Made available in DSpace on 2015-05-14T12:14:08Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1944924 bytes, checksum: e08f0978e6406af124c9fe4875d2aa1e (MD5) Previous issue date: 2013-06-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis we discuss some fundamental aspects of the quantum theory from a contemporaneous point of view, where we could develop three works. In the first we analyze theoretically an atomic double-slit interferometer. It has been shown that if the energy eigenstates of the atom are correlated with its particle and wave behaviors, complementary phenomena can be measured simultaneously, indicating a reinterpretation of the complementarity principle. We also demonstrate that this experiment possesses quantum erasure properties. In the second we present a two-particle interferometer in order to analyze the way in which decoherence affects quantum interference. It has been shown how the environmental constituents, here considered as photons, can destroy the oscillations in the coincidence detection rate of the particles. Due to the temporal characteristic of this kind of interference, we name this process as quantum temporal decoherence. In the last work we study the existence of a novel complete family of exact and orthogonal solutions of the paraxial wave equation. The complex amplitude of these beams is proportional to the confluent hypergeometric functions, which we name hypergeometric modes of type-II (HyG-II). It is formally demonstrated that a hyperbolic-index medium can generate and support the propagation of such a class of beams. Since these modes are eigenfunctions of the photon orbital angular momentum, we conclude that an optical fiber with hyperbolic-index profile could take advantage over other graded-index fibers by the capacity of data transmission. / Nesta tese discutimos alguns aspectos fundamentais da teoria quântica de um ponto de vista mais contemporâneo, onde também pudemos desenvolver três trabalhos. No primeiro analisamos teoricamente um interferômetro de fenda dupla para átomos. Mostramos que se os autoestados de energia do átomo estão correlacionados com os comportamentos de partícula e de onda do mesmo, fenômenos complementares podem ser medidos simultaneamente, indicando uma reinterpretação do princípio da complementaridade. O mesmo aparato também apresentou propriedades de apagador quântico. No segundo apresentamos um interferômetro de duas partículas e a maneira como a decoerência afeta o grau de interferência. Mostramos como os constituintes do ambiente, aqui considerados como fótons, podem destruir a oscilação na taxa de coincidência de detecção das partículas. Devido a sua característica temporal, chamamos este processo de decoerência temporal quântica. No último trabalho estudamos a existência de uma nova família de soluções ortogonais da equação paraxial da luz. A amplitude complexa desses feixes são proporcionais às funções hipergeométricas confluentes, que denominamos modos hipergeométricos do segundo tipo (HyG-II). Demonstramos formalmente que um meio com um perfil hiperbólico de índice de refração pode gerar e suportar essa classe de feixes. Uma vez que esses modos são autofunções do momento angular orbital do fóton, concluímos que uma fibra ótica com este perfil de índice, em certas situações, poderia levar vantagem em relação a outras fibras com índice variável na capacidade de transmissão de dados.

Nessa dissertação, abordamos o problema de dois qubits interagindo com campos externos e entre si controladamente, de acordo com um Hamiltoniano considerado realista para implementação da porta lógica quântica XOR. Introduzimos acoplamentos entre as observáveis do sistema de dois qubits e um banho de osciladores harmônicos a fim de tratarmos o problema da dissipação e da decoerência. Primeiramente nós consideramos o limite no qual a decoerência é mais rápida que qualquer processo gerado pelo Hamiltoniano do sistema. Prosseguimos então, através do método numérico conhecido como Integrador Unitário, com o estudo da matriz densidade do sistema durante a operação da porta lógica quântica sem incluir, inicialmente, o acoplamento com o banho de osciladores harmônicos. Finalmente, implementamos o método numérico conhecido como Propagador quase adiabático para estudar a decoerência e a dissipação durante a operação da porta lógica quântica XOR, a fim de analisarmos os aspectos perturbativos do sistema quântico de dois qubits. / In this dissertation, we approach the problem of two qubits interading with themselves and with externa1 fields in a controlled way, according to a Hamiltonian considered realistic to implement the XOR quantum gate. We introduce couplings between the observables of the two-qubits system and of a bath of harmonic oscillators, to treat the problems of dissipation and decoherence. Preliminarly, we consider the limit in which decoherence is faster than any process dictated by the Hamiltonian evolution of the system. Then, through a unitary-integrator numerical method, we proceed with the study of the evolution of the density matrix of the system during the operation of the logical quantum gate, initially, without the coupling with the bath of harmonic oscillators. Finally, we use the quasiadiabatic path integral method to study the dissipation and decoherence during the logical operation, through the inclusion of the bath.

Nesta tese abordamos o problema de transferência e manipulação de informação quântica em sistemas dissipativos. Inicialmente apresentamos uma técnica para construir, dentro de redes bosônicas dissipativas, canais livres de decoerência (CLD): um grupo de modos normais de osciladores com taxas de amortecimento efetivas nulas. Verificamos que os estados protegidos dentro do CLD definem subespaços livres de decoerência (SLD) quando mapeados de volta para a base dos osciladores naturais da rede. Portanto, a nossa técnica para obter canais protegidos formados por modos normais é uma forma alternativa para construir SLD, que oferece vantagens em relação ao método convencional. Nosso protocolo permite o cálculo de todos os estados da rede protegidos de uma só vez, assim como leva naturalmente ao conceito de subespaço quase livre de decoerência (SQLD), dentro do qual um estado de superposição é quase completamente protegido. O conceito de SQLD, é mais fraco do que a dos SLD, pode proporcionar um mecanismo mais manejável para controlar decoerência. Em seguida desenvolvemos um protocolo para transferência quase perfeita de estados de poláriton de um sistema emissor para um receptor, separados espacialmente, ambos acoplados por um canal de transmissão não ideal que é modelado por uma rede de cavidades dissipativas. Esse protocolo consiste no acoplamento dispersivo entre o estado de poláriton preparado no emissor com os modos normais da rede que forma o canal, o que possibilita que o estado tunele para o receptor. Após a obtenção de um Hamiltoniano efetivo para o acoplamento entre o emissor e receptor, calculamos a fidelidade para a transferência de alguns estados de poláriton, por exemplo, estados tipo gato de Schrödinger. Mostramos que as taxas de decaimento da fidelidade são proporcionais a cooperatividade, parâmetro esse que avalia a relação entre a taxa de dissipação e o acoplamento efetivo. Analisamos a dependência da fidelidade e do tempo de transferência em relação à topologia da rede. Por fim, propomos o mecanismo de tunelamento não local para transferência de estados bosônicos e fermiônicos com alta fidelidade. Demonstramos que a incoerência decorrente das não idealidades quânticas do canal é quase totalmente contornada pelo mecanismo de tunelamento que possibilita um processo de transferência de alta fidelidade. Aplicamos esse mecanismo para transferência e processamento de informações entre múltiplos circuitos quântico (CQs) não ideais. Um conjunto de saídas é simultaneamente acoplado ao conjunto correspondente de entradas de outro QC espacialmente separado do primeiro, através de um único canal quântico não ideal. Mostramos que além da transferência de estados, podemos realizar operações logicas entre qubits distantes e gerar uma pletora de estados quânticos emaranhados. / In this thesis we address the problem of transfer and manipulation of quantum information in dissipative systems. First we present a technique to build, within a dissipative bosonic network, decoherence-free channels (DFCs): a group of normal-mode oscillators with null effective damping rates. We verify that the states protected within the DFC define the wellknown decoherence-free subspaces (DFSs) when mapped back into the natural network oscillators. Therefore, our technique to build protected normal-mode channels turns out to be an alternative way to build DFSs, which offers advantages over the conventional method. It enables the computation of all the network-protected states at once, as well as leading naturally to the concept of the decoherence quasi-free subspace (DQFS), inside which a superposition state is quasi-completely protected against decoherence. The concept of the DQFS, weaker than that of the DFS, may provide a more manageable mechanism to control decoherence. Finally, as an application of the DQFSs, we show how to build them for quasi-perfect state transfer in networks of coupled quantum dissipative oscillators. Then we present a scheme for quasi perfect transfer of polariton states from a sender to a spatially separated receiver, both composed of high-quality cavities filled by atomic samples. The sender and the receiver are connected by a nonideal transmission channel the data bus modelled by a network of lossy empty cavities. In particular, we analyze the influence of a large class of data-bus topologies on the fidelity and transfer time of the polariton state. Moreover, we also assume dispersive couplings between the polariton fields and the data-bus normal modes in order to achieve a tunneling-like state transfer. Such a tunneling-transfer mechanism, by which the excitation energy of the polariton effectively does not populate the data-bus cavities, is capable of attenuating appreciably the dissipative effects of the data-bus cavities. After deriving a Hamiltonian for the effective coupling between the sender and the receiver, we show that the decay rate of the fidelity is proportional to a cooperativity parameter that weigh the cost of the dissipation rate against the benefit of the effective coupling strength. The increase of the fidelity of the transfer process can be achieved at the expense of longer transfer times. We also show that the dependence of both the fidelity and the transfer time on the network topology for distinct regimes of parameters. It follows that the data-bus topology can be explored to control the time of the state-transfer process. Finally we propose the nonlocal tunneling mechanism for high-fidelity state transfer between distant parties. We apply this mechanism for highfidelity information transfer and processing between remote multi-branch nonideal quantum circuits (QCs). We show that in addition to the transfer of states, we can perform logic operations between distant qubits and generate a plethora of entangled quantum states.

Realizamos nesse trabalho um tratamento abrangente da interação entre um sistema quântico e o meio ambiente modelado como um conjunto de osciladores harmônicos. Partimos para isso de um tratamento prévio de redes de osciladores harmônicos quânticos dissipativos. Utilizando a função característica, transformamos a equação de von Neumann em uma equação diferencial, e explorando a sua linearidade, essa é transformada em uma equação vetorial, cuja resolução é computacionalmente eficiente. Nosso formalismo, que parte de uma rede de osciladores harmônicos, não necessariamente dividida entre sistema e meio ambiente, permite que se contorne a necessidade da hipótese de acoplamento súbito sistema-reservatório para o tratamento exato da evolução do sistema. Em seguida, mostramos que essa evolução pode ser sempre descrita por uma equação mestra na forma usual de Lindblad, embora os coeficientes que a definem possam ser dependentes do tempo. Isso abre novas possibilidades para a dinâmica do sistema, e leva a efeitos que podem ser classificados de não-Markovianos, embora sejam descritos por uma equação mestra completamente local no tempo. Ressaltamos que, por ser baseado em uma solução exata, o método pode ser aplicado para qualquer intensidade de acoplamento, e é consideravelmente mais simples do que outros métodos disponíveis para esse fim, como os baseados em integrais de trajetória. Por fim, utilizamos simulações computacionais para explorar a validade das aproximações de ondas girantes e de Born-Markov, e os fenômenos que podem ser observados nos regimes em que elas deixam de ser válidas. / We present a comprehensive treatment of the interaction of a quantum system with an environment modeled as a set of harmonic oscillators. We start from a previous treatment of a network of quantum dissipative harmonic oscillators. Using the characteristic function, we transform the von Neumann equation in a differential equation, and exploring its linearity, this is transformed in a vector equation, whose solution is computationally efficient. Our method, whose origin lies on a network not necessarily divided into system and reservoir, allows us to circumvent the necessity of the sudden-coupling approximation for the exact treatment of the system evolution. After this, we show that this dynamics can always be described by a master equation in standard Lindblad form, although its coefficients may be functions of time. This opens new possibilities for the system dynamics, and lead to effects that may be called non-Markovian, even if they are described by a completely local-in-time master equation. It should be emphasized that, as it is based on an exact solution, the method may be applied for any strength of the system-reservoir interaction, and it is considerably simpler than other available methods, such as those based on path integrals. Finally, we employ computer simulations to investigate the validity of the rotating-wave and Born-Markov approximations, and the phenomena that migth be observed in regimes in which they fail to be valid.

Fenômenos que ocorrem a tempos curtos em sistemas quânticos abertos são caracterizados por possuírem um tempo característico de uma ordem muito menor que o tempo de relaxação do sistema. Como exemplos podemos citar o efeito de decoerência, que em resumo tenta explicar como a natureza quântica de um sistema é perdida ao longo da interação com o ambiente e o fenômeno de superradiância, onde estuda-se como alguns sistemas emitem um pulso energético muito rápido gerando um pico de intensidade fino localizado muito antes da relaxação do sistema. O objetivo desse trabalho é não só estudar esses fenômenos mas como apresentar uma técnica alternativa para a quantificação das medidas associadas e de seus tempos característicos. A técnica apresentada se baseia em fazer uma expansão perturbativa no tempo para o operador densidade a partir de uma equação mestra quântica e com seu uso calcular grandezas físicas relevantes a fenômenos que ocorrem a tempos curtos. A simplicidade da técnica e seu uso abrangente são os principais fatores motivadores deste trabalho. / Short-time phenomena in open quantum systems are characterized by having a characteristic time of a much lower order than the relaxation time of the system. As examples we can mention the effect of decoherence, which in summary tries to explain how the quantum nature of a system is lost along the interaction with the environment and the superradiance phenomenon, where is studied how some systems emit a very fast energy pulse generating a peak of fine intensity located long before the relaxation of the system. The aim of this work is not only study these phenomena but to present an alternative technique for quantifying the associated measures and their characteristic times. The presented technique is based on making a perturbative expansion in time for the density operator from a quantum master equation and use it to calculate physical quantities relevant to phenomena occurring at short times. The simplicity of the technique and its widespread use are the main motivating factors of this work.

Nesta dissertação apresentamos um estudo dos mecanismos de decoerência de sistemas quânticos de Ressonância Magnética Nuclear (RMN) e os seus efeitos sobre a evolução temporal das medidas de correlação não-clássica. Para tal, apresentaremos inicialmente uma revisão bibliográfica sobre alguns dos diversos quantificadores de discórdia quântica, tais como discórdia entrópica, geométrica e negatividade do caráter quântico. Para descrever os canais de atenuação de fase e de amplitude generalizada, que descrevem a relaxação de sistemas de RMN, utilizamos o formalismo de operações quânticas, através da descrição dos operadores de Kraus. As implementações experimentais foram realizadas a partir de sistemas de 2 q-bits descritos por sistemas de RMN de 2 spins 1/2 acoplados via acoplamento J e sistemas de spins 3/2 sujeitos ao acoplamento quadrupolar. Experimentalmente, observamos o surgimento do fenômeno de congelamento (freezing) da discórdia quântica para o sistema de 2 spins 1/2 e o fenômeno de duplo sudden-change em um sistema de spin 3/2. Além disso, propuzemos um método de medida direta para os elementos da matriz densidade de um sistema de 2 spins 1/2 acoplados via acoplamento J, que permite obter toda a informação necessária para o cálculo dos quantificadores de discórdia sem que seja preciso reconstruir completamente a matriz densidade, ou seja, sem empregar o dispendioso método de tomografia de estado quântico (TEQ). / We present a study of the decoherence processes in Nuclear Magnetic Resonance (NMR) quantum systems and their effects on the temporal evolution of non-classical correlations. For that, we review some quantum discord quantifiers, such as entropic and geometric discord as well as negativity of quantumness. To describe the relaxation of NMR systems, we use Kraus operators phase and generalized amplitude damping channels. The experimental demonstrations were achieved in 2 qubits systems implemented by J coupled spins 1/2 as well as spins 3/2 subject to quadrupolar interaction. We demonstrate the freezing phenomenon of quantum discord in a 2 spins 1/2 system, subject to phase and amplitude damping channel, and the phenomenon of double sudden-change in a spin 3/2 system, subject to amplitude damping channel. Furthermore, for spin 1/2 system, we introduce a method to selectively measure density matrix elements, that provide the necessary information to calculate discord quantifiers, without needing the full reconstruction provided by usual quantum state tomography.

Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature.

La simulation quantique consiste à réaliser expérimentalement des systèmes artificiels équivalent à des modèles proposés par les théoriciens. Pour réaliser ces systèmes, il est possible d'utiliser des atomes dont les états individuels et les interactions sont contrôlés par la lumière. En particulier, une fois excités dans un état de haute énergie (appelé état de Rydberg), les atomes peuvent être contrôlés individuellement et leurs interactions façonnées arbitrairement par des faisceaux laser. Cette thèse s'intéresse à deux types de simulateurs quantiques à base d'atomes de Rydberg, et en particulier à leurs potentielles limitations.Dans l'expérience du Joint Quantum Institute (USA), nous observons la décohérence dans une structure cubique contenant jusqu'à 40000 atomes. A partir d'atomes préparés dans un état de Rydberg bien défini, nous constatons l'apparition spontanée d'états de Rydberg voisins et le déclenchement d'un phénomène d'avalanche. Nous montrons que ce mécanisme émane de l'émission stimulée produite par le rayonnement du corps noir. Ce phénomène s'accompagne d'une diffusion induite par des interactions de type dipole-dipole résonant. Nous complétons ces observations avec un modèle de champ moyen en état stationnaire. Dans un second temps, l'étude de la dynamique du problème nous permet de mesurer les échelles de temps caractéristiques. La décohérence étant globalement néfaste pour la simulation quantique, nous proposons plusieurs solutions pour en atténuer les effets. Nous évaluons notamment la possibilité de travailler dans un environnement cryogénique, lequel permettrait de réduire le rayonnement du corps noir.Dans l'expérience du Laboratoire Charles Fabry à l'Institut d'Optique (France), nous analysons les limites d'un simulateur quantique générant des structures bi- et tridimensionnelles allant jusqu'à 70 atomes de Rydberg piégés individuellement dans des pinces optiques. Le système actuel étant limité par le temps de vie des structures, nous montrons que l'utilisation d'un cryostat permettrait d'atteindre des tailles de structures jusqu'à 300 atomes. Nous présentons les premiers pas d'une nouvelle expérience utilisant un cryostat à 4K, et en particulier les études amont pour le développement de composants optomécaniques placés sous vide et à froid. / Quantum simulation consists in engineering well-controlled artificial systems that are ruled by the idealized models proposed by the theorists. Such toy models can be produced with individual atoms, where laser beams control individual atomic states and interatomic interactions. In particular, exciting atoms into a highly excited state (called a Rydberg state) allows to control individual atoms and taylor interatomic interactions with light. In this thesis, we investigate experimentally two different types of Rydberg-based quantum simulators and identify some possible limitations.At the Joint Quantum Institute, we observe the decoherence of an ensemble of up to 40000 Rydberg atoms arranged in a cubic geometry. Starting from the atoms prepared in a well-defined Rydberg state, we show that the spontaneous apparition of population in nearby Rydberg states leads to an avalanche process. We identify the origin of the mechanism as stimulated emission induced by black-body radiation followed by a diffusion induced by the resonant dipole-dipole interaction. We describe our observations with a steady-state mean-field analysis. We then study the dynamics of the phenomenon and measure its typical timescales. Since decoherence is overall negative for quantum simulation, we propose several solutions to mitigate the effect. Among them, we discuss the possibility to work at cryogenic temperatures, thus suppressing the black-body induced avalanche.In the experiment at Laboratoire Charles Fabry (Institut d'Optique), we analyze the limitation of a quantum simulator based on 2 and 3 dimensional arrays of up to 70 atoms trapped in optical tweezers and excited to Rydberg states. The current system is limited by the lifetime of the atomic structure. We show that working at cryogenic temperatures could allow to increase the size of the system up to N=300 atoms. In this context, we start a new experiment based on a 4K cryostat. We present the early stage of the new apparatus and some study concerning the optomechanical components to be placed inside the cryostat.

No / We show that the multidimensional Zeno effect combined with non-holonomic control allows one to efficiently protect quantum systems from decoherence by a method similar to classical random coding. The method is applicable to arbitrary error-inducing Hamiltonians and general quantum systems. The quantum encoding approaches the Hamming upper bound for large dimension increases. Applicability of the method is demonstrated with a seven-qubit toy computer.

This thesis describes theoretical and experimental work whose main aim is the development of techniques for using trapped ⁴³Ca⁺ ions for quantum information processing. I present a rate equations model of ⁴³Ca⁺, and compare it with experimental data. The model is then used to investigate and optimise an electron-shelving readout method from a ground-level hyperfine qubit. The process is robust against common experimental imperfections. A shelving fidelity of up to 99.97% is theoretically possible, taking 100 μs. The laser pulse sequence can be greatly simplified for only a small reduction in the fidelity. The simplified method is tested experimentally with fidelities up to 99.8%. The shelving procedure could be applied to other commonly-used species of ion qubit. An entangling two-qubit quantum controlled-phase gate was attempted between a ⁴⁰Ca⁺ and a ⁴³Ca⁺ ion. The experiment did not succeed due to frequent decrystallisation of the ion pair, and strong motional decoherence. The source of the problems was never identified despite significant experimental effort, and the decision was made to suspend the experiments and continue them in an improved ion trap which is under construction. A sequence of pi-pulses, inspired by the Hahn spin-echo, was derived that is capable of greatly reducing dephasing of any qubit. If the qubit precession frequency varies with time as an nth-order polynomial, an (n+1) pulse sequence is theoretically capable of perfectly cancelling the resulting phase error. The sequence is used on a 43Ca+ magnetic-field-sensitive hyperfine qubit, with 20 pulses increasing the coherence time by a factor of 75 compared to an experiment without any spin-echo. In our ambient noise environment the well-known Carr-Purcell-Meiboom-Gill dynamic-decoupling method was found to be comparably effective.