Ultracold atoms have been successfully used to study numerous systems, previously unaccessible, but a precise control over the atom number of the sample still remains a challenge. This dissertation describes our progress towards achieving Fock states of atoms. The first three chapters cover the basic physics necessary to understand the techniques we use in our lab to manipulate atoms. We then summarize our experimental results from an earlier setup where we did two experiments. In the first experiment we compare the transport of cold atoms and a Bose Einstein Condensate (BEC) in a periodic potential. We find a critical potential height beyond which the condensate behavior deviates significantly from that of thermal atoms. In the second experiment we study the effect of periodic temporal kicks by a spatially periodic potential on a BEC in a quasi one dimensional trap. We observe a limit on the energy that the system can absorb from the kicks, which we conclude is due to the finite height of the trap rather than quantum effects. The majority of the dissertation discusses our experimental setup designed to produce Fock states. The setup is designed to use the method of laser culling to produce Fock states. We are able to create a BEC and transport it into a glass cell 25 cm away. We tried different innovative methods to reduce vibrations during transport before finally settling to a commercial air bearing translation stage. We create a high confinement one dimensional optical trap using the Hermite Gaussian TEM₀₁ mode of a laser beam. Such a trap gives trapping frequencies comparable to an optical lattice and allows us to create a single one dimensional trap. We creating the TEM₀₁ mode using an appropriate phase object (phase plate) in the path of a TEM₀₀ mode beam. The method for producing the phase plate was very well controlled to obtain a good quality mode. Once the atoms are loaded into this one dimensional trap we can proceed to do laser culling to observe Sub-Poissonian number statistics and eventually create Fock states of few atoms. Finally, we describe a novel method to create a real time tunable optical lattice which would provide us with the ability of spatially resolved single atom detection. The majority of the dissertation discusses our experimental setup designed to produce Fock states. The setup is designed to use the method of laser culling to produce Fock states. We are able to create a BEC and transport it into a glass cell 25 cm away. We tried different innovative methods to reduce vibrations during tr₀ansport before finally settling to a commercial air bearing translation stage. We create a high confinement one dimensional optical trap using the Hermite Gaussian TEM₀₁ mode of a laser beam. Such a trap gives trapping frequencies comparable to an optical lattice and allows us to create a single one dimensional trap. We creating the TEM₀₁ mode using an appropriate phase object (phase plate) in the path of a TEM₀₀ mode beam. The method for producing the phase plate was very well controlled to obtain a good quality mode. Once the atoms are loaded into this one dimensional trap we can proceed to do laser culling to observe Sub-Poissonian number statistics and eventually create Fock states of few atoms. Finally, we describe a novel method to create a real time tunable optical lattice which would provide us with the ability of spatially resolved single atom detection. The majority of the dissertation discusses our experimental setup designed to produce Fock states. The setup is designed to use the method of laser culling to produce Fock states. We are able to create a BEC and transport it into a glass cell 25 cm away. We tried different innovative methods to reduce vibrations during transport before finally settling to a commercial air bearing translation stage. We create a high confinement one dimensional optical trap using the Hermite Gaussian TEM₀₁ mode of a laser beam. Such a trap gives trapping frequencies comparable to an optical lattice and allows us to create a single one dimensional trap. We creating the TEM₀₁ mode using an appropriate phase object (phase plate) in the path of a TEM₀₀ mode beam. The method for producing the phase plate was very well controlled to obtain a good quality mode. Once the atoms are loaded into this one dimensional trap we can proceed to do laser culling to observe Sub-Poissonian number statistics and eventually create Fock states of few atoms. Finally, we describe a novel method to create a real time tunable optical lattice which would provide us with the ability of spatially resolved single atom detection. The majority of the dissertation discusses our experimental setup designed to produce Fock states. The setup is designed to use the method of laser culling to produce Fock states. We are able to create a BEC and transport it into a glass cell 25 cm away. We tried different innovative methods to reduce vibrations during transport before finally settling to a commercial air bearing translation stage. We create a high confinement one dimensional optical trap using the Hermite Gaussian TEM₀₁ mode of a laser beam. Such a trap gives trapping frequencies comparable to an optical lattice and allows us to create a single one dimensional trap. We creating the TEM₀₁ mode using an appropriate phase object (phase plate) in the path of a TEM₀₀ mode beam. The method for producing the phase plate was very well controlled to obtain a good quality mode. Once the atoms are loaded into this one dimensional trap we can proceed to do laser culling to observe Sub-Poissonian number statistics and eventually create Fock states of few atoms. Finally, we describe a novel method to create a real time tunable optical lattice which would provide us with the ability of spatially resolved single atom detection. / text

Mon projet de thèse a eu pour objectif l'étude des propriétés magnétiques de condensats de Bose-Einstein d'atomes de Sodium confinés dans un piège optique. Dans la première partie, nous présentons le dispositif expérimental et le protocole suivi pour la production tout-optique de condensats. La première étape consiste dans le chargement d'un piège dipolaire croisé désaccordé vers le rouge à partir d'atomes pré-refroidis dans un piège magnéto-optique. La deuxième étape est le refroidissement évaporatif dans un piège dipolaire composite, combinaison du piège dipolaire croisé avec un faisceau fortement focalisé. Nous sommes ainsi capables de réaliser des condensats de Bose-Einstein quasi-purs contenant environ 3000 atomes. Dans la deuxième partie, nous nous intéressons aux propriétés magnétiques qui découlent de la présence de trois espèces de spin simultanément piégées. Nous présentons des méthodes de contrôle de la magnétisation des nuages ultra-froids, ainsi que des procédures de diagnostic de la composition de spin. Nous utilisons ces échantillons pour explorer le diagramme de phase à basse température, en fonction de la magnétisation et du champ magnétique. Nous montrons l'accord satisfaisant de ces résultats expérimentaux avec une théorie de champ champ moyen dans l'approximation de mode commun. Enfin, nous observons des fluctuations anormales des populations à bas champ et basse magnétisation. On les relie à des fluctuations collectives tendant à restaurer la symmétrie de spin, qui disparaissent à la limite thermodynamique mais sont présentes dans nos échantillons de taille finie.

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.

This thesis describes the design, construction and optimisation of a new apparatus to produce Bose-Einstein condensates (BECs) of 87Rb atoms. The main aim in building this system was to include a high resolution imaging system capable of resolving single atoms. Optical access for the imaging system was created by including a stage of atom transport in which the atoms are magnetically transferred ~50 cm from a magneto-optical trap (MOT), where they are initially collected, to a glass science cell where experiments are carried out and imaging takes place. Two magnetic transport schemes have been demonstrated, based on approaches first used in other laboratories. First, a scheme in which the atoms are transferred in a moving pair of magnetic trapping coils. Second, a hybrid scheme where the atoms are translated part of the distance in the moving coils, and the rest of the way by switching the current in a chain of fixed coils. This second scheme was designed to allow optical access for a high numerical aperture microscope objective to be placed immediately next to the science cell for high resolution imaging. The atoms were first collected in a large pyramid MOT which can be loaded with 3 × 10^9 atoms in a time of 20 s. Around half of these atoms – those in the |F = 1, mF = −1> magnetic substate – were then magnetically trapped prior to transport. The typical fraction of the trapped atoms transferred to the science cell was ~30% and ~18% for the moving coils and hybrid schemes respectively. Evaporative cooling was carried out on the atom cloud following transport with the moving coils and loading into a time-orbiting potential trap. The optimised cooling sequence lasted for 28 s and consistently produced a pure condensate with 5 × 10^5 atoms. A BEC has also been produced by evaporative cooling following hybrid transport. The next experimental steps will be to optimise the hybrid transfer approach further and install the high resolution imaging system. The system is well-placed to continue an ongoing series of experiments in which ultracold atoms are trapped in RF-dressed potentials. These potentials will be used to study low-dimensional quantum gases as well as in experiments where small atom number BECs are rapidly rotated to enter the fractional quantum Hall regime.

Neste trabalho estudamos um sistema bidimensional composto de duas espécies atômicas condensadas, uma delas contendo uma rede de vórtices. Analogamente ao modelo desenvolvido para tratar de átomos ultrafrios em redes ópticas, mapeamos o Hamiltoniano do nosso sistema com o Hamiltoniano do modelo Bose-Hubbard (BH), com o potencial periódico da rede advindo da interação de campo médio entre as duas espécies. A variação do comprimento de espalhamento atômico permite alterar as propriedades do potencial confinante, com a indução da transição de fase quântica na espécie aprisionada nos vórtices. O novo aspecto trazido pela rede de vórtices advém dos seus modos de excitação de baixa energia, os modos de Tkachenko. Consideramos os efeitos da dinâmica própria desse potencial sobre a espécie aprisonada através de um modelo BH efetivo, com novos valores para interação local e tunelamento, além de um termo adicional de interação de longo alcance, mediada pelos modos da rede. Além de complementar os estudos com redes ópticas estáticas, a proposta teórica desenvolvida apresenta grande viabilidade experimental no contexto das técnicas atuais para manipulação de átomos ultrafrios. / In this work we consider a two dimensional system composed of two condensed atomic species, one containing a vortex lattice. Analogously to the model used to describe ultracold atoms in optical lattices, we mapped our system Hamiltonian in the Hamiltonian of the Bose-Hubbard (BH) model, with the periodic lattice potential arising from the meanfield interaction between the two species. The variation of the atomic scattering length allow us to change the properties of the confining potential, to induce the quantum phase transition in the species trapped in the vortices. The new aspect brought by the vortex lattice comes with its low energy normal modes, the Tkachenko modes. We considered the effects of such dynamic potential over the confined species thought an effective BH model, with new values for the local interaction and tunneling parameters, besides an additional long-range interaction term mediated by the lattice modes. Our theoretical proposal goes beyond the studies with static optical lattice. Additionally, it has great feasibility in the current context of ultra-cold atoms experimental techniques.

This thesis details the design, construction and characterisation of an ultracold atoms system, developed in conjunction with a flexible optical trapping scheme which utilises a Liquid Crystal Spatial Light Modulator (LC SLM). The ultracold atoms system uses a hybrid trap formed of a quadrupole magnetic field and a focused far-detuned laser beam to form a Bose-Einstein Condensate of 2×105 87Rb atoms. Cold atoms confined in several arbitrary optical trapping geometries are created by overlaying the LC SLM trap on to the hybrid trap, where a simple feedback process using the atomic distribution as a metric is shown to be capable of compensating for optical aberrations. Two novel methods for creating flexible optical traps with the LC SLM are also detailed, the first of which is a multi-wavelength technique which allows several wavelengths of light to be smoothly shaped and applied to the atoms. The second method uses a computationally-efficient minimisation algorithm to create light patterns which are constrained in both amplitude and phase, where the extra phase constraint was shown to be crucial for controlling propagation effects of the LC SLM trapping beam.

Orientador: Valery Shchesnavich / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós-Graduação em Física, 2012.

Orientador: Valery Shchesnovich / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós-Graduação em Física, 2014

Orientador: Marcelo Batista Hott / Coorientador: Alvaro de Souza Dutra / Banca: Denis Dalmazi / Banca: Roberto André Kraenkei / Banca: Othon Cabo Winter / Wesley Bueno Cardoso / Resumo: Nesta tese lidamos com a equação de Schroedinger não linear com coeficientes modulados em diferentes contextos. Esta equação diferencial não linear é amplamente usada para descrever a propagação de pulsos de luz através de uma fibra óptica ou para modelar a dinâmica de um condensado de Bose-Einstein. Primeiro, aplicamos as transformações canônicas de ponto para resolver algumas classes de equação de Schroedinger não linear com coeficientes modulados ou seja, aqueles que possuem não linearidades cúbica e quântica (dependentes do espaço e tempo) específicas. O método aplicado aqui nos permite encontrar soluções tipo sólitons localizados (no espaço) para a equação de Schroedinger não linear com coeficientes modulados, que não foram apresentados antes. No contexto de condensados de Bose-Einstein, nós generalizamos o potencial externo o qual armadilha o sistema, e os termos de não linearidade da equação diferencial. Em seguida, aplicamos as transformações canônicas de ponto para resolver algumas classes de duas equações de Schroedinger não lineares acopladas com coeficientes modula-dos isto é, não linearidades cúbica e quântica - dependentes do espaço e tempo - específicas. O método aplicado aqui nos permite encontrar uma classe de soluções de sólitons tipo vetoriais localizados (no espaço) das duas equações de Schroedinger não linear acopladas. Os sólitons vetoriais encontrados aqui podem ser aplicados a estudos teóricos de condensados de Bose-Einstein de átomos com dois estados internos diferentes ou á propagação de pulsos de luz através de fibras ópticas focalizadoras ou desfocalizadoras. Finalmente, usando transformações canônicas de ponto obtemos soluções exatas localizadas (no espaço) da equação de Schroedinger não linear com não linearidades cúbica e quântica moduladas no espaço e tempo ...(Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this thesis we deal with the nonlinear Schrödinger equation with modulated coefficients in different contexts. This nonlinear differential equation is widely used to describe light pulses propagating through an optical fiber or to model the dynamics of a Bose-Einstein condensate. First, we apply point canonical transformations to solve some classes of nonlinear Schrödinger equation with modulated coefficients namely, those which possess specific cubic and quantic (time- and space-dependent) nonlinearities. The method applied here allows us to find wide localized (in space) soliton solutions to the nonlinear Schrödinger equation, which were not presented before. In the context of Bose-Einstein condensates, we also generalize the external potential which traps the system and the nonlinearities terms. Then, we apply point canonical transformations to solve some classes of two coupled nonlinear Schrödinger equations with modulated coefficients namely, specific cubic and quantic - time and space dependent - nonlinearities. The method applied here allows us to find a class of wide localized (in space) vector soliton solutions of two coupled nonlinear Schrödinger equations. The vector solitons found here can be applied to theoretical studies of Bose-condensed atoms in two different internal states and of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities. Finally, we use point canonical transformations to obtain localized (in space) exact solutions of the nonlinear Schrödinger equation with cubic and quantic space and time modulated nonlinearities and in the presence of time-dependent and inhomogeneous external potentials and amplification or absorption (source or drain) term. We obtain a class of wide localized exact solutions of nonlinear Schrödinger equation in the presence of a number of non-Hermitian ... (Complete abstract click electronic access below) / Doutor

Mon travail de thèse s'inscrit dans le développement de l'optique atomique. Ce manuscrit décrit les trois sujets traités pendant ma thèse. Dans un premier temps mon travail a été de construire une nouvelle expérience permettant de produire des condensats de Bose-Einstein. Nous nous intéressons d'abord au dispositif utilisant le refroidissement laser et l'évaporation micro-onde permettant d'obtenir un nuage d'atomes froids dans un piège magnétique quadrupolaire. Nous présentons ensuite les montages optiques permettant d'obtenir les différents faisceaux laser nécessaires au fonctionnement du dispositif. Enfin, nous détaillons le protocole permettant de produire des condensats de Bose-Einstein dans notre piège hybride combinant les avantages d'un piège magnétique à ceux d'un piège dipolaire et nous le caractérisons à l'aide d'une méthode d'analyse statistique nommée Analyse par Composante Principale. Le deuxième sujet concerne l'étude de la propagation d'une onde de matière dans un réseau de taille finie. Nous démontrons le piégeage d'atomes dans une cavité de Bragg produite par l'enveloppe gaussienne d'un réseau optique. Les atomes confinés dans le réseau oscillent et nous observons le découplage du réseau de paquets d'atomes par effet tunnel, démontrant ainsi un nouveau type de barrières tunnel. L'étude de la probabilité de transmission à travers ce type de barrières montre qu'elles sont équivalentes à des barrières répulsives submicronique. Enfin, de manière théorique, nous étudions un formalisme basé sur la fonction de Wigner et l'utilisation d'une loi d'échelle permettant d'imaginer des protocoles de manipulation de fonctions d'onde à N corps dans l'espace des phases. Nous appliquons d'abord ce formalisme à un protocole de refroidissement en deux étapes, impliquant un temps de vol et l'application soudaine d'un potentiel harmonique. Nous discutons ensuite l'effet des interactions répulsives entre atomes et de l'anharmonicité du potentiel. Enfin nous proposons deux protocoles de manipulations de fonctions d'onde dans l'espace des phases. Le premier est un protocole de refroidissement analogue au protocole en deux étapes mais dont la robustesse est augmentée vis-à-vis d'un défaut du potentiel appliqué. Le deuxième protocole proposé permet d'accélérer le mode de respiration d'un nuage d'atomes dans un piège décomprimé. / My thesis work is part of the development of atomic optics.First my work has been to build a new experience to produce Bose-Einstein condensates. We will see how we produce a cold atoms cloud in a magnetic quadrupole trap using laser cooling and micro-wave evaporation. We then present the optical setup to produce the laser beams needed for the apparatus operation. At last, we detail the protocol allowing to produce Bose-Einstein condensates in our hybrid trap, combining the advantages of a magnetic trap and a dipole trap. We then characterize the hybrid trap using a statistical analysis method named Principal Component Analysis. The second subject concerns the study of the propagation of a matter-wave in a finite size lattice. We demonstrate the trapping of atoms inside a Bragg cavity produced by the gaussian enveloppe of an optical lattice. The confined atoms oscillate inside the lattice and we observe the tunnel decoupling of atoms from the cavity, demonstrating a new kind of tunnel barrier. The study of the transmission probability through these barriers shows that they are equivalent to submicronic repulsive barriers. Finally, I studied a theoretical formalism based on the Wigner function and the use of a scaling law, allowing to imagine protocols to manipulate many-body wave functions in phase space. We apply this formalism to a two steps cooling protocol involving a time of flight and the sudden application of an harmonic potential. We discuss the effects of repulsive interactions between atoms and of the anharmonicities in the potential. At last, we propose two protocols to manipulate the phase space distribution of wave functions. The first aim to enhance the robustness of the to step cooling protocol regarding a flaw of the harmonic potential. The second allows to accelerate the breathing mode of an atomic cloud in a decompressed trap.