Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-05-02T12:20:47Z No. of bitstreams: 1 DissOFG.pdf: 1455470 bytes, checksum: 9d1a7b11f10dc60d101427a7db7287f8 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-04T12:06:15Z (GMT) No. of bitstreams: 1 DissOFG.pdf: 1455470 bytes, checksum: 9d1a7b11f10dc60d101427a7db7287f8 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-04T12:06:22Z (GMT) No. of bitstreams: 1 DissOFG.pdf: 1455470 bytes, checksum: 9d1a7b11f10dc60d101427a7db7287f8 (MD5) / Made available in DSpace on 2017-05-04T12:10:29Z (GMT). No. of bitstreams: 1 DissOFG.pdf: 1455470 bytes, checksum: 9d1a7b11f10dc60d101427a7db7287f8 (MD5) Previous issue date: 2009-08-12 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / In this dissertation we presente a study on the entanglement between two identical and noninteracting two-level atoms, generated by their interaction with only a singl cavity filed mode. We also show how to calculate the intensity of correlation between thes atoms by Concurrence. Besides, was show the entanglement evolution for different field states and parameters for these states in two intaraction regimes: ressonant and dispersive, showing numerically how the maximum entanglement evolves form one regime to other for each cavity filed state. We are also abble to identify wich parameters influence the intensity and shape of entanglement, allowing us to define a non-classicality criterion for the radiation field. / Nesta dissertação apresentamos um estudo sobre o emaranhamento entre dois átomos de dois níveis idênticos e que não interagem entre si, gerado a partir da interação desses com um único modo do campo eletromagnético contido em uma cavidade. Apresentamos também uma maneira de se calcular a correlação entre esses dois átomos através da Concurrence. Além disso, mostramos a evolução do emaranhamento para diferentes estados do campo e variados parâmetros do mesmo em dois regimes de interação: ressonante e disperssivo. Mostramos numericamente como o emaranhamento máximo de cada um dos casos estudados evolui de um regime para o outro. Por fim, pudemos identificar quais são os parâmetros que influenciam na intensidade e na forma do emaranhamento buscando assim, um critério de não-classicalidade para o campo de radiação.

This thesis contains several theoretical studies on optomechanical systems, i.e. physical devices where mechanical degrees of freedom are coupled with optical cavity modes. This optomechanical interaction, mediated by radiation pressure, can be exploited for cooling and controlling mechanical resonators in a quantum regime. The goal of this thesis is to propose several new ideas for preparing meso- scopic mechanical systems (of the order of 10^15 atoms) into highly non-classical states. In particular we have shown new methods for preparing optomechani-cal pure states, squeezed states and entangled states. At the same time, proce-dures for experimentally detecting these quantum effects have been proposed. In particular, a quantitative measure of non classicality has been defined in terms of the negativity of phase space quasi-distributions. An operational al- gorithm for experimentally estimating the non-classicality of quantum states has been proposed and successfully applied in a quantum optics experiment. The research has been performed with relatively advanced mathematical tools related to differential equations with periodic coefficients, classical and quantum Bochner’s theorems and semidefinite programming. Nevertheless the physics of the problems and the experimental feasibility of the results have been the main priorities. / Die vorliegende Arbeit besteht aus verschiedenen theoretischen Untersuchungen von optomechanischen Systemen, das heißt physikalische Bauteile bei denen mechanische Freiheitsgrade mit Lichtmoden in optischen Kavitäten gekoppelt sind. Diese optimechanischen Wechselwirkungen, die über den Strahlungsdruck vermittelt werden, lassen sich zur Kühlung und Kontrolle von mechanischen Resonatoren im Quantenregime verwenden. Das Ziel dieser Arbeit ist es, verschiedene neue Ideen für Methoden vorzuschlagen, mit denen sich mesoskopische mechanische Systeme (bestehend aus etwa 10^15 Atomen) in sehr nicht-klassischen Zuständen präparieren lassen. Außerdem werden Techniken beschrieben, mit denen sich diese Quateneffekte experimentell beobachten lassen. Insbesondere wird ein quantitatives Maß für Nichtklassizität auf der Basis von Quasiwahrscheinlichkeitsverteilungen im Phasenraum definiert und ein operationeller Algorithmus zu dessen experimenteller Beschrieben, der bereits erfolgreich in einem quantenoptischen Experiment eingesetzt wurde.

[pt] A Mecânica Quântica é uma das teorias mais bem sucedidas de todos os tempos. Não apenas tem um grande poder preditivo, como também mudou completamente a maneira como entendemos a física. No entanto, a Mecânica Quântica não prevê o próprio alcance, e, em princípio, a descrição probabilística deveria ser válida em nosso mundo macroscópico. Mas isso não acontece. Um ponto central do porquê a descrição quântica é substituída pela Mecânica Clássica, é a descoerência. A interação dos muitos graus de liberdade de um ambiente macroscópico faz com que seja extremamente difícil medirmos as propriadades quânticas de um sistema. Nesse contexto, exploramos como ainda podemos detectar efeitos não-clássicos de osciladores harmônicos em um regime intermediário, através da optomecânica. Neste trabalho apresentamos fundamentos do formalismo da optomecânica, tanto a dinâmica unitária, quanto para sistemas quânticos abertos. Depois, discutimos dois sistemas optomecânicos distintos, ressaltando como podemos investigar a presença de características quânticas. Além disso, discutiremos outras abordagens para identifcar características quânticas de osciladores harmônicos em situações cada vez mais próximas ao regime macroscópico. / [en] Quantum Mechanics is one of the most successful theories of all time. It not only has a great predictive power, but also has completely changed the way physics is understood. However, Quantum Mechanics does not predict its own range of validity, and, in principle, the probabilistic description should be valid in our macroscopic world. But it does not happen. In the core of the explanation of why the description from Quantum Mechanics is substituted by Classical Mechanics lies decoherence. The interaction of the many unseen degrees of freedom from a macroscopic environment with a quantum system makes it extremely hard to measure its quantum properties. In this context, we explore how one can still detect non-classicality of oscillators in a intermediate regime, whether in a mesoscopic scale or a oscillator with a macroscopic number of excitations, via an optomechanical description. In this work, we present the basics of the formalism of optomechanics, both in the unitary dynamics and in an open quantum system approach. We then discuss two different optomechanical systems, highlighting how we can perceive its quantum features. At last, we discuss other possible schemes to identify the quantum nature of harmonic oscillators in situations of increasing macroscopic nature.