The present thesis is devoted to an analysis of the possibility of Bose condensates supporting persistent currents in the ring geometry. Our analysis is based on an approach developed by F. Bloch which focuses on the ground state energy of the condensate as a function of its angular momentum L. According to this approach, persistent currents are stable if the energy exhibits a local minimum at some nonzero angular momentum. We have used this approach for a single-species gas within a mean- eld approximation to show that persistent currents are stable at integral multiples of N*hbar, where N is the number of atoms in the system, provided a certain interaction parameter exceeds some critical value. These results are extended to a binary mixture of bosonic atoms and we show that the system is still capable of supporting persistent currents under certain conditions. Some of our conclusions contradict those appearing in the earlier literature. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2012-03-27 10:05:21.831

Heidelberg, Univ., Diss., 2007.

Zugl.: Stuttgart, Univ., Diss., 2008

Proefschrift Universiteit van Amsterdam. / Met een samenvatting in het Nederlands.

Includes bibliographical references (p. 81-82).

Universiẗat, Diss., 2002--München.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Mark G. Raizen. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-Graduação em Física. / Made available in DSpace on 2012-10-24T18:23:18Z (GMT). No. of bitstreams: 1 266969.pdf: 26600994 bytes, checksum: 8dffc317975a25dd4cc0d78fda8738f2 (MD5) / Revisamos brevemente o fenômeno da condensação de Bose-Einstein em poços simples e duplos e a utilização da aproximação de dois modos para descrever os condensados duplos espaciais. Usando a aproximação de dois modos para descrever o duplo condensado espacial encontramos a hamiltoniana semi-clássica que descreve o sistema seguindo dois caminhos distintos de obtenção da descrição semi-clássica, campo médio e segunda quantização, e notamos a consistência entre os resultados encontrados. Analisamos detalhadamente o comportamento da superfície hamiltoniana semi-clássica ao serem variados, independentemente, as magnitudes de cada um dos três parâmetros nela presentes. Notamos que o forçamento periódico do parâmetro de tunelamento de um corpo da hamiltoniana por um tempo determinado possibilita modificar de modo controlado o regime dinâmico em que o sistema se encontra. Isso abre as portas para o controle de população em cada um dos poços de uma armadilha de duplo poço. Finalmente, em uma analogia com um pêndulo de pivô verticalmente forçado, apresentamos a hamiltoniana média resultante do forçamento periódico a altas freqüências do termo de tunelamento de um corpo, resultado este válido somente para os regimes dinâmicos em que a diferença de população é muito pequena.

Ce manuscrit présente les travaux que j'ai effectués au Laboratoire de Physique Théorique durant ma thèse. Ils portent sur l'interaction d'ondes de matière avec des réseaux optiques modulables en temps et en espace. L'utilisation de ces réseaux a permis de contrôler de manière cohérente les propriétés dynamiques d'un gaz d 'atomes ultra-froids. Cette étude théorique a été réalisée en collaboration avec le groupe Atomes Froids du Laboratoire LCAR. Les variations spatiales de l'enveloppe d u réseau créent, localement, des gaps spatiaux créant une cavité de Bragg pour onde de matière, dont nous avons étudié en détail les propriétés et qui a fait l'objet d'une réalisation expérimentale impliquant la propagation d'un condensat de Bose-Einstein de rubidium 85 dans un guide d'onde. Nous avons également étudié la propagation d'un nuage d 'atomes dans un réseau bichromatique qui permet de réaliser un simulateur quantique du modèle de Harper. Le spectre du hamiltonien de ce système a une dimension fractale pouvant être caractérisée nu­ mériquement. Nous avons montré, par ailleurs, qu'il est possible d'exploiter les interactions inter-atomiques répulsives d'un condensat de Bose-Einstein afin d'amplifier les corrélations position-vitesse lors de sa pro­ pagation dans un guide. Notre étude montre qu'une mesure des grandeurs dynamiques locales du nuage atomique permet de sonder expérimentalement les résonances d'un potentiel optique jusqu'à l'échelle du picoKelvin. Enfin, un nuage d'atomes en interaction attractive admet une solution d'équilibre : le soliton. Nous avons démontré, numériquement, que celui-ci peut être utilisé pour sonder des états liés d'un poten­ tiel de taille finie, en peuplant ces états lors d'une expérience de diffusion comme, par exemple, des états de surface. / This thesis presents the studies that I did at the Laboratoire de Physique Théorique. It concerns the interaction between matter waves and time and space depandant optical lattices. Using such lattices allows one to manipulate coherently the dynamical properties of ultra cold atoms. This theoretical study has been done in collaboration with the Cold Atoms group at the LCAR laboratory. The spatial variations of the lattice envelope locally create spatial gaps which create a Bragg cavity for matter waves. We have st udied in detail their properties and the cavity has been realized experimentally by using a Ru bid ium 85 Bose-Einstein condensate in a wave guide. We have also studied the propagation of an atomic cloud in a bichromatic optical lattice which allows us to make a quantum simulator of the Harper madel. The spectrum of the system Hamiltonian· posseses a fractal dimension which can be numerically characterized. We have also shawn that it is possible to use the repulsive interatomic interaction of a Bose-Einstein condensate in arder to amplify the momentum-position correlation during propagation in a guide. Our st udy shows that a mesure of local dynamical quantities of the atomic cloud enables one to experimentally probe resonances of an optical potential down to the picoKelvin scale. At last, an atomic cloud with attractive interactions admit a stable solution, the soliton. We have numerically demonstrated that this soliton can be used to probe bound states of a potential by populating those states through a scattering experiment, for example surface states.