In this thesis we study the physics of quantum many-body systems confined to one-dimensional geometries. The work was motivated by the recent success of experimentalists in developing atom traps, capable of restricting the motion of the individual atoms to a single spatial dimension. Specifically, we look at aspects of the one-dimensional Bose gas including; excitation spectrum, correlation functions, and dynamical behaviour. In Chapter \ref{ch:excitation1D} we consider the Lieb-Liniger model of interacting bosons in one-dimension. We numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss novel features of the solutions, including deviations from the well-known string solutions due to finite size effects. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Our results are compared to those obtained via exact diagonalization of the Hamiltonian in a truncated basis. In Chapter \ref{ch:g2} we analytically calculate the spatial nonlocal pair correlation function for an interacting uniform one dimensional Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects. In Chapter \ref{ch:casimirdrag} we study the drag force below the critical velocity for obstacles moving in a superfluid. The absence of drag is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytic solutions to the Bogoliubov-de Gennes equations for a gray soliton. In Chapter \ref{ch:solitons} we study the effect of quantum noise on the stability of a soliton. We find the soliton solutions exactly define the reflectionless potentials of the Bogoliubov-de Gennes equations. This results in complete stability of the solitons in a purely one dimensional system. We look at the modifications to the density profile of a black soliton due to quantum fluctuations.

In this thesis we study the physics of quantum many-body systems confined to one-dimensional geometries. The work was motivated by the recent success of experimentalists in developing atom traps, capable of restricting the motion of the individual atoms to a single spatial dimension. Specifically, we look at aspects of the one-dimensional Bose gas including; excitation spectrum, correlation functions, and dynamical behaviour. In Chapter \ref{ch:excitation1D} we consider the Lieb-Liniger model of interacting bosons in one-dimension. We numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss novel features of the solutions, including deviations from the well-known string solutions due to finite size effects. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Our results are compared to those obtained via exact diagonalization of the Hamiltonian in a truncated basis. In Chapter \ref{ch:g2} we analytically calculate the spatial nonlocal pair correlation function for an interacting uniform one dimensional Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects. In Chapter \ref{ch:casimirdrag} we study the drag force below the critical velocity for obstacles moving in a superfluid. The absence of drag is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytic solutions to the Bogoliubov-de Gennes equations for a gray soliton. In Chapter \ref{ch:solitons} we study the effect of quantum noise on the stability of a soliton. We find the soliton solutions exactly define the reflectionless potentials of the Bogoliubov-de Gennes equations. This results in complete stability of the solitons in a purely one dimensional system. We look at the modifications to the density profile of a black soliton due to quantum fluctuations.

Thesis (Ph.D.)--University of Melbourne, School of Physics, 2007. / Typescript. Includes bibliographical references (leaves 275-308).

Thesis (Ph.D.); Submitted to Iowa State Univ., Ames, IA (US); 12 Dec 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "IS-T 2100" Gang Li. 12/12/2003. Report is also available in paper and microfiche from NTIS.

La problématique de cette thèse est l'étude de la localisation d'un condensat de Bose-Einstein confiné harmoniquement et quasi-1D à travers lequel différents potentiels désordonnés sont transportés. Cette problématique qui se veut pleinement pertinente pour les expérimentalistes est à priori difficile à traiter. Cela est dû au caractère non-linéaire, inhomogène et hors-équilibre du système. De ce fait, la plage des vitesses du désordre est limitée d'une part par la vitesse critique de superfluidité et d'autre part par la configuration inhomogène du système. Des notions habituelles de localisation telles que transmission ou exposant de Lyapunov ne sont plus applicables. Donc, il a fallu apporter une nouvelle mesure de localisation pour notre problématique: le ratio du déplacement du centre de masse du condensat au déplacement du désordre qu'on a identifié à la fraction d'atomes localisés. De plus, nous avons des corrélations dans le désordre qui introduisent l'effet d'un comportement non-monotone de l'efficacité de la localisation du potentiel désordonné en fonction de l'énergie. Ainsi, les corrélations peuvent être un moyen pour mettre en évidence la nature quantique de la localisation. Chose que nous avont fait dans un premier temps avec du désordre de type Modèle d'Edwards et dans une seconde partie avec du désordre de type speckle, qu'on nomme le Random Dimer speckle. Pour ce deuxième cas, nous avons proposé une procédure pour contrôler les corrélations et introduire un pic de localisation dans une certaine région énergétique. Cette configuration pourrait être vérifié dans les expériences à l'aide d'un modulateur spatial de lumière. / The topic of this thesis is the study of localization of a quasi-one-dimensional and harmonically trapped Bose-Einstein condensate through which various disordered potentials are transported. This problem, which wants itself to be fully relevant to experimenters, is a priori difficult to deal with. This is due to the non-linear, inhomhogeneous and out-of-equilibrium nature of the system. Because of this, the range of speeds of disorder is limited on one side by the critical speed of superfluidity and on the other side by the inhomogeneous setting of the system. Usual notions of localization like transmission and Lyapunov exponent are no longer applicable. Thus, we had to introduce a novel measure of localization for our problem: the ratio of the distance moved by the condensate center of mass to the distance moved by the disordered potential that we identify as the fraction of localized atoms. Furthermore, we have correlations in the disorder that introduce the effect of non-monotonic behavior of the localization efficiency of the disordered potential as a function of energy. A a result, correlations can be used as a tool to point the quantum nature of the localization. We did this in a first part with Edwards Model type disorders and in a second part with speckle type disorders, a new one that we call the Random Dimer speckle. For this second part, we propose a scheme to control the correlations and introduce a localization peak in a certain energy region. This device can be verified in experiments with the help of a Spatial Light Modulator.

Flows of normal and superfluid 4 He (He I and He II, respectively) are investigated experimentally. Relatively small particles of solid hydrogen and deuterium are suspended in the experimental volume and their motions are tracked in both mechanically and thermally driven flows. A statistical study of the particle velocity and velocity increment distributions is performed at scales smaller and larger than the mean distance between quantized vortices, the quantum length scale of the investigated flows. We show that, at small scales, the observed particle dynamics in He II is greatly influenced by that of quantized vortices. We, additionally, report that this behavior is independent of the imposed large-scale flow. Instead, at large scales, we observe that particle motions are quasiclassical, that is, very similar to those reported to occur in turbulent flows of viscous fluids. The study reinforces therefore the idea of close similarity between viscous flows and large-scale (mechanically-driven) flows of He II, and simultaneously highlights the small-scale differences due to the presence of quantized vortices in He II.

Les atomes ultrafroids constituent depuis une vingtaine d’années un domaine fructueux pour l’étude de la physique à N corps. Cependant l’inhomogénéité des nuages atomiques, induite par les méthodes de piégeage utilisées habituellement, constitue une limite pour les études portant sur de grandes échelles de longueur. Nous reportons ici la mise en place d’un nouveau dispositif expérimental, combinant un potentiel modulable à bords raides et fond plat dans le plan atomique, avec un confinement versatile dans la troisième direction. Nous nous intéressons à différentes excitations du système, premièrement des degrés de liberté internes des atomes via leur interaction avec la lumière, puis deuxièmement de leur mouvement collectif avec la propagation de phonons. La répartition des atomes dans un plan est particulièrement adaptée aux études de diffusion de la lumière. Elle permet en effet de sonder de fortes densités atomiques, entraînant de fortes interactions dipôle-dipôle induites, tout en gardant un signal transmis suffisant pour effectuer des mesures. Nous avons mesuré la déviation au comportement d’un atome isolé pour de la lumière proche de résonance lorsque la densité atomique est modifiée. Nous avons également étudié la diffusion de photons dans un disque d’atomes en injectant de la lumière seulement au centre du disque. Nous nous sommes ensuite intéressés aux excitations collectives du gaz. Nous avons mesuré la vitesse du son dans le milieu, qui est liée à la fraction superfluide du système, et comparé nos résultats aux prédictions d’un modèle hydrodynamique à deux fluides. En utilisant une géométrie adaptée, nous avons en outre étudié la dynamique de retour à l’équilibre d’un système isolé, en imageant la phase du condensat de Bose-Einstein résultant de la fusion de jusqu’à douze condensats. / Ultracold atoms have proven to be a powerful platform for studying many-body physics. However the inhomegeneity of atomic clouds induced by potentials commonly used to trap the atoms constitutes a limitation for studies probing large length scales. Here we present the implementation of a new versatile setup to study two-dimensional Bose gases, combining a tunable in-plane box potential with a strong and efficient confinement along the third direction. We study different excitations of the system, either of internal degrees of freedom of the atoms with light scattering, or of their collective motion with phonon propagation. The slab geometry is particularly well suited for light scattering studies. It allows one to probe high atomic densities, leading to strong induced dipole-dipole interactions, while keeping a good enough light transmission for measurements. We monitor the deviation from the single atom behavior for near resonant light by varying the atomic density. We additionally monitor the spreading of photons inside the slab by injecting light only at the center of a disk of atoms. We also investigate collective excitations of the atomic gas. We measure the speed of sound which is linked to the superfluid density of the cloud and compare our results to a two-fluid hydrodynamic model predictions. Using a relevant geometry, we additionally study how an isolated system goes back to equilibrium. This is done by imaging the phase of the resulting Bose-Einstein condensate (BEC) after merging up to twelve BECs.

L'objectif de cette thèse est d'étudier différents aspects microscopiques et macroscopiques liés à la présence de superfluidité dans les étoiles à neutrons. Dans un premier temps, nous avons calculé des configurations stationnaires d'étoiles à neutrons superfluides en rotation, en relativité générale, basées sur l'utilisation d'équations d'état réalistes. A l'aide de ces configurations d'équilibre, nous avons ensuite développé un modèle simple de glitch, en relativité générale, vu comme un transfert de moment cinétique entre les neutrons superfluides et les particules chargées constituant l'étoile. Cela nous a permis d'obtenir des temps caractéristiques de montée qui pourront être comparés à de futures observations précises de glitches afin d'apporter de meilleures contraintes sur l'intérieur de ces étoiles. Enfin, nous nous sommes également intéressés à la dynamique des vortex superfluides, en présence de tubes de flux, dans le cas où les protons dans le coeur des étoiles formeraient un supraconducteur de type II. / The aim of this thesis is to study different aspects, both microscopic and macroscopic, associated with the presence of a large amount of superfluid matter inside neutron stars. First, we computed stationary configurations of rotating superfluid neutron stars, in general relativity, using realistic equations of state. Based on these equilibrium configurations, we then developed a simple model of pulsar glitches, in general relativity, seen as angular momentum transfers between the superfluid neutrons and the charged particles composing the star. This enables us to infer spin-up time scales that could be compared with future accurate glitch observations, in order to get some constraints on the interior of neutron stars. Finally, we also focused on the dynamics of superfluid vortex lines, accounting for the presence of fluxtubes, if the protons are forming a type II superconductor in the core of neutron stars.

doctoral thesis, Ph.D, University of California, Berkeley, Berkeley, CA. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--55855" Gedik, Nuh. USDOE Director. Office of Science. Office of Basic Energy Sciences 05/20/2004. Report is also available in paper and microfiche from NTIS.

Thesis (Ph.D.); Submitted to the University of California, Berkeley, CA (US); 24 Nov 2004. / Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--56751" McGuire, John Andrew. USDOE Director. Office of Science. Office of Basic Energy Sciences. Materials Science and Engineering Division (US) 11/24/2004. Report is also available in paper and microfiche from NTIS.