No description available.

No description available.

The generation and propagation of harmonics in an atomic gas are described for the case of an incident Bessel-Gauss beam. Theoretical expressions are derived for the far-field amplitude of the harmonic field by solving the propagation equation using an elaborate integral formalism. We establish simple rules which determine the optimum Bessel-Gauss beam with respect to phase-matching as a function of the medium properties, such as the dispersion and the gas density. Target depletion due to photoionization and refractive index variations originating from both free electrons and dressed linear atomic susceptibilities are taken into account. The intensity-dependent complex atomic dipole moment is calculated using nonpertur- bative methods. Numerical propagation calculations for hydrogen, xenon and argon are presented. For hydrogen we consider the third harmonic of a 355-nm, 15-ps pump beam up to 3 X 10(^13) W/cm(^2) intensity, similarly for xenon, but at lower intensities. For argon we consider the 17th and 19th harmonic of a 810-nm, 30-fs pump beam around 10(^14) W/cm(^2) intensity. We compare conversion efficiencies and both spatial and temporal far-field profiles for an optimized Bessel-Gauss beam with respect to a Gaussian beam of same power and/or peak focal intensity. For the case of hydrogen, we investigate the effect of an ac-Stark-shift induced atomic resonance. We find all results in good agreement with our theoretical predictions. We conclude from our studies that Bessel-Gauss beams can perform better in terms of conversion efficiency than a comparable Gaussian beam. We find this to originate essentially from the more flexible phase-matching conditions for Bessel-Gauss beams. Bessel-Gauss beams also allow for spatial separation of the harmonic and the incident field in the far-field region, owing to the conical shape of their spatial far-field profile. Both features make Bessel-Gauss beams an attractive alternative to Gaussian beams in a limited but substantial number of experimental conditions.

Para atingir o regime de condensação de Bose-Einstein (CBE) em gases de metais alcalinos são necessárias várias etapas: feixe desacelerado, aprisionamento magneto-óptico, aprisionamento magnético e por fim o resfriamento evaporativo. Como estamos interessados em atingir o regime de CBE precisamos nos preocupar com as várias etapas intermediárias. Neste trabalho apresentaremos a construção e caracterização de uma armadilha magnética para um gás de átomos neutros de sódio. O sistema optado por nós foi o \"folha de trevo\", com o qual conseguimos a seguinte configuração de campos magnéticos: 140 gauss de campo de fundo na direção axial, 117 gauss/cm de gradiente radial e 106 gauss/cm 2 de curvatura na direção axial. Para gerarmos esta configuração de campo e desligarmos estes campos em um tempo menor que um milisegundo foi necessária a construção de um sistema de chaveamento e controle que será descrito e caracterizado neste trabalho. Com este sistema em funcionamento observamos aproximadamente 10 8 átomos aprisionados e um tempo de 1 segundo. Além disso, observamos os átomos adaptando-se a diferentes formas de potenciais de aprisionamento / In order to obtain Bose- Einstein condensation ( BEC ) in alkali gases several steps are needed : slowing beam , magneto- optical trapping , trapping magnetic and finally evaporative cooling . Since, we are interested in achieving BEC regime we need to consider about the various intermediate steps . In this work, we present the construction and characterization of a magnetic trap for a gas neutral atom of sodium. The system we chose was the \" clover leaf \" , with which we got the following configuration of magnetic fields : 140 gauss field background in the axial direction , 117 gauss / cm radial gradient and 106 gauss / cm 2 of curvature axial direction . For generating this field configuration and disconnecting these fields in a time of less than one millisecond required the construction of a switching system and control that will be described and characterized in this work. With this system, noted in about 10 8 trapped atoms and a time of 1 second. Besides, we observe the atoms adapting to different forms of potential imprisonment

Ma, Kwok Wai = 相互作用的超冷原子於一維系統之有關課題 / 馬國威. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 69-74). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Ma, Kwok Wai = Xiang hu zuo yong de chao leng yuan zi yu yi wei xi tong zhi you guan ke ti / Ma Guowei.

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.

Ab initio prediction of the electronic properties of solids is traditionally performed using groundstate Density Functional Theory. These methods are unreliable however, for a class of important problems involving weak attractive forces. These problems include (i) the energetics of hydrogen storage and metal interactions in graphene, (ii) cohesion properties of some polymer systems and (iii) possibly, the weak hydrophobic forces in biomolecules. For these cases a more powerful method than groundstate DFT are timedependent DFT (tdDFT) methods related to the Random-Phase Approximation (RPA). All of these methods proceed by looking at the dynamic density-density response function, whose long-ranged properties naturally lead to the weak forces referred to above. In this thesis we have tested these ideas by investigating electronic response and correlation on the predicted properties of spherical atoms. We have developed and tested a variety of approximations to the timedependent response function through approximations of the tdDFT class and a new method involving greater self-consistency in the screening equation, the inhomogenous STLS approach. Through the development of new methods and computer code, we have solved the response equation allowing us to test our approximations on atoms. Calculation of certain dynamic and static properties of a variety of atoms within our approximations generally agree well with known results. In this thesis we have calculated excitation energies of Helium, dipole polarisabilities and C6 van der Waals (vdW) coefficients of a variety of atoms, and groundstate correlation energies Ec of some atoms. The excitation spectra of Helium generated in our new PGG+c approximation are in good agreement with experiment. The dipole polarisabilities are generally in good agreement with known results, with the exception of Magnesium, Beryllium and Sodium. The C6 coefficients are a little poorer with the exception of Helium where they are nearly exact. Correlation energies are generally reasonable in the PGG+c approximation although they are considerably less accurate than the other properties we have calculated for all atoms other than He. The ISTLS correlation energy of Helium is within 5% suggesting that this method may perform well for larger atoms where our present numerical techniques require improvement. These generally positive results suggest that the approximations we have developed may be applied to more complicated systems such as those described above with good results.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

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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.