A three-level system can be used in a Λ-type configuration in order to construct auniversal set of non-adiabatic quantum gates through the use of non-Abelian non-adiabatic geometrical phases. Such construction allows for high-speed operation times which diminish the effects of decoherence. This might be, however, accompanied by a breakdown of the validity of the rotating wave approximation (RWA) due to the comparable timescale between the counter-rotating terms and the pulse length, which greatly affects the dynamics. Here we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-18T11:29:37Z No. of bitstreams: 1 arquivototal.pdf: 1956067 bytes, checksum: 845c3d0cd5113c8498d955af9cdcd907 (MD5) / Made available in DSpace on 2017-09-18T11:29:37Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1956067 bytes, checksum: 845c3d0cd5113c8498d955af9cdcd907 (MD5) Previous issue date: 2016-09-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, we deal with a particular geometric scalar tensor theory, which is a version of the Brans-Dicke gravitation, formulated in aWeyl integrable space-time. This formulation is done using the Palatini's variation procedure. The main point of our work is to perform two particular applications of the geometrical Brans-Dicke theory. The rst one is the study of geometric fase transition phenomena, that's related to a continuous change in the space-time structure of the universe from a Riemann's geometry to a Weyl's geometry, or in the inverse sense, from Weyl's geometry to Riemann's geometry. This phenomena seems to take place when the universe starts to expand in a accelerated rate. The second one is the investigation of classical and quantum behaviour of a anisotropic n-dimensional universe . To nd solutions that display the dynamical compacti cation of non observed extra dimensions is the main motivation to study such universe. / Nesta tese, reapresentamos uma teoria escalar tensorial geométrica, que é uma versão da gravitação de Brans-Dicke formulada em um espaço-tempo de Weyl integrável. Com esta teoria fazemos duas aplicações especí cas. Uma delas para o estudo de um fenômeno, que chamamos de transição de fase geométrica, uma mudança contínua na estrutura geom étrica do espaço-tempo. Este fenômeno parece ocorrer quando o universo se expande aceleradamente. A segunda aplicação reside no estudo clássico e quântico do comportamento de um modelo de universo n-dimensional anisotrópico. A motivação para esta investigação é a busca de soluções que exibem o compactação dinâmica das dimensões extras, que não são observadas.

Nous avons étudié, par RPE impulsionnelle, la cohérence quantique et des spins électroniques des ions de transition Mn2+, Co2+, Fe3+, et des complexes Fe3+/Cs+ et Fe3+/Na+, tous présents dans le ZnO monocristallin. Nous avons trouvé que l’anisotropie magnétique peut altérer la cohérence de la phase dynamique des qubits des spins électroniques. Nous avons mesuré une faible décohérence pour les spins d’ions Mn2+et Fe3+ dans ZnO, qui ont tous deux une faible anisotropie magnétique uniaxiale, tandis que les ions Co2+ isolés avec une très forte anisotropie magnétique uniaxiale, une décohérence rapide a été mis en évidence. Nous avons trouvé que les spins électroniques des complexes de type Fe3+/Cs+, ayant un tenseur d’anisotropie magnétique plus complexe que la simple anisotropie uniaxiale des ions Fe3+ isolés, possèdent presque le même temps de décohérence. Par la méthode des perturbations, nous avons mis en évidence théoriquement un terme supplémentaire à la phase habituelle de Berry, dû à l’anisotropie magnétique et qui existe dans tout système ayant un spin S>1/2. / We studied by pulsed EPR (p-EPR), the quantum coherence of electronic spins qubits of isolated transition metal ions of Mn2+, Co2+, Fe3+ and Fe3+/Cs+ as well as Fe3+/Na+ complexes, all found as traces in mono-crystalline ZnO. Indeed, we experimentally demonstrated that the magnetic anisotropy can alter the coherence of the dynamic phase of electronic spins qubits. We found a small decoherence for Mn2+ and Fe3+, spins having a small uniaxial magnetic anisotropy, and on the contrary, we found a very strong decoherence for Co2+ spins having a very strong uniaxial magnetic anisotropy. We found that the electronic spins of the Fe3+/Cs+ complex, having a more complex tensor magnetic anisotropy compared to the simplest uniaxial one of isolated Fe3+ spins in ZnO, have almost the same coherence time. By the perturbation method, we have found theoretically an additional term to the usual geometric Berry phase, due to the magnetic anisotropy which exists in any system having a spin S>1/2.