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.

Made available in DSpace on 2016-12-12T20:15:54Z (GMT). No. of bitstreams: 1 introducao.pdf: 91836 bytes, checksum: cb92c1e5e08cf2686a55fb3fdfcba785 (MD5) Previous issue date: 2011-07-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we present the building and characterization of a Magneto-Optical Trap (from now on named MOT) for Rubidium atoms. We perform experiments for studying the e¤ect of a broadband light over trapped atoms. In order to carry out this study we used a incandescent lamp which is broad in the wavelength spectrum. We observed in a MOT, with a number of 109 trapped atoms, that the broadband light increases the emitted .uorescence by the cloud of atoms. This could indicate an e¤ective enlargement in the trap e¢ciency. However, we cannot distinguish, based on our experiments, if this di¤erence is due to an increasing in the number of the trapped atoms or if it is just scattered light caused by the increasing in the intensity of the incident light over the cloud. Thus, we did an analysis in the answer of the laser beam versus the variation in the intensity of lasers used for trapping. In a second step, we perform this study but with a lower number of trapped atoms, 108 atoms, and we verify that the heating of the lamps implies in the increasing of the loss of atoms in the trap, diminishing the number of trapped atoms. Hence, this lead us to make a study on the collisions dynamics that are in the trap, in order to understand the in.uence of the temperature on the trap e¢ciency. We observe that a small uniform increasing in the chamber temperature would lead to a great loss in the trap , but the increasing in the temperature caused by the lamps is a local increasing and generates a degassing of the chamber, increasing the quantity of the background vapour. / Neste trabalho apresentamos a construção e caracterização de uma armadilha magneto-óptica, a qual utilizamos para aprisionamento de átomos de Rb. Após a construção da armadilha e sua caracterização, fizemos experimentos para estudar os efeitos da luz de banda larga sobre os átomos aprisionados. Para esse estudo, utilizamos lâmpadas incandescentes que possuem um espectro largo de comprimentos de onda. Verificamos que em uma armadilha com 109 átomos aprisionados, a luz de banda larga aumenta a fluorescência emitida pela nuvem de átomos, tendo fortes indícios que isto representa efetivamente um aumento na eficiência da armadilha. No entanto, com os experimentos que fizemos, não podemos distinguir se essa diferença é referente a um aumento de átomos aprisionados ou apenas espalhamento de luz causado pelo aumento da intensidade de luz incidida sobre a nuvem. Fizemos então uma comparação da resposta dos átomos, frente a variações na intensidade dos feixes de laser utilizados para o aprisionamento. Por motivos que serão discutidos neste trabalho, refizemos esse estudo com um número menor de átomos aprisionados, 108 átomos, e verificamos que o aquecimento das lâmpadas reflete no aumento das perdas na armadilha, diminuindo então o número de átomos aprisionados. Isto nos levou a fazer um estudo sobre a dinâmica das colisões presentes na armadilha, para entendermos a influência da temperatura na eficiência da armadilha. Verificamos que um pequeno aumento uniforme na temperatura da câmara levaria a grandes perdas na armadilha, mas o aumento da temperatura causado pelas lâmpadas é um aumento local, e gera um processo de desgaseificação da câmara, aumentando a quantidade de átomos, "diferentes de Rb", presentes no vapor de fundo.

Le couplage de guides d'ondes nanoscopiques et d'atomes froids a récemment ouvert de nouvelles voies de recherche. Le guide d'onde dans notre cas est une nanofibre qui confine la lumière transversalement à une échelle inférieure à la longueur d'onde. La lumière guidée présente un fort champ évanescent permettant une interaction atome-photon exaltée au voisinage de la nanofibre. Dans notre expérience, un nuage atomique froid est d'abord superposé à une nanofibre optique. Puis, en utilisant un piège dipolaire via le champ évanescent de la nanofibre, les atomes froids sont piégés à proximité de sa surface. Avec cette plateforme, nous avons obtenu des épaisseurs optiques élevées OD ~ 100 et de longues durées de vie ~ 25 ms en utilisant un schéma de piégeage qui préserve les propriétés internes des atomes. Une direction intéressante est alors d'explorer les effets collectifs résultant de l'ordre spatial des atomes. Lorsque la période du réseau est proche de la longueur d'onde de résonance, une réflexion de Bragg aussi élevée que 75% est observée. Cette réflexion dépend de la polarisation de la sonde par rapport aux réseaux atomiques - une signature de la chiralité dans les systèmes à guide d'ondes nanoscopiques. La possibilité de contrôler le transport de photons dans les guides d'ondes couplés à des systèmes de spin permettrait de nouvelles fonctionnalités pour les réseaux quantiques et l'étude d'effets collectifs résultant d'interactions à longue distance. / The coupling of cold atoms to 1D nanoscale waveguides have opened new avenues of research. The waveguide in our case is a nanofiber, which confines light transversally to a subwavelength scale. The guided light exhibits a strong evanescent field allowing enhanced atom-photon interaction in the vicinity of nanofiber. In our experiment, a cold atomic cloud is first interfaced with an optical nanofiber. By using an optical lattice in the evanescent field, the atoms are then trapped in 1D atomic arrays close to the nanofiber. In this platform, we reach high optical depth OD ~ 100 and long lifetimes ~ 25 ms by using a dual-color compensated trapping scheme that preserves the internal properties of atoms. In this thesis, we explore collective effects emerging from the spatial ordering of atoms. When the period of the lattice is made close to commensurate with the resonant wavelength, Bragg reflection, as high as 75%, is observed. The reflection shows dependency on orientation of the probe polarization relative to the atomic arrays - a chiral signature in nanoscale waveguide-QED systems. The ability to control photon transport in 1D waveguides coupled to spin systems would enable novel quantum networking capabilities and the study of many-body effects arising from long-range interactions.

Cette thèse porte sur la conception et la réalisation d’une nouvelle expérience d’interféromètre atomique au SYRTE. Elle permettra de réaliser des mesures ultrasensibles du gradient vertical de gravité. Cette expérience fonctionnera à terme en utilisant comme source des atomes ultra-froids, préparés sur une puce à atomes. Elle utilisera comme séparatrices des transitions multiphotoniques, obtenues par diffraction de Bragg d’ordre élevé. Le transport des atomes sera assuré par des réseaux optiques en mouvement. Une première partie du dispositif expérimental a été assemblée et son fonctionnement a été validé en réalisant un interféromètre dual. Cet interféromètre est réalisé sur deux ensembles d’atomes produits successivement à partir de la même source d’atomes froids, et interrogés par une même paire de faisceaux Raman. Une nouvelle méthode d’extraction de la phase différentielle a été démontrée expérimentalement. Elle repose sur l’exploitation des corrélations entre les mesures de phase des interféromètres et une estimation de la phase sismique fournie par la mesure annexe d’un capteur classique. / This thesis is about the design and realisation of a new atomic interferometer experiment at SYRTE. It will allow ultra-sensitive measurements of the vertical gradient of gravity. This experiment will work using ultra-cold atoms as a source, prepared on an atom chip. It will use large momentum transfer beam-splitter, obtained by high order Bragg diffraction. The transport of atoms will be provided by moving optical lattices. A first part of the experimental setup was assembled and its operation was validated by producing a dual interferometer. This interferometer is performed on two atomic clouds produced successively from the same source of cold atoms, and interrogated by the same pair of Raman beams. A new method of differential phase extraction has been experimentally demonstrated. It is based on the exploitation of the correlations between the interferometer phase measurements and the estimation of the seismic phase provided by an additional classical sensor.

L’objet de cette thèse est le développement d’un standard de fréquence optique base sur l’atome de mercure 199Hg piégé dans un réseau optique. Je présenterai le dispositif expérimental et les améliorations apportées au cours de la thèse qui ont permis d’effectuer la spectroscopie de la transition doublement interdite 1S0 – 3P0 du mercure dans le domaine ultraviolet avec une résolution de l’ordre du Hz. Une telle résolution nous a permis de mener une étude approfondie des effets physiques affectant la fréquence de la transition d’horloge. Cette étude a permis un gain d’un facteur 60 sur la connaissance de la fréquence de la transition d’horloge, et de pousser l’incertitude au-delà de la réalisation de la seconde si par les étalons de fréquence basés sur le césium. Enfin je présenterai les résultats de plusieurs campagnes de comparaison entre notre étalon au mercure et d’autres horloges de très haute précision fonctionnant dans le domaine optique ainsi que dans le domaine micro-onde. / This thesis presents the development of a high-accuracy optical frequency standard based on neutral mercury 199Hg atoms trapped in an optical lattice.I will present the experimental setup and the improvements that were made during this thesis, which have allowed us to perform spectroscopy on the doubly forbidden 1S0 - 3P0 mercury clock transition with Hz level resolution. With such a resolution, we have been able to conduct an in-depth study of the physical effects affecting the clock transition. This study represents a factor 60 in accuracy on the knowledge of the clock transitions frequency, pushing the accuracy below the current realization of the si second by the best cesium atomic fountains. Finally, i will present the results of several comparison campaigns between the mercury clock and other state-of-the-art frequency standards, both in the optical and in the microwave domain.

xvi, 176 p. : ill. (some col.) / The research presented in this dissertation aims to contribute to the field of atom optics via the implementation and demonstration of an all-optical one-way barrier for 87 Rb atoms--a novel tool for controlling atomic motion. This barrier--a type of atomic turnstile--transmits atoms traveling in one direction but hinders their passage in the other direction. We create the barrier with two laser beams, generating its unidirectional behavior by exploiting the two hyperfine ground states of 87 Rb. In particular, we judiciously choose the frequency of one beam to present a potential well to atoms in one ground state (the transmitting state) and a potential barrier to atoms in the other state (the reflecting state). The second beam optically pumps the atoms from the transmitting state to the reflecting state. A significant component of the experimental work presented here involves generating ultra-cold rubidium atoms for demonstrating the one-way barrier. To this end, we have designed and constructed a sophisticated 87 Rb cooling and trapping apparatus. This apparatus comprises an extensive ultra-high vacuum system, four home-built, frequency-stabilized diode laser systems, a high-power Yb:fiber laser, a multitude of supporting optics, and substantial timing and control electronics. This system allows us to cool and trap rubidium atoms at a temperature of about 30 μK. The results presented in this dissertation are summarized as follows. We successfully implemented a one-way barrier for neutral atoms and demonstrated its asymmetric nature. We used this new tool to compress the phase-space volume of an atomic sample and examined its significance as a physical realization of Maxwell's demon. We also demonstrated the robustness of the barrier's functionality to variations in several important experimental parameters. Lastly, we demonstrated the barrier's ability to cool an atomic sample, substantiating its potential application as a new cooling tool. This dissertation includes previously published coauthored material. / Committee in charge: Dr. Hailin Wang, Chair; Dr. Daniel A. Steck, Research Advisor; Dr. Jens U. Nockel; Dr. David M. Strom; Dr. Jeffrey A. Cina

Les gyromètres Sagnac atomiques ont un grand potentiel en raison de leur sensibilité élevée à la rotation. Le gyromètre atomique du SYRTE utilise des atomes de césium refroidis par lasers. À l'aide de transitions Raman stimulées, nous formons un interféromètre de type Mach-Zehnder replié. L'instrument permet d'atteindre un temps d'interrogation maximal de 800 ms, ce qui correspond à une aire Sagnac de 11 cm², la plus grande démontrée pour un interféromètre atomique. Les objectifs de ma thèse sont de tirer au mieux parti du potentiel de l'instrument, et d'étudier des modes d'interrogations jointif et jointif entrelacé. C'est une étape importante pour l'application de tels instruments entre autres en navigation inertielle. Je décris les méthodes mises en place pour pousser la sensibilité court terme et mené une première étude détaillée des effets systématiques. Nous avons démontré une stabilité à court terme de 30 nrad/s/Hz^1/2 en interrogation jointive triplement entrelacée, ce qui est une amélioration d'un facteur 3 de l'état de l'art pour les gyromètres à atomes froids. L'état de l'art a également été amélioré d'un facteur 4 à long terme avec une stabilité de 0,23 nrad/s en 30 000 s. / Sagnac atomic gyroscopes have great potential due to their high sensitivity to rotation. The SYRTE atomic gyroscope uses laser cooled cesium atoms. Thank to stimulated Raman transitions, we form a folded Mach-Zehnder type interferometer. The instrument allows interrogation times up to 800~ms, which corresponds to a 11~cm$^2$ Sagnac area, the largest demonstrated for atom interferometers. This is a major step toward the use of such instruments in inertial navigation. I describe the methods implemented to push the short-term sensitivity and performed the first detailed study of systematics, such as those linked to light-shifts due to the preparation and the detection of the atoms and those linked to misalignment of parallelism of the mirrors and of the trajectories of the atoms. I demonstrated a short-term stability of 30~nrad.s$^{-1}$.Hz$^{-1/2}$ in triple interleaved joint interrogation which improves the state of the art by a factor 3. The state of the art has also been improved by a factor 5 in long-term with a 0,2~nrad.s$^{-1}$ stability in 30~000~s.

Made available in DSpace on 2016-12-12T20:15:48Z (GMT). No. of bitstreams: 1 capa ate a Introducao.pdf: 95782 bytes, checksum: 9c1b33c935822f8b7b9fab4eec59cfc6 (MD5) Previous issue date: 2012-03-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work presents a study about infuences that a quadripolar magnetic field periodically time dependent, can promote in a magneto-optical trap (MOT). The intention reflects the interest in finding an oscillating field configuration that enables the capture and provide benefits if compared to the typical process of trapping. In many papers that will be cited here, a MOT uses a magnetic field that promotes a linear steady magnetic field gradient from the center of the trap. Applying experimental results involving magnetic field oscillations, which will be quoted in detail throughout this text, came the initiative to mathematically model the problem and seek a form of oscillation that may result in a more efficient trapping. Numerical results in a one-dimensional model suggests that the number of atoms is strongly aflected by fuctuations, but we have not found, for the modulations suggests in this work, an oscillation model that could provide an increase of the trap atoms. It was noted that the oscillation frequency of the atom is subjected, aflect the amplitude of the oscillations in the number of trapped atoms. / Neste trabalho apresentamos um estudo sobre as influências que um campo quadripolar magnético, periodicamente dependente do tempo, pode promover em uma armadilha magnético-óptica (Magneto Optical Trap - MOT). O objetivo deste trabalho reflete o interesse em encontrar uma configuração de campo oscilante que possibilite o aprisionamento e forneça vantagens em relação ao processo típico de armadilhamento. Em muitos dos trabalhos que serão citados aqui, um MOT utiliza um campo magnético quadripolar estacionário que promove um gradiente de campo magnético linear à partir do centro da armadilha. Usando resultados experimentais envolvendo oscilações no campo magnético, que serão citados mais detalhadamente no decorrer deste texto, surgiu a iniciativa de modelar o problema matematicamente e buscar uma forma de oscilação que possa resultar em um aprisionamento mais eficiente. Resultados numéricos concebidos em um modelo unidimensional sugerem que o número de átomos é fortemente afetado pelas oscilações, mas não foi possível encontrar, para as modulações sugeridas neste trabalho, uma modulação que pudesse fornecer aumento expressivo no número de átomos armadilhados. Foi possível constatar que a freqüência da oscilação a que o átomo é submetido, afetará a amplitude das oscilações no número de átomos armadilhados.

Dans le cadre de l’étude expérimentale des états quantiques intriqués de particules uniques, il est nécessaire de développer des systèmes compacts, robustes et polyvalents. Motivés par la miniaturisation, la stabilité et la flexibilité apportées par les fibres optiques, nous présentons deux expériences où les fibres optiques servent d’interfaces pour piéger des atomes uniques et collecter les photons uniques émis. Dans un premier temps, en combinant une fibre optique monomode avec une lentille asphérique, un faisceau dipolaire permet de piéger un atome de rubidium unique par blocage collisionnel. Le refroidissement et le taux de pertes par collisions assistées par la lumière dans le piège dipolaire sont augmentés via une modulation de l’intensité du faisceau dipolaire dont l’effet sur la durée de vie de l’atome est expliqué. Une source fibrée de photons uniques à la demande est obtenue avec ce dispositif, produisant des photons dans un mode spatial et temporel à priori bien défini. Dans un second temps, nous présentons la conception d’une expérience couplant optimalement une chaîne d’atomes uniques piégés à une cavité Fabry-Pérot fibrée combinée avec une lentille à forte ouverture numérique pour imager et adresser les atomes individuellement. Un dispositif d’ablation laser de précision submicrométrique est alors construit pour réaliser et analyser in situ les formes de miroirs voulues à l’extrémité des fibres optiques. Nous présentons ensuite les cavités fibrées doublement résonantes avec une biréfringence contrôlée réalisées. Nous décrivons également le système expérimental construit pour la production rapide d’un nuage d’atomes froids et leur transport vers la cavité. / The experimental study of entangled quantum states of single particle ensembles requires development of compact, robust and versatile systems. Motivated by miniaturization, stability and flexibility provided by optical fibers as light wave-guides, we present two experiments where optical fibers are used as interfaces for single atoms trapping and single photons collection into their guided modes. The first experiment combines a single mode fiber with an aspherical lens to produce a dipolar beam in which we trap a single rubidium atom by collisional blockade. This fiber-pigtailed optical tweezer is a simple, compact and versatile tool for single cold atom production. Cooling and light-assisted collisional loss rate in the dipole trap are increased by modulating the dipole beam intensity. The modulation and beam polarization effects on atom lifetime are presented and explained. With this setup, we realized a triggered single photon source, whose photons have a priori well defined spatial and spectral mode due to the optical fiber and the atomic transition.In a second part, we present the design of an experiment which optimally couples a trapped single atom register to a fiber Fabry-Pérot cavity and where a high numerical aperture lens allows for individual imaging and addressing. A sub-micron precision laser ablation setup is built to create and to analyze in situ desired mirror shapes on optical fiberend faces. Then, we present the produced double resonant fiber cavities with controlled birefringence. Eventually, we describe the created experimental setup for fast cold atom cloud production and transport towards the cavity.

Armadilhamento duplo de átomos neutros constitui um dos avanços mais recentes no estudo de colisões frias. Obtivemos experimentalmente as taxas de perda devido a interação de espécies alcalinas mistas (Cs/Rb). Utilizamos uma armadilha magneto-óptica mista operando com feixes de alta intensidade permitindo o resfriamento e confinamento das amostras com sucesso. Esse trabalho apresenta-se de forma relevante pois corresponde a primeira etapa para o estudo do processo de formação de moléculas frias heteronucleares. Uma comparação entre duas técnicas de monitoramento dos processos de carga de átomos foi realizada. Os resultados tanto qualitativamente como quantitativamente foram satisfatórios. Determinamos as taxas de perda, de interesse e analisamos essas taxas considerando a proporção entre as massas dos átomos envolvidos e enfocando o efeito causado pela diferença de massa entre eles concluindo assim o objetivo principal dessa dissertação. / Double trapping of neutral atoms is one of the most recent advances in the study of collisions cold. Experimentally obtained the rates of loss due to the interaction of species alkaline mixed (Cs / Rb). We use a magneto-optical trap mixed operating with beams of high intensity allowing the cooling and containment of the samples successfully. This work is so important because it represents the first step to study the process of formation of molecules heteronucleares cold. A comparison between two techniques of monitoring procedures for cargo of atoms was performed. The results both qualitatively and quantitatively were satisfactory. And the rates of loss of interest and analyze the rates considering the ratio between the masses of atoms involved and focusing on the effect caused by the difference of mass between them thus completing the main objective of this dissertation.