Le projet HORACE consiste en la réalisation d'une horloge atomique compacte de hautes performances exploitant le refroidissement laser d'atomes de 133Cs en "lumière isotrope", en visant principalement le marché des horloges embarquées. Afin d'obtenir un dispositif de faible encombrement, nous réalisons en un lieu unique l'ensemble des phases de la séquence d'horloge (refroidissement, préparation, interrogation et détection). Ceci est rendu possible grâce à l'utilisation d'une cavité d'interrogation à la fois résonnante à la fréquence de la transition d'horloge, et faisant office de sphère intégrante pour la lumière de refroidissement. L'essentiel du travail de thèse présenté ici est consacré à l'étude expérimentale du refroidissement dans le champ de speckle 3D généré à l’intérieur de cette cavité. En limitant le refroidissement à une simple phase de capture, environ 3x108 atomes sont refroidis à des températures cinétiques inférieures à 60 K. Nous montrons par ailleurs qu'une répartition inhomogène de l'énergie optique dans la cavité conduit à scinder la phase de refroidissement sub-Doppler en deux étapes. Malgré le caractère aléatoire de la polarisation entre « grains » de speckle adjacents, la dynamique du refroidissement en régime sub-Doppler que nous observons est identique à celle suivie par des atomes refroidis au sein d’un réseau optique conventionnel. La dernière partie de ce mémoire est consacrée à l’aspect métrologique du projet où la séquence complète de l’horloge est démontrée pour la 1ère fois dans une zone d’interaction unique. Une stabilité relative de fréquence de 2x10-13-1/2 est attendue pour un fonctionnement terrestre de l’horloge. / The HORACE project consists in the development of a high-performance compact atomic clock based on isotropic laser cooling of 133Cs atoms, targeting the needs for on-board clocks. In order to minimize the clock size, the entire clock sequence is performed inside one interaction zone only, including atomic cooling, preparation, interrogation and detection. This is made possible with a microwave interrogation cavity that is both resonant at the clock transition frequency, and used as an integrating sphere for the cooling light as well. This thesis work is mainly dedicated to the experimental study of the atomic cooling in the 3D speckle field generated inside the cavity. By limiting the cooling sequence to a capture phase, about 3x108 atoms can be cooled to kinetic temperatures lower than 60 microkelvins. Besides, we show that an inhomogeneous optical energy repartition in the cavity leads us to perform the sub-Doppler cooling phase in 2 steps. Despite random polarization change from one speckle grain to another, the atomic cooling dynamics observed in the sub-Doppler regime is similar to the one observed in conventional optical lattices. The last part of this thesis is devoted to the metrological aspect where the entire clock sequence is demonstrated for the first time at the same place. The fractional frequency stability of 2x10-13-1/2 should be reached on Earth.

Un réseau optique, créé par des lasers, permet de piéger des atomes refroidis à ultra-basse température. Il permet d'obtenir une contrainte comme s'il s'agissait d'un cristal idéal (un cristal sans agitation thermique). Je décris les états des particules dans un potentiel périodique (un réseau optique) à l'aide d'ondes de probabilité (physique quantique) stationnaires (théorie indépendante du temps). Le caractère ondulatoire de la matière est exacerbé à très basse température et donne lieu à des phénomènes d'interférence et de résonance particuliers. / An optical lattice, created by lasers, can trap atoms cooled to ultra-low temperatures. It provides a constraint as if it were a perfect crystal (a crystal without thermal agitation). I describe the states of particles in a periodic potential (optical network) using probability waves (quantum physics) stationary (independent theory of time). The wave nature of the material is exacerbated at very low temperatures and gives rise to interference phenomena and individual resonance.

In this thesis, we investigate the coherent scattering of light by atoms randomly distributed in space. As described by a model of coupled dipoles, the cooperation in the spontaneous emission process results from purely optical interactions between the atomic internal degrees of freedom. In the optically dilute regime, where the atomic medium can be described by a refractive index, we have shown that light can be deflected with the application of a gradient of magnetic field. In the dense regime, short-range interactions appear to suppress Anderson localization of light even in two dimensions, a result which disassembles the common belief that all waves are localized in two dimensions. We also find that the fringe pattern, resulting from the interference between light scattered by an atomic cloud and that of its specular image, is robust to both disorder averaging and saturation. Finally, we demonstrate two-atom bound states in the two-dimensional motion through the long-range optical coupling. This optical binding effect with an atom pair will be important to investigate the all-optical stabilization of large clouds. / Nesta tese, investigamos o espalhamento coerente de luz por átomos distribuídos aleatoriamente no espaço. Conforme descrito por um modelo de dipolos acoplados, a cooperação no processo de emissão espontânea resulta de interações puramente ópticas entre os graus internos de liberdade dos átomos. No regime opticamente diluído, onde o meio atômico pode ser descrito por um índice de refração, mostramos que a luz pode ser desviada com a aplicação de um gradiente de campo magnético. No regime denso, as interações de curto alcance parecem suprimir a localização de Anderson da luz mesmo em duas dimensões, resultado que desmonta a crença comum de que todas as ondas estão localizadas em duas dimensões. Também descobrimos que o padrão de franjas, resultante da interferência entre a luz espalhada por uma nuvem atômica e a de sua imagem especular, é robusto tanto contra a média em disordem quanto contra saturação. Finalmente, demonstramos estados ligados de dois átomos no movimento bidimensional através do acoplamento óptico de longo alcance. Este optical binding effect com um par de átomos será importante para investigar a estabilização totalmente óptica de nuvens extensas.

Usando a técnica de resfriamento evaporativo para átomos comprimidos numa armadilha magnética tipo QUIC, implementamos experimentos para observar Condensação de Bose-Einstein de átomos de sódio. Nessa armadilha magnética temos átomos advindos de uma armadilha magneto-óptica, a qual é carregada por um feixe desacelerado como etapa de pré-resfriamento. Nossas medidas foram baseadas em imagens de absorção fora de ressonância de um feixe de prova pela amostra atômica. Essas imagens foram feitas in situ, ou seja, na presença do campo da armadilha magnética, pelo fato do número de átomos ser baixo e a técnica de tempo de vôo não ser adequada a essa situação. Baseado no perfil de densidade e na temperatura medidos, calculamos a densidade de pico no espaço de fase D, a qual é seguida nas várias etapas de evaporação. Nossos resultados mostram que para uma freqüência final de evaporação de 1,65 MHz nós superamos o valor esperado para D (2,612) alcançar o ponto crítico, no centro da amostra, para obter a condensação. Devido ao baixo número de átomos restantes no potencial, a interação não produz efeitos consideráveis e dessa forma um modelo de gás ideal permite justificar essa observação. / Using a system composed of a QUIC trap loaded from a slowed atomic beam, we have performed experiments to observe the Bose-Einstein Condensation of Na atoms. In order to obtain the atomic distribution in the trap, we use an in situ out of resonance absorption image of a probe beam to determine the temperature and the density, which are use to calculate the phase space D. We have followed D as a function of the final evaporation frequency. The results show that at 1.65 MHz we crossed the critical value for D which corresponds to the point to start Bose-Condensation of the sample. Due to the low number of atoms remaining in the trap at the critical point, the interaction produce minor effects and therefore an ideal gas model explains well the observations.

Tendo por objetivo principal a implementação de um laboratório de pesquisa em tempo e freqüência, tomamos como primeiro alvo a ser alcançado a realização da definição primária do segundo, conforme estabelecido pelo BIPM, baseado no átomo de 133CS. Seguindo os passos nessa linha de pesquisa, o laboratório construiu um primeiro padrão baseado em feixe efusivo e operado opticamente. Atualmente, os sistemas com maior capacidade de determinação do segundo são os padrões de átomos frios, denominados chafarizes, dado o seu esquema de funcionamento. O objetivo principal desse trabalho foi o desenvolvimento de um padrão de tempo e freqüência baseado em um sistema de átomos frios, passando por todas as fases de sua implementação. Tais fases dizem respeito à construção de sistemas de controle de lasers de diodo, síntese de freqüências, avaliação de sinais de tempo e freqüência e controle e aquisição dos sinais de interrogação atômica. Adicionada a isso a necessidade de estabelecer um ambiente próprio ao desenvolvimento de tal experimento. Os resultados observados até aqui permitem que sejam estabelecidas novas metas, em busca do refinamento desse padrão. Além disso, os tipos de sistemas abordados são passíveis de utilização no desenvolvimento de outros padrões, tanto primários como secundários, sendo requisitos fundamentais no estabelecimento de metrologia científica de tempo e freqüência. / Having as a main goal the implementation of a research laboratory in time and frequency, we set the first target to be reached the realization of the primary definition of the second, as stated by BIPM, based on the 133CS atom. Following the steps in this research line our laboratory constructed a first standard based on an effusive beam optically operated. Nowadays, the most capable systems in the determination of the second are the cold atoms standards, called fountains, due to their operation mode. The main subject of this thesis is the development of a time and frequency standard based in cold atoms doing all the steps to implement it. These steps concern to the construction of diode lasers control systems, frequency synthesis, time and frequency signal characterization and atomic interrogation signal acquisition, added the need to the establishment of an appropriate environment to develop such experiment. The observed results until now allowed the determination of the new goals in the search of the standard refinement. Moreover, the kind of systems described here can be used in the development of other standards, either primary or secondary, being fundamental requisites in the establishment of time and frequency scientific metrology.

In this thesis, we investigate the coherent scattering of light by atoms randomly distributed in space. As described by a model of coupled dipoles, the cooperation in the spontaneous emission process results from purely optical interactions between the atomic internal degrees of freedom. In the optically dilute regime, where the atomic medium can be described by a refractive index, we have shown that light can be deflected with the application of a gradient of magnetic field. In the dense regime, short-range interactions appear to suppress Anderson localization of light even in two dimensions, a result which disassembles the common belief that all waves are localized in two dimensions. We also find that the fringe pattern, resulting from the interference between light scattered by an atomic cloud and that of its specular image, is robust to both disorder averaging and saturation. Finally, we demonstrate two-atom bound states in the two-dimensional motion through the long-range optical coupling. This optical binding effect with an atom pair will be important to investigate the all-optical stabilization of large clouds. / Nesta tese, investigamos o espalhamento coerente de luz por átomos distribuídos aleatoriamente no espaço. Conforme descrito por um modelo de dipolos acoplados, a cooperação no processo de emissão espontânea resulta de interações puramente ópticas entre os graus internos de liberdade dos átomos. No regime opticamente diluído, onde o meio atômico pode ser descrito por um índice de refração, mostramos que a luz pode ser desviada com a aplicação de um gradiente de campo magnético. No regime denso, as interações de curto alcance parecem suprimir a localização de Anderson da luz mesmo em duas dimensões, resultado que desmonta a crença comum de que todas as ondas estão localizadas em duas dimensões. Também descobrimos que o padrão de franjas, resultante da interferência entre a luz espalhada por uma nuvem atômica e a de sua imagem especular, é robusto tanto contra a média em disordem quanto contra saturação. Finalmente, demonstramos estados ligados de dois átomos no movimento bidimensional através do acoplamento óptico de longo alcance. Este optical binding effect com um par de átomos será importante para investigar a estabilização totalmente óptica de nuvens extensas.

Si les systèmes quantiques à une dimension ont longtemps été vus comme de simples modèle-jouets, bon nombre sont à présent réalisés dans les expériences d’atomes ultra-froids. Dans ces expériences, le potentiel de confinement du gaz induit nécessairement une inhomogénéité spatiale. Cette inhomogénéité brise l'invariance par translation qui joue un rôle clé dans les solutions analytiques, notamment celle de l'Ansatz de Bethe. On propose dans cette thèse de développer une théorie des champs effective à même de caractériser ces gaz quantiques inhomogènes, en généralisant la théorie du liquide de Luttinger. Dans ces conditions la métrique de l'action effective est courbe. Sous une hypothèse de séparation des échelles, les paramètres de l'action peuvent néanmoins être fixés par les solutions de l'Ansatz de Bethe. Le problème peut alors se ramener au cas d'un espace plat en faisant appel aux théories conformes. On est ainsi amené à résoudre le champ libre gaussien inhomogène, qui donne accès à toutes les fonctions de corrélations du modèle considéré. Dans cette thèse, on s'intéresse plus particulièrement au modèle de Lieb-Liniger. Les résultats obtenus sont comparés au système simulé par DMRG. / One-dimensional quantum systems have long been seen as simple toy-models but are nowadays often realized in ultracold atoms experiments. In those experiments the confining potential creates a spatial inhomogeneity. This breaks the translation invariance which plays a key role in exact analytical solutions as the Bethe Ansatz. In this thesis, we propose an effective theory generalizing the Luttinger liquid approach for inhomogeneous systems. In this setup, the effective action lives in curved space. However, making the hypothesis of separation of scales allow to compute the action's parameters by using Bethe Ansatz. The problem can then be solved in flat space by using tools from conformal theory. This leads us to solving the inhomogeneous gaussian free field that gives access to all correlation functions of the model under investigation. Here we focus on the Lieb-Liniger model. Our results are tested against DMRG simulations.

Dans cette thèse, nous étudions la propagation des atomes dans un guide magnétique toroïdal, dans le but de développer un capteur inertiel. Ici, nous présentons différentes stratégies pour créer un guide sur une puce atomique pour un interférometre Sagnac atomique guidé. Nous avons mis au point trois solutions qui peuvent être realisé avec la même configuration des fils. Ils utilise la technique de modulation de courant avec un nouveau point de vue qui traite simultanément la problème de rugosité des fils et les pertes de Majorana dépendant du spin. L'effect de la propagation multimode des atomes dan le guide est aussi quantifié dans cette thèse. En utilisant un modèle simple, nous avons couvert les cas de la propagation de gaz non interactif ultra froids et thermique. Nous avons identifié les conditions operationelles pour realiser un interferometre à atomes froids avec une grande gamme dynamique, essentielle pour les application en navigation inertielle. Expérimentalement, cette thèse decrit la réalisation et la characterisation de la source atomes froids proche d'un substrat avec un dépôt d'or, ainsi que l'implémentation et la caracterisation des systèmes de détection. / In this thesis we study the propagation of atoms in a magnetic toroidal waveguide, with the aim of developing an inertial sensor. Here, we present different strategies to create the waveguide on an atom chip for a guided Sagnac atom interferometer. We devised three solutions which can be achieved using the same wire configuration. They use the current modulation technique, from a new point of view, which simultaneously tackles the problem of wire corrugation and spin dependent Majorana atom losses. The effect of the multimode propagation of the atoms in the guide is also quantified in this thesis. Using a simple model, we covered the propagation of noninteracting ultracold and thermal gases. We identified the operating conditions to realize a cold atom interferometer with a large dynamic range essential for applications in inertial navigation. Experimentally, the thesis describes the realisation and characterisation of the cold atom source close to a gold coated substrate, as well as the implementation and the characterisation of the atom detection systems.

In this thesis, we investigate strongly correlated phenomena in quantum spin systems. In the first part of this work, we study geometrically frustrated antiferromagnets (AFMs). Generalizing the SU(2) Heisenberg Hamiltonian to Sp(N) symmetry, we obtain, in the large-N limit, the mean-field phase diagrams for the planar pyrochlore and cubic AFMs. We then use gauge theories to consider fluctuation effects about their respective mean-field configurations. We find, in addition to conventional Neel states, a plethora of novel magnetically disordered phases: two kinds of spin liquids, Z2 in 2+1D and U(1)in 3+1D, and several valence bond solids such as two and three-dimensional plaquette and columnar singlet states. We use the same approach to study the diamond lattice AFM which possesses extended classical ground state degeneracy. We demonstrate that quantum and entropic fluctuations lift this degeneracy in different ways. In the second part of the thesis, we study ultracold spinor atoms confined in optical lattices. We first demonstrate the feasibility of experimental realization of rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice. We show that the ground state of such disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense, and suggest an imaging experiment to detect the biaxial nematicity in such systems. Finally, using variational wavefunction methods, we study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with n = 1 and n = 2 atoms per lattice site. We show that the long-range dipolar interaction stabilizes a state characterized by antiferromagnetic chains made of ferromagnetically aligned spins. We also obtain the mean-field phase boundary for the superfluid-insulator transition, and show that inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first order antiferromagnetic-ferromagnetic spin ordering transition.

In this thesis, we investigate strongly correlated phenomena in quantum spin systems. In the first part of this work, we study geometrically frustrated antiferromagnets (AFMs). Generalizing the SU(2) Heisenberg Hamiltonian to Sp(N) symmetry, we obtain, in the large-N limit, the mean-field phase diagrams for the planar pyrochlore and cubic AFMs. We then use gauge theories to consider fluctuation effects about their respective mean-field configurations. We find, in addition to conventional Neel states, a plethora of novel magnetically disordered phases: two kinds of spin liquids, Z2 in 2+1D and U(1)in 3+1D, and several valence bond solids such as two and three-dimensional plaquette and columnar singlet states. We use the same approach to study the diamond lattice AFM which possesses extended classical ground state degeneracy. We demonstrate that quantum and entropic fluctuations lift this degeneracy in different ways. In the second part of the thesis, we study ultracold spinor atoms confined in optical lattices. We first demonstrate the feasibility of experimental realization of rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice. We show that the ground state of such disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense, and suggest an imaging experiment to detect the biaxial nematicity in such systems. Finally, using variational wavefunction methods, we study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with n = 1 and n = 2 atoms per lattice site. We show that the long-range dipolar interaction stabilizes a state characterized by antiferromagnetic chains made of ferromagnetically aligned spins. We also obtain the mean-field phase boundary for the superfluid-insulator transition, and show that inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first order antiferromagnetic-ferromagnetic spin ordering transition.