interesse em intervalos de tempo mais curtos que a menor escala de tempo acessível aos graus de liberdade do reservatório. No domínio da engenharia de estados em eletrodinâmica quântica de cavidades, mostramos como preparar modos não estacionários através da interação dispersiva do campo com átomos de dois níveis submetidos `a amplificação linear. Tratamos, em seguida, de diferentes aspectos do efeito Casimir dinâmico (ECD) através da derivação de hamiltonianos efetivos capazes de descrever convenientemente os principais aspectos do fen omeno. Começamos pelo ECD não ideal a temperaturas finitas. Obtivemos expressões gerais tanto para número médio de partículas criadas como para a entropia linear de um estado arbitrário preparado em um modo selecionado da cavidade, expressões estas que se aplicam a qualquer lei de movimento da fronteira móvel. Desenvolvemos, através destas expressões, uma análise abrangente das ressonâncias presentes tanto na criação de partículas como na perda de pureza e decoerência de estados. Consideramos também o ECD no contexto de um campo escalar não massivo confinado, sob as condições de contorno de Dirichlet, entre duas cascas esféricas concêntricas. Utilizamos dois diferentes métodos, o operador densidade e os coeficientes de Bogoliubov, para o cálculo da expressão geral para o número médio de partículas criadas, válida para qualquer lei de movimento das cascas esféricas. Aplicamos esta expressão para o cálculo do número de partículas produzidas quando apenas uma das cascas oscila ou quando ambas oscilam em fase ou fora de fase, e v comparamos os resultados com aqueles associados `a geometria plana. Por fim, analisamos a ação do campo gravitacional sobre o ECD. Para tal, consideramos um campo escalar não massivo confinado numa cavidade cubóide localizada em um campo gravitacional descrito por uma métrica estática e diagonal. Assumindo que uma das paredes planas da cavidade seja móvel, obtivemos o número de partículas criadas no interior da cavidade através do cálculo, via expansões perturbativas, dos coeficientes de Bogoliubov. Aplicamos o resultado para o caso particular de um movimento oscilatório da fronteira móvel, considerando um campo gravitacional fraco descrito pela métrica de Schwarzschild. O regime de amplificação paramétrica é detalhadamente analisado, demonstrando que nosso resultado para o número médio de partículas criadas, está em acordo com resultados particulares previamente apresentados na literatura.

Made available in DSpace on 2016-06-02T20:15:36Z (GMT). No. of bitstreams: 1 TeseJPCL.PDF: 1080081 bytes, checksum: 07c76f2cdbae84f911a239fe1765ffbe (MD5) Previous issue date: 2006-02-24 / Universidade Federal de Sao Carlos / On this thesis some aspects of relaxation processes and decoherence processes using deformed algebras of the harmonic oscillator, particularly the generalized deformed algebra (GDA algebra) and Kerr algebra were studied.Two situations were considered for this study: a) The system of interest is described as a non-linear harmonic oscillator interacting with a dissipative environment (thermal reservoir), b) the system of interest ( non deformed harmonic oscillator) interacts with a thermal reservoir described by a group of nonlinear quantum harmonic oscillators. An interesting result was found for the two situations , where we notice that the master equation and the expressions found, show the strong dependence of the nonlinearity introduced by the deformed algebra. On case (b) the obtained equations have a form identical to the nondeformed equations, but show new nonlinear coefficients not obtained in the reading.The influence of the reservoirs nonlinearity is noticed in the coefficients found. The phenomenon of decoherence, considered the thermal nonlinear reservoir and the compressed air reservoir that were studied. The master equation that rules the dynamics of the system and an estimated a time of decoherence were obtained , along with important results. It was observed that when there is an increase on the deformed parameter there is also an increase on the decoherence time, showing the nonlinearity contained in the reservoir acts in a significant way over the time of decoherence of the system. / Nesta tese nós estudamos alguns aspectos dos processos de relaxação e de decoerência utilizando as álgebras deformadas do oscilador harmônico, particularmente a álgebra deformada generalizada (GDA álgebra) e álgebra tipo Kerr. Para este estudo consideramos duas situações: (a) O sistema de interesse é descrito como um oscilador harmônico quântico não-linear interagindo com um meio dissipativo (reservatório térmico), e (b) O sistema de interesse (oscilador harmônico quântico sem deformação) interage com um reservatório térmico descrito por um conjunto de osciladores harmônicos quânticos não-lineares. Resultado interessante foi encontrado para as duas situações estudadas, onde observamos que a equação mestra e as expressões obtidas, mostram forte dependência da não-linearidade introduzida pela álgebra deformada. Para o caso (b) as equações obtidas possuem forma idêntica as equações sem deformação, mas apresentam novos coeficientes não-lineares ainda não obtidos na literatura. A influência da não-linearidade do reservatório é observada nos coeficientes encontrados. Também estudamos o fenômeno da decoerência considerando o reservatório térmico não-linear e o reservatório comprimido nãolinear. Obtemos a equação mestra que rege a dinâmica do sistema e estimamos o tempo de decoerência, onde obtemos um resultado importante. Para o tempo de decoerência observamos um crescimento do tempo a medida que os parâmetros de não-lineridade da álgebra crescem, mostrando que não-linearidade contida no reservatório age de maneira significativa sobre o tempo de decoerência do sistema.

Made available in DSpace on 2016-06-02T20:16:52Z (GMT). No. of bitstreams: 1 DissAC.pdf: 4023404 bytes, checksum: c7e0e9de3dacfa2ff41e7b68a4df957d (MD5) Previous issue date: 2005-03-11 / Universidade Federal de Minas Gerais / In this work, we analyse the dissipation and interchange of energy in a system composed by two harmonic oscillators, each one associated with a thermal reservoir. To this end, we employ the Caldeira & Leggett approach, based on path integral formulation, to obtain the time evolution of the reduced density operator of the system composed by both oscillators. / Tratamos, neste trabalho, os processos de troca e dissipação de energia num sistema composto por dois osciladores harmônicos cada qual associado a um reservatório térmico. Para isso, empregamos a abordagem de Caldeira & Leggett, baseada na formulação de integrais de trajetória, para a obtenção da evolução temporal do operador densidade reduzido do sistema composto por ambos os osciladores.

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.