In this thesis we study various dissipative processes that are associated with the flow of an atomic Bose-Einstein condensate at zero temperature. In particular, we investigate the effect of a weak correlated disorder potential on the collective dipole motion of a harmonically-confined elongated condensate. By using an extension of the Harmonic Potential Theorem, we demonstrate that the dynamics of the system can be described equivalently in terms of a disorder potential oscillating relative to a stationary condensate. This latter point of view allows the application of linear response theory to determine the drag force experienced by the condensate and to evaluate the damping rate of the centre of mass oscillation. The density response function for the elongated condensate is determined with a new local density approximation that takes into account the tight radial confinement of the atomic cloud. Our linear response theory reveals the detailed dependence of the damping rate on various system parameters. A comparison with available experimental data is only partially successful and points to the need for additional experiments. In addition to disorder induced dissipation, we also consider a variety of other problems that can be addressed by means of linear response theory. For example, we study momentum transferred to a condensate by a Bragg pulse and the energy absorption of a gas in an optical lattice that is parametrically modulated in different ways. All of these applications demonstrate the utility of linear response theory in describing the dynamics of Bose-condensed systems which are subjected to weak perturbations. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-04-26 10:54:11.915

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Este trabalho consiste basicamente em dois experimentos: Determinação da equação de estado de um gás frio aprisionado, e na comparação das temperaturas de uma amostra de átomos confinadas em dois tipos de armadilhas magneto-ópticas. No primeiro experimento utilizamos a generalização do conceito de pressão e volume que foram redefinidos de maneira apropriada para alcançamos uma equação de estado. Experimentalmente nossa amostra apresentou um desvio do esperado para um gás ideal, dessa forma utilizamos uma expansão virial com as novas definições de pressão e volume para investigar as interações entre os átomos. Já no segundo experimento utilizamos uma técnica que mede transiente temporal da absorção do feixe pelos átomos através de um fotodetector para a obtenção da temperatura. Neste experimento obtemos temperaturas equivalentes para as duas armadilhas. / This work consists of two experiments: Determination of the state equation a trapped cold gas, and the comparison of the temperatures of confined atoms in two types of magneto-optical traps. For the first experiment we generalized and defined a new pressure and volume concept and we reached a state equation. Experimentally our sample presented a deviation of the ideal gas, in that way we used a virial expansion with the new pressure and volume definitions to investigate the interactions among the atoms. In the second experiment we used a technique that measures temporal variation of the absorption of a probe beam that crosses the atoms by a photodetector, witch gives us the information about the temperature. We have found equivalent temperatures for the two traps.

The first and main part of this thesis concerns the quantization of the transverse transport in diverse periodic quantum systems. From a theoretical point of view, the Hall conductivity's quantization may be understood at the single-particle level in terms of topological invariants. In periodic media such as crystals, the single-particle energy spectrum depicts a specific band structure. A modern approach, based on topology and differential geometry, consists in assigning an abstract mathematical object, a fibre bundle, to each energy band. The fibre bundle's topology is measured by a topological invariant, called the Chern number, which only takes integral values. Surprisingly, the transverse conductivity can be expressed as a sum of Chern numbers. In this work, one provides a rigorous derivation of this fact and one presents several methods which allow the numerical and analytical computation of the Chern numbers for diverse systems. The first original study concerns the physics of ultracold atoms trapped in optical lattices. These very popular experimental setups, which are currently designed in several laboratories worldwide, allow for the exploration of fundamental problems encountered in modern physics. In particular atoms trapped in optical lattices reproduce with a very high accuracy the physics of the Hubbard-type models which describe a huge variety of condensed matter phenomena, such as high-Tc superconductivity and the Mott quantum phase transition. Particularly interesting is the possibility to create artificial magnetic fields in optical lattices. Generated by complex laser configurations or by rotation of the trap, these artificial fields allow the simulation of electronic systems subjected to intense magnetic fields. In this thesis, one explores the possibility of a quantum Hall-like effect for neutral particles in such arrangements. In particular one focuses on the exotic situation in which non-Abelian gauge potentials are generated in the system. In these interesting arrangements, the atomic hoppings are assisted by external lasers and are described by non-commutating translation operators. The non-Abelian fields which are generated in these systems are well known in high-energy physics, where they play a key role in modern theories of fundamental interactions. Thereafter, our study of the IQHE in periodic systems concerns quantum graphs. These models which describe the propagation of a quantum wave within an arbitrary complex object are extremely versatile and hence allow the study of various interesting quantum phenomena. Quantum graphs appear in diverse fields such as solid state physics, quantum chemistry, quantum chaology and wave physics. On the other hand, in the context of quantum chaology, graphs have been the vehicle to confirm important conjectures about chaos signatures. In this thesis, one studies the spectral and chaological properties of infinite rectangular quantum graphs in the presence of a magnetic field. One then establishes the quantization of the Hall transverse conductivity for these systems. The second part of the thesis is devoted to the physics of interacting atoms trapped in optical lattices and subjected to artificial gauge potentials. One explores the Mott quantum phase transition in both bosonic and fermionic optical lattices subjected to such fields. The optical lattices are described through the Hubbard model in which the dynamics is ruled by two competing parameters: the interaction strength U and the tunneling amplitude t. The Mott phase is characterized by a commensurate filling of the lattice and is reached by increasing the ration U/t, which can be easily achieved experimentally by varying the depth of the optical potential. In this thesis one studies how this quantum phase transition is modified when the optical lattice is subjected to diverse artificial gauge potentials. Moreover, one shows that vortices are created in bosonic optical lattices in the vicinity of the Mott regime. The vortices are topological defects in the macroscopic wave function that describes the superfluid. One comments on the vortex patterns that are observed for several configurations of the gauge potential. %%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%% La physique statistique quantique prédit l’émergence de propriétés remarquables lorsque la matière est soumise à des conditions extrêmes de basses températures. Aujourd’hui ces nouvelles phases de la matière jouent un rôle fondamental pour les technologies actuelles et ainsi méritent d’être étudiées sur le plan théorique. Dans le cadre de ma thèse, j’ai étudié l’effet Hall quantique qui se manifeste dans des systèmes bidimensionnels ultra froids et soumis à des champs magnétiques intenses. Cet effet remarquable se manifeste par la quantification parfaite d’un coefficient de transport appelé conductivité de Hall. Cette grandeur physique évolue alors sur divers plateaux qui correspondent à des valeurs entières d’une constante fondamentale de la nature. D’un point de vue théorique, cette quantification peut être approchée par la théorie des espaces fibrés qui permet d’exprimer la conductivité de Hall en termes d’invariants topologiques. Nous explorons l'effet Hall quantique pour différents systèmes en nous appuyant sur l’interprétation topologique de la quantification de la conductivité de Hall. Nous démontrons ainsi que l’effet Hall quantique se manifeste aussi bien dans les métaux que dans les graphes quantiques et les réseaux optiques. Les graphes quantiques sont des modèles permettant l’étude du transport dans des circuits fins, alors que les réseaux optiques sont des dispositifs actuellement réalisés en laboratoire qui piègent des atomes froids de façon périodique. Considérant différents champs magnétiques externes et variant la géométrie des systèmes, nous montrons que cet effet subit des modifications remarquables. Notamment, l’effet Hall quantique est représenté par des diagrammes des phases impressionnants : les multiples phases correspondant à la valeur entière de la conductivité de Hall se répartissent alors dans des structures fractales. De plus, ces diagrammes des phases se révèlent caractéristiques des différents systèmes étudiés. D’autre part, nous étudions la transition quantique de Mott dans les réseaux optiques. En augmentant l’interaction entre les particules, le système devient isolant et se caractérise par le remplissage homogène du réseau. Nous étudions également l’apparition de tourbillons quantiques lorsque le système est soumis à un champ magnétique au voisinage de la phase isolante.

This thesis describes the advances made towards a dual-species magneto-optical trap (MOT) of Li and Rb for use in photoassociation spectroscopy, Feshbach resonance studies, and, as long-term aspirations, the formation of ultracold heteronuclear polar molecules. The initial discussion will focus on a brief theoretical overview of laser cooling and trapping and the production of ultracold molecules from a cold atom source. Subsequently, details of the experimental system, including those pertaining to the required laser light, the vacuum chamber, and the computer control system will be presented. Finally, preliminary optimization and characterization measurements showing the performance of a single species Li MOT are introduced. These measurements demonstrated the loading of over 8 x 107 Li atoms directly into a MOT without the need for a Zeeman slower.

This thesis describes the advances made towards a dual-species magneto-optical trap (MOT) of Li and Rb for use in photoassociation spectroscopy, Feshbach resonance studies, and, as long-term aspirations, the formation of ultracold heteronuclear polar molecules. The initial discussion will focus on a brief theoretical overview of laser cooling and trapping and the production of ultracold molecules from a cold atom source. Subsequently, details of the experimental system, including those pertaining to the required laser light, the vacuum chamber, and the computer control system will be presented. Finally, preliminary optimization and characterization measurements showing the performance of a single species Li MOT are introduced. These measurements demonstrated the loading of over 8 x 107 Li atoms directly into a MOT without the need for a Zeeman slower.

Este trabalho consiste basicamente em dois experimentos: Determinação da equação de estado de um gás frio aprisionado, e na comparação das temperaturas de uma amostra de átomos confinadas em dois tipos de armadilhas magneto-ópticas. No primeiro experimento utilizamos a generalização do conceito de pressão e volume que foram redefinidos de maneira apropriada para alcançamos uma equação de estado. Experimentalmente nossa amostra apresentou um desvio do esperado para um gás ideal, dessa forma utilizamos uma expansão virial com as novas definições de pressão e volume para investigar as interações entre os átomos. Já no segundo experimento utilizamos uma técnica que mede transiente temporal da absorção do feixe pelos átomos através de um fotodetector para a obtenção da temperatura. Neste experimento obtemos temperaturas equivalentes para as duas armadilhas. / This work consists of two experiments: Determination of the state equation a trapped cold gas, and the comparison of the temperatures of confined atoms in two types of magneto-optical traps. For the first experiment we generalized and defined a new pressure and volume concept and we reached a state equation. Experimentally our sample presented a deviation of the ideal gas, in that way we used a virial expansion with the new pressure and volume definitions to investigate the interactions among the atoms. In the second experiment we used a technique that measures temporal variation of the absorption of a probe beam that crosses the atoms by a photodetector, witch gives us the information about the temperature. We have found equivalent temperatures for the two traps.

This thesis describes the advances made towards a dual-species magneto-optical trap (MOT) of Li and Rb for use in photoassociation spectroscopy, Feshbach resonance studies, and, as long-term aspirations, the formation of ultracold heteronuclear polar molecules. The initial discussion will focus on a brief theoretical overview of laser cooling and trapping and the production of ultracold molecules from a cold atom source. Subsequently, details of the experimental system, including those pertaining to the required laser light, the vacuum chamber, and the computer control system will be presented. Finally, preliminary optimization and characterization measurements showing the performance of a single species Li MOT are introduced. These measurements demonstrated the loading of over 8 x 107 Li atoms directly into a MOT without the need for a Zeeman slower. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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