Cette thèse traite du problème à N+1 corps dans les gaz de fermions ultrafroids fortement polarisés. Il s'agit de la situation où un unique atome d'une espèce de spin est immergé dans une mer de Fermi d'atomes de l'autre espèce.<br /> <br /> La première partie utilise une approche hamiltonienne basée sur un développement général de la fonction d'onde du système faisant intervenir un nombre arbitraire de paires particule-trou. Nous montrons que la série d'approximations successives construite converge très rapidement et nous obtenons ainsi une solution essentiellement exacte pour l'énergie et la masse effective du polaron. En dimension 1, dans deux cas particuliers, ce problème peut être résolu analytiquement. La comparaison avec notre série d'approximations est excellente et confirme l'efficacité de ce développement. Enfin, nous précisons les différents cas limites, ainsi que l'influence du rapport des masses entre les deux espèces de spin.<br /> <br /> Dans une deuxième partie, nous utilisons le formalisme des diagrammes de Feynman pour décrire à la fois le polaron et l'état lié. Pour le polaron, nous construisons une théorie équivalente à l'approche hamiltonienne. Pour l'état lié, nous obtenons à nouveau une série d'approximations dont la convergence très rapide vers la solution exacte est parfaitement comprise. Cette approche nous fournit donc une solution quasi-exacte au problème tout au long de la transition BEC-BCS. Enfin, en comparant les énergies des deux quasi-particules, nous étudions la position de la transition polaron - état lié.

L'utilisation des pompes centrifuges à volute joue un rôle important dans divers secteurs de l'industrie en général. Parmi eux on peut mentionner l'automobile, la construction des installations navales, etc. Elles sont couramment employées par leurs prestations concernant leurs performances globales et leur comportement hydroacoustique. Il est bien connu que le comportement du fluide interne est caractérisé par des fortes interactions entre les parties mobiles et fixes qui sont à l'origine du bruit et des vibrations. Dans les cas des pompes centrifuges, le bruit se caractérise particulièrement à la fréquence aubage dû à l'interaction hydrodynamique entre la roue et le bec de volute. L'intensité de cette excitation, qui dépend de la géométrie et des conditions de fonctionnement, peut être nuisible dans certaines conditions et exigences. Les travaux de recherche effectués nous ont permis de contribuer à l'analyse et à la maîtrise des fluctuations de pression dans les pompes centrifuges grâce aux apports conjugués de simulations numériques et d'études expérimentales spécifiques. Une procédure numérique de prédiction du bruit tonal à la fréquence aubage est développée et validée par comparaison aux essais expérimentaux. En outre, l'amélioration des algorithmes numériques ainsi que le développement du matériel informatique ont permis l'émergence de codes de simulation d'écoulements plus avancés. Cependant, étant donné les exigences de précision pour prédire les fluctuations de pression et la difficulté des codes commerciaux d'atteindre des schémas d'ordre élevé nous mènent à développer notre propre code. Ce nouveau code (FV-MLS) plus précis, basé sur la méthode de volumes finis et les approximations de moindres carrés mobiles (Moving Least Squares - MLS), est couplé avec la technique de maillage glissant pour être appliqué dans une configuration 2D d'une pompe centrifuge.

Ultracold Fermi gas is an exciting field benefiting from atomic physics, optical physics and condensed matter physics. It covers many aspects of quantum mechanics. Here I introduce some of my work during my graduate study. We proposed an optical spectroscopic method based on electromagnetically-induced transparency (EIT) as a generic probing tool that provides valuable insights into the nature of Fermi paring in ultracold Fermi gases of two hyperfine states. This technique has the capability of allowing spectroscopic response to be determined in a nearly non-destructive manner and the whole spectrum may be obtained by scanning the probe laser frequency faster than the lifetime of the sample without re-preparing the atomic sample repeatedly. Both quasiparticle picture and pseudogap picture are constructed to facilitate the physical explanation of the pairing signature in the EIT spectra. Motivated by the prospect of realizing a Fermi gas of 40 K atoms with a synthetic non-Abelian gauge field, we investigated theoretically BEC-HCS crossover physics in the presence of a Rashba spin-orbit coupling in a system of two-component Fermi gas with and without a Zeeman field that breaks the population balance. A new bound state (Rashba pair) emerges because of the spin-orbit interaction. We studied the properties of Rashba pairs using a standard pair fluctuation theory. As the two-fold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet pairings (referred to as rashbons) emerge, leading to an anisotropic superfluid. We discussed in detail the experimental signatures for observing the condensation of Rashba pairs by calculating various physical observables which characterize the properties of the system and can be measured in experiment. The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we studied the effect of a single classical impurity in trapped ultracold Fermi superfluids. Although a non-magnetic impurity does not change macroscopic properties of s-wave Fermi superfluids, depending on its shape and strength, a magnetic impurity can induce single or multiple mid-gap bound states. The multiple mid-gap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the Scanning Tunneling Microscope, we proposed a modified radio frequency spectroscopic method to measure the focal density of states which can be employed to detect these states and other quantum phases of cold atoms. A key result of our self consistent Bogoliubov-de Gennes calculations is that a magnetic impurity can controllably induce an FFLO state at currently accessible experimental parameters.

The primary study of this thesis is spin-nematic squeezing in a spin-1 condensate. The measurement of spin-nematic squeezing builds on the success of previous experiments of spin-mixing together with advances in low noise atom counting. The major contributions of this thesis are linking theoretical models to experimental results and the development of the intuition and tools to address the squeezed subspaces. Understanding how spin-nematic squeezing is generated and how to measure it has required a review of several theoretical models of spin-mixing as well as extending these existing models. This extension reveals that the squeezing is between quadratures of a spin moment and a nematic (quadrapole) moment in abstract subspaces of the SU(3) symmetry group of the spin-1 system. The identification of the subspaces within the SU(3) symmetry allowed the development of techniques using RF and microwave oscillating magnetic fields to manipulate the phase space in order to measure the spin-nematic squeezing. Spin-mixing from a classically meta-stable state, the phase space manipulation, and low noise atom counting form the core of the experiment to measure spin-nematic squeezing. Spin-nematic squeezing is also compared to its quantum optics analogue, two-mode squeezing generated by four-wave mixing. The other experimental study in this thesis is performing spin-dependent photo-association spectroscopy. Spin-mixing is known to depend on the difference of the strengths of the scattering channels of the atoms. Optical Feshbach resonances have been shown to be able to alter these scattering lengths but with prohibitive losses of atoms near the resonance. The possibility of using multiple nearby resonances from different scattering channels has been proposed to overcome this limitation. However there was no spectroscopy in the literature which analyzes for the different scattering channels of atoms for the same initial states. Through analysis of the initial atomic states, this thesis studies how the spin state of the atoms affects what photo-association resonances are available to the colliding atoms based on their scattering channel and how this affects the optical Feshbach resonances. From this analysis a prediction is made for the extent of alteration of spin-mixing achievable as well as the impact on the atom loss rate.

Ultracold atoms provide a powerful tool for studying quantum control of interacting many-body systems with well-characterized and controllable Hamiltonians. In this thesis, we demonstrate quantum control of a many-body system consisting of a ferromagnetic spin-1 Bose-Einstein condensate (BEC). By tuning the Hamiltonian of the system, we can generate either a phase space with an unstable hyperbolic fixed point or a phase space with an elliptical fixed point. A classical pendulum with a stable oscillation about the "down" position and an inverted pendulum with unstable non-equilibrium dynamics about the "up" position are classical analogs of the quantum spin dynamics we investigate in this thesis. In one experiment, we dynamically stabilize the system about an unstable hyperbolic fixed point, which is similar to stabilizing an inverted pendulum. In a second experiment, we parametrically excite the system by modulating the quadratic Zeeman energy. In addition, we demonstrate rectifier phase control as a new method to manipulate the quantum states of the many-body system. This is similar to parametric excitation and manipulation of the oscillation angle of a classical pendulum. These experiments demonstrate the ability to control a quantum system realized in a spinor BEC, and they also can be applied to other quantum systems. In addition, we extend our studies to atoms above the Bose-Einstein transition temperature, and we present results on thermal spin relaxation processes and equilibrium spin populations.

Two-component fluids can be miscible (if they overlap in space) or immiscible (if they remain phase-separated). In the context of trapped two-species Bose-Einstein condensates (BECs), these miscibility regions can only be fully characterize if one considers the interspecies interaction, the mass ratio and the number of atoms in each species. The dynamics of coupled vortices is different for each miscibility region and exotic vortices configurations (such as, square vortex lattices, \"vortex sheets\", skyrmions, etc.) are expected to occur. In this thesis, we present the construction of a new experimental system able to produce a two-species Bose-Einstein condensate of 23Na-41K atoms with tunable interspecies interactions and study the dynamics of coupled vortices in the different miscibility regimes. The BEC of sodium atoms obtained first in a Plug trap and later, in a crossed optical dipole trap, is fully characterized as well as the cold atomic cloud of potassium atoms produced by means of a Gray molasses cooling procedure. In the crossed optical dipole trap, the vortices will be nucleated with the use of a stirring beam. Therefore, in the end of this thesis, we present the stirring beam setup and its characterization prior aligning it into the 23Na BEC. / Um sistema de dois fluídos pose ser miscível (se os fluídos ocupam a mesma região do espaço) ou imiscível (se eles permanecem separados). No caso de condesados de Bose-Einstein (do inglês, \"Bose-Einstein condensate\" - BEC) de duas espécies atômicas aprisionados, as regiões de miscibilidade só podem ser completamentamente caracterizadas se considerarmos a interção entre as espécies, a razão entre as massas e o número de átomos em cada uma das espécies. A dinâmica de vórices é diferente para cada região de miscibilidade possibilitando a obtenção de configurações exóticas de vórtices (como, a produção de redes de vórtices quadradas, de folhas de vórtices (do inglês, \"vortex sheets\"), skyrmions, etc.). Nesta tese, apresentamos a construção de um novo sistema experimental capaz de produzir um condensado de Bose-Einstein de duas espécies atômicas, 23Na-41K, com interação variável e estudar a dinâmica de vórtices em diferentes regimes de miscibilidade. O condensado de átomos de sódio, inicialmente obtido na armadilha Plug e depois, em uma armadilha ótica cruzada, é completamentamente caracterizado assim como a nuvem atômica ultra-fria produzida a partir da técnica de molasses cinza (do inglês, \"Gray molasses\"). Na armadilha ótica, os vórtices serão produzidos a partir da utilização de um feixe de laser denominado stirring. Assim, ao final da tese, apresentamos o esquema ótico para a produção deste feixe de laser e a sua caracterização antes de alinhá-lo nos átomos.

Nous étudions la dynamique non linéaire en champ moyen de la formation de molécules diatomiques par photo-association ou magnéto-association d’atomes ultra froids pour un système entièrement atomique dans l’état initial. Nous montrons que dans la limite d’une forte interaction non linéaire entre un système atome-molécule ultra froid et un champ électromagnétique quasi résonnant, le processus de formation du condensat moléculaire peut évoluer suivant deux scénarios en fonction des caractéristiques du champ : régime faiblement oscillatoire ou régime fortement oscillatoire. Dans le cas du régime faiblement oscillatoire, le nombre de molécules augmente sans oscillations prononcées des populations atomiques et moléculaires alors que de fortes oscillations de Rabi apparaissent dans le second cas. Nous présentons des solutions analytiques décrivant la dynamique temporelle du système dans ces deux cas. Nous étudions ensuite l’influence de la diffusion élastique entre particules sur la dynamique de formation cohérente de molécules sous l’action d’un champ extérieur représenté par le modèle de Landau-Zener. Nous déterminons une solution approchée qui décrit bien toute la dynamique temporelle de formation moléculaire dans ce cas général. / We study the nonlinear mean-field dynamics of diatomic molecule formation at coherent photo- and magneto-association of ultracold atoms focusing on the case when the system is initially in the all-atomic state. We show that in the limit of strongly nonlinear interaction between an ultra-cold atomic-molecular system and a quasi-resonant electromagnetic field, the molecule formation process, depending on the characteristics of the associating field, may evolve according two different scenarios, namely, weak- and strong-oscillatory regimes. In the first case the number of molecules increases without pronounced oscillations of atom-molecule populations, while in the second case high-amplitude Rabi-type oscillations arise. Assuming an arbitrary external field configuration, we construct analytical solutions to describe the system’s temporal dynamics in the both interaction regimes. Further, we investigate the influence of inter-particle elastic scattering on the dynamics of coherent molecule formation subject to an external field configuration of the resonance-crossing Landau-Zener model. We derive an approximate solution which for the first time describes the whole temporal dynamics of the molecule formation in this general case.

Ce travail porte sur la caractérisation d'anches simples utilisées pour la clarinette ou le saxophone. Sachant que les musiciens perçoivent des différences importantes dans la qualité des anches de caractéristiques identiques (même marque, coupe et force), cette thèse propose des nouveaux outils pour la caractérisation des anches en situation de jeu.Un bec instrumenté utilisant des capteurs embarqués est développé de façon à mesurer le déplacement de l'anche et la différence de pression de part et d’autre de l'anche. À partir de ces signaux, il est possible d'estimer des paramètres d'anche associés à différents modèles physiques. Les résultats obtenus montrent que la complexité du modèle décrivant le comportement de l'anche doit augmenter avec la nuance de jeu. Le bec instrumenté est utilisé dans une campagne de mesures comportant 7 musiciens et 20 anches, et permet de quantifier la variabilité des résultats due aux musiciens. Des tests subjectifs sont réalisés avec ces mêmes musiciens, et montrent que les différences entre les anches se réduisent à une seule dimension (facilité de jeu ou timbre). Les corrélations entre les descripteurs subjectifs et les paramètres objectifs mesurés sont étudiées afin de mieux comprendre les différences perçues entre les anches, permettant le développement d'un modèle prédictif de la qualité des anches.De façon à éviter la variabilité produite par le musicien, une bouche artificielle aspirante est développée. La comparaison des mesures réalisées par la bouche artificielle et par un musicien permet d'identifier la plage de fonctionnement optimale où la bouche artificielle imite au mieux le jeu du musicien. / This work deals with the characterisation of single cane reeds used for clarinet or saxophone. Musicians perceive important differences of quality between reeds of the same brand, cut and strength. This thesis proposes new tools for reed characterisation in playing conditions.An instrumented mouthpiece is developed to enable the measurement of reed displacement and pressure difference on both sides of the reed using embedded sensors. From these signals, it is possible to estimate reed parameters of different physical models. Results reveal that the complexity of the physical model describing the reed behaviour must increase with the dynamic level.The instrumented mouthpiece is used in a measurement campaign involving 7 players and 20 reeds, quantifying the variability of the results due the musicians. Subjective tests conducted with these musicians show that reeds can be mainly described by one dimension (ease of playing or timbre). The correlations between the subjective descriptors and the measured objective parameters are studied to better understand the perceived differences between reeds, developing a predictive model of reed quality.In order to avoid the variability of the musician, an aspirating artificial mouth is developed. It uses the instrumented mouthpiece and it can be played by a musician or artificially. The comparison of the measurements made in both cases allows for the identification of the optimal working range in which the artificial mouth best reproduces the musician's playing according to intonation and playing level.

In recent years, improved control of the motional and internal quantum states of ultracold neutral atoms and ions has opened intriguing possibilities for quantum simulation and quantum computation. Many-body effects have been explored with hundreds of thousands of quantum-degenerate neutral atoms and coherent light-matter interfaces have been built. Systems of single or a few trapped ions have been used to demonstrate universal quantum computing algorithms and to detect variations of fundamental constants in precision atomic clocks. Now in our experiment we investigate how the two systems can be advantageously combined. We immerse a single trapped Yb+ ion in a Bose-Einstein condensate of Rb atoms. Our hybrid setup consists of a linear RF-Paul trap which is overlapped with a magnetic trap and an optical dipole trap for the neutral atoms. A first synergetic effect is the sympathetic cooling of the trapped ions to very low temperatures through collisions with the ultracold neutral gas and thus without applying laser light to the ions. We observe the dynamics of this effect by measuring the mean ion energy after having an initially hot ion immersed into the condensate for various interaction times, while at the same time monitoring the effects of the collisions on the condensate. The observed ion cooling effect calls for further research into the possibility of using such hybrid systems for the continuous cooling of quantum computers. To this end a good understanding of the fundamental interaction processes between the ion and the neutrals is essential. We investigate the energy dependent elastic scattering properties by measuring neutral atom losses and temperature increase from an ultracold thermal cloud of Rb. By comparison with a Monte-Carlo simulation we gain a deeper understanding of how the different parameters affect the collisional effects. Additionally, we observe charge exchange reactions at the single particle level and measure the energy-independent reaction rate constants. The reaction products are identified by in-trap mass spectrometry, revealing the branching ratio between radiative and non-radiative charge exchange processes.

No description available.