This dissertation presents several experimental methods that were devised to generate or manipulate quantized vortices in highly oblate dilute-gas Bose-Einstein condensates (BECs). Studies that involve single vortex dynamics, vortex-vortex interactions, and vortex-impurity interactions are essential in developing a deeper understanding of the nature of superfluidity and in particular, superfluid turbulence. In highly oblate systems, vortex dynamics have a two-dimensional (2D) nature and the resulting superfluid characteristics may be substantially different from those in three-dimensional (3D) superfluids. However, there have been remarkably few experimental studies of 2D vortex dynamics in superfluids. Therefore, to study 2D vortex dynamics and interactions, it is necessary to first develop experimental methods that can generate vortices and vortex distributions in nominally 2D systems, such as highly oblate BECs. Four main experiments are discussed in this dissertation. Two of these experiments generate multiple singly quantized vortices in a relatively stochastic manner leading to disordered vortex distributions. From these two vortex methods, the physics of high vorticity and highly disordered systems may be observed and studied in a highly oblate system. These methods may prove useful in studies of 2D quantum turbulence. The other two experiments involve newly developed techniques for controlled generation and manipulation of vortices. One of these methods creates multiply quantized pinned vortices with a control in the generated vorticity. The other method reliably creates a pair of singly quantized vortices of opposite circulation, whose positions can be easily manipulated after creation, such that they can be placed in any location within the BEC. The two techniques may be scalable to higher number of vortices and may prove useful in superfluid dynamics and vortex interactions that require repeatable vortex distributions. Taken together, these tools and methods may be applicable to many further studies of vortex physics in highly oblate BECs.

The Bogoliubov theory of excitations in superfluid helium is used to study collective modes at zero temperature. A repulsive delta function shell potential is used in the quasiparticle excitation energy spectrum to fit the observed elementary excitation spectrum, except in the plateau region. The linearized equation of motion method is used to obtain the secular equation for a collective mode consisting of a linear combination of one and two free quasiparticles of zero total momentum. It is shown that in this case for high-lying collective modes, vertices involving three quasiparticles cancel, and only vertices involving four quasiparticles are important. A decomposition into various angular momentum states is then made. Bound roton pairs in the angular momentum D-state observed in light-scattering experiments exist only for an attractive coupling between helium atoms in this oversimplified model. Thus, the interaction between particles can be reinterpreted as a phenomenological attractive coupling between quasiparticles, in order to explain the Raman scattering from bound roton pairs in superfluid helium.

Ce travail se décompose en trois parties : dans un premier temps, nous présentons de nouveaux résultats dans le cadre du projet ULTIMA. Ce projet vise à utilliser des bolomètres d'3He superfluide pour un détecteur de matière noire. Nous démontrons l'importance de couvrir de deux monocouches d'4He les parois des cellules bolométriques . Nous étudions de même l'influence du champ magnétique sur la calibration du bolomètre. L'observation la plus importante est que la forme des pulses enregistrés varie selon la nature de la particule incidente. Une étude détaillée de ce phénomène est présentée et nous discutons son application à la discrimination d'évènements dans un futur détecteur. Dans une deuxième partie, nous utilisons le même dispositif expérimental pour étudier les propriétés fondamentales de l'3He. Premièrement, nous mesurons la chaleur spécifique des couches adsorbés d'3He à ultra basses températures en présence d'un champs magnétique. Deuxièmement, la transition rapide de la phase normale vers la phase superfluide est étudiée et interprétée dans le cadre du scénario de Kibble-Zurek de création de vortex. Dans la troisième partie, nous étudions l'influence du confinement de l'3He dans un aérogel anisotrope sur les états superfluides. Au moyen de techniques RMN, nous testons la prédiction de l'apparition d'une nouvelle phase nommée “phase polaire” et nous mettons en évidence l'existence d'un nouveau mode de précession.

<p>The Large Hadron Collider (LHC) is the next large particle accelerator developed at CERN, constructed to enable studies of particles. The acceleration of the particles is carried out using magnets operating at about 1.9 K, a temperature achieved by regulating flow of superfluid helium. For economical reasons, control of the helium flow is based on feedback of virtual flow meter (VFT) estimates instead of real instrumentation.</p><p>The main purpose of this work is to develop a virtual flow meter with the possibility to estimate the flow by means of two different flow estimation methods; the Samson method that has previously been tested for the LHC, and the Sereg- Schlumberger method that has never before been implemented in this environment.</p><p>The virtual flow meters are implemented on PLCs using temperature and pressure measurements as input data, and a tool for generating the virtual flow meters and connect them to the appropriate physical instrumentation has also been developed.</p><p>The flow through a valve depends, among others, on some pressure and temperature dependent physical properties that are to be estimated with high accuracy. In this project, this is done by bilinear interpolation in twodimensional tables containing physical data, an approach that turned out to be more accurate than the previously used method with polynomial interpolation.</p><p>The flow measurement methods have been compared. Since they both derive from empirical studies rather than physical relations it is quite futile to find theoretical correspondencies, but the simulations of the mass flows can be compared. For low pressures, the results are fairly equal but they differ more for higher pressures. The methods have not been validated against true flow rates since there were no real measurements available before the end of this project.</p> / <p>Le Grand Collisionneur de Hadrons (Large Hadron Collider, LHC) est le prochain grand accélérateur de particules du CERN, construit pour permettre l’étude des particules. L’accélération des particules sera réalisée en utilisant des aimants supraconducteurs qui fonctionneront à 1.9 K et la température sera régulée en contrôlant le débit d’hélium superfluide. Pour des raisons économiques, la régulation du débit d’hélium sera basée sur les réponses des estimations des débitmètres</p><p>virtuels (Virtual flow meters, VFT) au lieu d’instrumentation réelle.</p><p>Le but principal de ce projet est de développer un débitmètre virtuel qui estimera le débit avec deux méthodes différentes ; la méthode Samson qui a déjà été mise en oeuvre pour le LHC, et la méthode Sereg-Schlumberger qui n’a pas encore été implémentée dans cet environnement.</p><p>Les débitmètres virtuels seront implémentés sur des PLCs avec des mesures de température et de pression comme données d’entrée. De plus, un outil pour générer les débitmètres et les relier avec l’instrumentation physique adéquat a été développé.</p><p>Le débit à travers d’une vanne dépend entre autres des propriétés physiques qui dépendent à leur tour de la température et de la pression. Ces propriétés devront être estimées avec une grande précision. Dans ce projet, cela est fait en appliquant une interpolation bilinéaire dans des tableaux de deux dimensions. Cette méthode s’est montrée plus précise qu’avec une méthode d’interpolation polynomiale.</p><p>Les deux méthodes de mesures de débit ont été comparées. Elles dérivent toutes les deux des études empiriques et non physiques, alors les similarités théoriques sont donc peu pertinentes, mais les résultats des simulations des débits peuvent être comparés. Pour des pressions basses, les méthodes sont quasiment équivalentes, mais les différences sont plus importantes pour les pressions plus hautes. Étant donné qu’il n’y avait pas de mesures disponibles avant la fin de ce projet, les méthodes n’ont pas été validées avec des débits réels.</p>

Esta tesis es un trabajo teórico, en el que estudiamos la física de los átomos dipolares bosónicos ultrafríos en retículos ópticos. Éstos gases consisten de átomos o moléculas bosónicas, enfriados bajo la temperatura de degeneración cuántica, típicamente del orden de nK. En éstas condiciones, en una trampa armónica tridimensional (3D), los bosones que interaccionan débilmente condensan y forman un Condensado de Bose Einstein (BEC). Cuando se carga un BEC en un retículo óptico producido por ondas estacionarias de luz láser, se producen nuevos fenómenos físicos. Estos sistemas entonces realizan modelos de tipo Hubbard y pueden ser llevados a regimenes fuertemente correlacionados.En 1989, M. Fisher et. al. predecían que el modelo de Bose-Hubbard homogéneo (BH) presenta la transición de fase cuántica Superfluid-Mott insulator (SF-MI). En 2002, la transición entre éstas dos fases fue observada experimentalmente por primera vez en el grupo de T. Esslinger e I. Bloch. La realización experimental de un BEC dipolar de cromo en el grupo de T. Pfau, y los progresos recientes en las técnicas de enfriamiento y atrapamiento de moléculas dipolares en los grupos de D. Jin e J. Ye, han abierto el camino hacia los gases cuánticos ultra-fríos dominados por la interacción dipolar. La evolución natural, y el reto de hoy en día por parte experimental, es de cargar BEC dipolares en retículos ópticos y estudiar los gases dipolares fuertemente correlacionados.Antes de éste trabajo de doctorado, estudios sobre modelos de BH con interacciones extendidas a los primeros vecinos mostraron la evidencia de nuevas fases cuánticas, como el supersólido (SS) y la fase checkerboard (CB). Debido al carácter de largo alcance de la interacción dipolo-dipolo, que decae con la potencia cúbica inversa de la distancia, es necesario incluir más de un primer vecino para obtener una descripción fiel y cuantitativa de los sistemas dipolares. De hecho, al incluir más vecinos se permiten y se estabilizan aún más nuevas fases.En esta tesis estudiamos modelos de BH con interacciones dipolares, investigando más allá del estado fundamental. Estudiamos un retículo bidimensional (2D) donde los dipolos están polarizados en dirección perpendicular al plano 2D, dando lugar a una interacción dipolar repulsiva e isotrópica. Utilizamos aproximaciones de campo-medio y un ansatz Gutzwiller, que son suficientemente correctos y adecuados para describir este sistema. Encontramos que los gases dipolares en 2D presentan una multitud de estados metaestables de tipo MI, que compiten con el estado fundamental, de modo parecido a sistemas desordenados. Estudiamos en detalle el destino de estos estados metaestables: como pueden ser preparados de manera controlada, como pueden ser detectados, cual es su tiempo de vida debido al tunnelling, y cual es su rol en los procesos de enfriamiento. Además, encontramos que el estado fundamental está caracterizado por estados MI de tipo checkerboard con coeficiente de ocupación n fraccionario (numero medio de partículas por sitio) que depende del cut-off utilizado en el radio de alcance de la interacción. Confirmamos esta predicción estudiando el mismo sistema con métodos Quantum Monte Carlo (worm algorithm). En este caso no utilizamos ningún cut-off en el radio de alcance de la interacción, y encontramos pruebas de una "Devil's staircase" en el estado fundamental, i.e. donde las fases MI aparecen en todos los n racionales del retículo subyacente. Encontramos además, regiones de los parámetros donde el estado fundamental es supersólido, obtenido drogando los sólidos con partículas o con agujeros.En este trabajo, investigamos también como cambia la estructura precedente en 3D. Nos focalizamos en el retículo 3D más sencillo compuesto de dos planos 2D, en el cual los dipolos están polarizados perpendicularmente a los planos; la interacción dipolar es entonces repulsiva por partículas del mismo plano, mientras es atractiva por partículas en el mismo sitio de dos planos diferentes. En cambio suprimimos el tunnelling entre los planos, lo cual hace el sistema equivalente a una mezcla bosónica en un retículo 2D. Nuestros cálculos muestran que las partículas se juntan en parejas, y demostramos la existencia de la nueva fase cuántica Pair Super Solid (PSS).Actualmente estamos estudiando un retículo 2D donde los dipolos están libres de apuntar en ambas direcciones perpendicularmente al plano, lo cual resulta en una interacción a primeros vecinos repulsiva (atractiva) por dipolos alineados (anti-alineados). Encontramos regiones de parámetros donde el estado fundamental es ferromagnético u anti-ferromagnético, y encontramos pruebas de la existencia de la fase cuántica Counterflow Super Solid (CSS).Las nuestras predicciones tienen directas consecuencias experimentales, y esperamos que vengan pronto controladas en experimentos con gases dipolares atómicos y moleculares ultra-fríos. / This thesis is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules, cooled below the quantum degeneracy temperature, typically in the nK range. In such conditions, in a three-dimensional (3D) harmonic trap, weakly interacting bosons condense and form a Bose-Einstein Condensate (BEC). When a BEC is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur.These systems realize then Hubbard-type models and can be brought to a strongly correlated regime. In 1989, M. Fisher et. al. predicted that the homogeneous Bose-Hubbard model (BH) exhibits the Superfluid-Mott insulator (SF-MI) quantum phase transition. In 2002 the transition between these two phases were observed experimentally for the first time in the group of T. Esslinger and I. Bloch. The experimental realisation of a dipolar BEC of Chromium by the group of T. Pfau, and the recent progresses in trapping and cooling of dipolar molecules by the groups of D. Jin and J. Ye, have opened the path towards ultra-cold quantum gases with dominant dipole interactions. A natural evolution and present challenge, on the experimental side is then to load dipolar BECs into optical lattices and study strongly correlated ultracold dipolar lattice gases.Before this PhD work, studies of BH models with interactions extended to nearest neighbours had pointed out that novel quantum phases, like supersolid (SS) and checkerboard phases (CB) are expected. Due to the long-range character of the dipole-dipole interaction, which decays as the inverse cubic power of the distance, it is necessary to include more than one nearest neighbour to have a faithful quantitative description of dipolar systems. In fact, longer-range interactions tend to allow for and stabilize more novel phases.In this thesis we study BH models with dipolar interactions, going beyond the ground state search. We consider a two-dimensional (2D) lattice where the dipoles are polarized perpendicularly to the 2D plane, resulting in an isotropic repulsive interaction. We use the mean-field approximations and a Gutzwiller ansatz which are quite accurate and suitable to describe this system. We find that dipolar bosonic gas in 2D exhibits a multitude of insulating metastable states, often competing with the ground state, similarly as in a disordered system. We study in detail the fate of these metastable states: how can they be prepared on demand, how they can be detected, what is their lifetime due to tunnelling, and what is their role in various cooling schemes. Moreover, we find that the ground state is characterized by insulating checkerboard-like states with fractional filling factors v&#61472;(average number of particles per site) that depend on the cut-off used for the interaction range. We confirm this prediction by studying the same system with Quantum Monte Carlo methods (the worm algorithm). In this case no cut-off is used, and we find evidence for a Devil's staircase in the ground state, i.e. where insulating phases appear at all rational &#61550;&#61472;of the underlying lattice. We also find regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies.In this work, we also investigate how the previous scenario changes in 3D. We focus on the simplest 3D lattice composed of two 2D layers in which the dipoles are polarized perpendicularly to the planes; the dipolar interaction is then repulsive for particles laying on the same plane, while it is attractive for particles at the same lattice site on different layers. Instead we consider inter-layer tunnelling to be suppressed, which makes the system analogous to a bosonic mixture in a 2D lattice. Our calculations show that particles pair into composites, and demonstrate the existence of the novel Pair Super Solid (PSS) quantum phase.Currently we are studying a 2D lattice where the dipoles are free to point in both directions perpendicularly to the plane, which results in a nearest neighbour repulsive (attractive) interaction for aligned (antialigned) dipoles. We find regions of parameters where the ground state is ferromagnetic or antiferromagnetic, and find evidences for the existence of a Counterflow Super Solid (CSS) quantum phase.Our predictions have direct experimental consequences, and we hope that they will be soon checked in experiments with ultracold dipolar atomic and molecular gases.

The Large Hadron Collider (LHC) is the next large particle accelerator developed at CERN, constructed to enable studies of particles. The acceleration of the particles is carried out using magnets operating at about 1.9 K, a temperature achieved by regulating flow of superfluid helium. For economical reasons, control of the helium flow is based on feedback of virtual flow meter (VFT) estimates instead of real instrumentation. The main purpose of this work is to develop a virtual flow meter with the possibility to estimate the flow by means of two different flow estimation methods; the Samson method that has previously been tested for the LHC, and the Sereg- Schlumberger method that has never before been implemented in this environment. The virtual flow meters are implemented on PLCs using temperature and pressure measurements as input data, and a tool for generating the virtual flow meters and connect them to the appropriate physical instrumentation has also been developed. The flow through a valve depends, among others, on some pressure and temperature dependent physical properties that are to be estimated with high accuracy. In this project, this is done by bilinear interpolation in twodimensional tables containing physical data, an approach that turned out to be more accurate than the previously used method with polynomial interpolation. The flow measurement methods have been compared. Since they both derive from empirical studies rather than physical relations it is quite futile to find theoretical correspondencies, but the simulations of the mass flows can be compared. For low pressures, the results are fairly equal but they differ more for higher pressures. The methods have not been validated against true flow rates since there were no real measurements available before the end of this project. / Le Grand Collisionneur de Hadrons (Large Hadron Collider, LHC) est le prochain grand accélérateur de particules du CERN, construit pour permettre l’étude des particules. L’accélération des particules sera réalisée en utilisant des aimants supraconducteurs qui fonctionneront à 1.9 K et la température sera régulée en contrôlant le débit d’hélium superfluide. Pour des raisons économiques, la régulation du débit d’hélium sera basée sur les réponses des estimations des débitmètres virtuels (Virtual flow meters, VFT) au lieu d’instrumentation réelle. Le but principal de ce projet est de développer un débitmètre virtuel qui estimera le débit avec deux méthodes différentes ; la méthode Samson qui a déjà été mise en oeuvre pour le LHC, et la méthode Sereg-Schlumberger qui n’a pas encore été implémentée dans cet environnement. Les débitmètres virtuels seront implémentés sur des PLCs avec des mesures de température et de pression comme données d’entrée. De plus, un outil pour générer les débitmètres et les relier avec l’instrumentation physique adéquat a été développé. Le débit à travers d’une vanne dépend entre autres des propriétés physiques qui dépendent à leur tour de la température et de la pression. Ces propriétés devront être estimées avec une grande précision. Dans ce projet, cela est fait en appliquant une interpolation bilinéaire dans des tableaux de deux dimensions. Cette méthode s’est montrée plus précise qu’avec une méthode d’interpolation polynomiale. Les deux méthodes de mesures de débit ont été comparées. Elles dérivent toutes les deux des études empiriques et non physiques, alors les similarités théoriques sont donc peu pertinentes, mais les résultats des simulations des débits peuvent être comparés. Pour des pressions basses, les méthodes sont quasiment équivalentes, mais les différences sont plus importantes pour les pressions plus hautes. Étant donné qu’il n’y avait pas de mesures disponibles avant la fin de ce projet, les méthodes n’ont pas été validées avec des débits réels.

<p>This thesis is a study of the heat transfer correlations between a wire and liquid helium cooled to either 1.9 or 4.3 K. The wire resembles a part of a superconducting magnet used in the Large Hadron Collider (LHC) particle accelerator currently being built at CERN. The magnets are cooled to 1.9 K and using helium as a coolant is very efficient, especially at extremely low temperatures since it then becomes a superfluid with an apparent infinite thermal conductivity. The cooling of the magnet is very important, since the superconducting wires need to be thermally stable.</p><p>Thermal stability means that a superconductive magnet can remain superconducting, even if a part of the magnet becomes normal conductive due to a temperature increase. This means that if heat is generated in a wire, it must be transferred to the helium by some sort of heat transfer mechanism, or along the wire or to the neighbouring wires by conduction. Since the magnets need to be superconductive for the operation of the particle accelerator, it is crucial to keep the wires cold. Therefore, it is necessary to understand the heat transfer mechanisms from the wires to the liquid helium.</p><p>The scope of this thesis was to describe the heat transfer mechanisms from a heater immersed in liquid and superfluid helium. By performing both experiments and simulations, it was possible to determine properties like heat transfer correlations, critical heat flux limits, and the differences between transient and steady-state heat flow. The measured values were in good agreement with values found in literature with a few exceptions. These differences could be due to measurement errors. A numerical program was written in Matlab and it was able to simulate the experimental temperature and heat flux response with good accuracy for a given heat generation.</p>

Bose-Einstein condensates (BECs), with their superfluid behavior, quantized vortices, and high-level of control over trap geometry and other system parameters provide a compelling environment for studies of quantum fluid dynamics. Recently there has been an influx of theoretical and numerical progress in understanding the superfluid dynamics associated with two-dimensional quantum turbulence, with expectations that complementary experiments will soon be realized. In this dissertation I present progress in the development of an experimental toolkit that will enable such experimental studies of two-dimensional quantum turbulence. My approach to developing this toolkit has been twofold: first, efforts aimed at the development of experimental techniques for generating large disordered vortex distributions within a BEC; and second, efforts directed towards the design, implementation, and characterization of a quantum vortex microscope. Quantum turbulence in a superfluid is generally regarded as a disordered tangle of quantized vortices in three dimensions, or a disordered planar distribution of quantized vortices in two dimensions. However, not all vortex distributions, even large disordered ones, are expected to exhibit robust signatures of quantum turbulence. Identification and development of techniques for controlled forcing or initialization of turbulent vortex distributions is now underway. In this dissertation, I will discuss experimental techniques that were examined during the course of my dissertation research, namely generation of large disordered distributions of vortices, and progress towards injecting clusters of vortices into a BEC. Complimentary to vortex generation is the need to image these vortex distributions. The nondeterministic nature of quantum turbulence and other far-from-equilibrium superfluid dynamics requires the development of new imaging techniques that allow one to obtain information about vortex dynamics from a single BEC. To this end, the first vortex microscope constructed as part of my dissertation research enabled the first in situ images of quantized vortices in a single-component BEC, obtained without prior expansion. I have further developed and characterized a second vortex microscope, which has enabled the acquisition of multiple in situ images of a lattice of vortex cores, as well as the acquisition of single in situ images of vortex cores in a BEC confined in a weak hybrid trap. In this dissertation, I will discuss the state-of-the-art of imaging vortices and other superfluid phenomena in the University of Arizona BEC lab, as indicated by the examined performance of the quantum vortex microscope.

This thesis is a study of the heat transfer correlations between a wire and liquid helium cooled to either 1.9 or 4.3 K. The wire resembles a part of a superconducting magnet used in the Large Hadron Collider (LHC) particle accelerator currently being built at CERN. The magnets are cooled to 1.9 K and using helium as a coolant is very efficient, especially at extremely low temperatures since it then becomes a superfluid with an apparent infinite thermal conductivity. The cooling of the magnet is very important, since the superconducting wires need to be thermally stable. Thermal stability means that a superconductive magnet can remain superconducting, even if a part of the magnet becomes normal conductive due to a temperature increase. This means that if heat is generated in a wire, it must be transferred to the helium by some sort of heat transfer mechanism, or along the wire or to the neighbouring wires by conduction. Since the magnets need to be superconductive for the operation of the particle accelerator, it is crucial to keep the wires cold. Therefore, it is necessary to understand the heat transfer mechanisms from the wires to the liquid helium. The scope of this thesis was to describe the heat transfer mechanisms from a heater immersed in liquid and superfluid helium. By performing both experiments and simulations, it was possible to determine properties like heat transfer correlations, critical heat flux limits, and the differences between transient and steady-state heat flow. The measured values were in good agreement with values found in literature with a few exceptions. These differences could be due to measurement errors. A numerical program was written in Matlab and it was able to simulate the experimental temperature and heat flux response with good accuracy for a given heat generation.

Orientador: Sadhan Kumar Adhikari / Banca: Roberto André Kraenkel / Banca: Vanderlei Salvador Bagnato / Resumo: Neste trabalho consideramos um gás diluído de átomos de Fermi a baixas temperaturas, com igual numero de átomos de espin para acima (↑) e espin para abaixo (↓) formando um conjunto de N pares de átomos fermiônicos prisioneiros pela ação de uma armadilha com diferentes simetrias, nos distintos limites: de interação fraca, no limite da unitariedade, e no chamado crossover BEC-unitariedade, empregando uma equação de funcional densidade cujas soluções descrevem adequadamente as características principais do superfluido, como são: a densidade de partículas, o tamanho médio, o potencial químico e a energia do sistema / Abstract: In this work we considered a Fermi gas diluted at low temperatures, to equal number of atoms with spin up (↑) and spin down (↓) into a system of N fermion pairs prisoners for the action of a trap with different symmetries, in different limits: weak-coupling, unitarity limit, and the call crossover BEC-unitarity, using a densityfunctional equation whose solutions describe some characteristics of the superfluid appropriately, for example: density profiles of particles, radius, chemical potential and the energy of the system / Mestre