Dissertations / Theses on the topic 'Quantum degeneracy; Bose-Einstein condensation'

Le piégeage d’atomes sur puce ouvre de nouvelles possibilités pour la métrologie temps-fréquence et l’interférométrie atomique intégrée. L’expérience TACC (Trapped Atomic Clock on a Chip) a pour but d’étudier le potentiel des gaz quantiques, dégénérés ou non, pour la métrologie, et d’élaborer de nouveaux outils pour la manipulation des atomes. Elle vise notamment la réalisation d’un étalon secondaire de fréquence avec une stabilité de quelques 10-13 à une seconde. Cette thèse s’inscrit dans ce contexte. Nous y présentons les résultats de quelques expériences de métrologie réalisées avec des nuages thermiques ou des condensats de Bose-Einstein. Dans un premier temps nous démontrons une stabilité de 5. 8 x 10-13 à une seconde et caractérisons les bruits techniques limitant cette stabilité. Nous présentons ensuite une étude de la cohérence des condensats et en particulier l’effet des interactions. Les données sont comparées à un modèle numérique. Dans un deuxième temps nous présentons quelques outils développés pour la production et la manipulation d’atomes sur puce. Nous démontrons d’abord la réalisation d’un puissancemètre atomique pour la micro-onde et estimons les limites actuelles de ses performances. Nous démontrons ensuite que des champs micro-onde ayant des gradients élevés permettent la manipulation cohérente de l’état externe des atomes. Enfin nous présentons et caractérisons un nouveau dispositif pour la production de nuages d’atomes froids à haute cadence consistant en la modulation rapide de la pression de rubidium dans une cellule
Atom trapping on chip opens new perspectives for time and frequency metrology and integrated atom interferometry. The TACC experiment (Trapped Atomic Clock on a Chip) was built to study the potential of degenerate and non-degenerate quantum gases for metrology and to develop new tools for atom manipulation. One of the aims is the demonstration of a secondary frequency standard with a stability of a few 10-13 at one second. This is the context of this thesis. We report on several metrology experiments carried out with thermal clouds or Bose-Einstein condensates. Firstly, we demonstrate a stability of 5. 8 x 10-13 at one second and characterize the limiting technical noise. We then present a study of the coherence of Bose-Einstein condensates and, in particular, the effect of interactions. The data is compared with a numerical model. Secondly, we introduce several tools for producing and manipulating atoms on a chip. We show the realization of an atomic microwave powermeter and assess the current limits of its performance. We then demonstrate that high-gradient microwave fields allow one to coherently manipulate the atoms’ external motion. Finally, we present and characterize a new device for high-repetition rate atom loading involving fast modulation of the rubidium pressure

The quantum phase of a Bose-Einstein condensate has long been a subject fraught with misunderstanding and confusion. In this thesis we provide a consis- tent description of this phenomenon and, in particular, discuss how phase may be defined, created, manipulated, and controlled. We begin by describing how it is possible to set up a reference condensate against which the phase of other condensates can be compared. This allows us to think of relative phases as if they were absolute and gives a clear and precise definition to 'the phase of a condensate'. A relative phase may also be established by coupling condensates and we show how this can be controlled. We then extend this model to explain how the phase along a chain of coupled condensates can lock naturally without the need for any measurements. The second part of the thesis deals primarily with the link between entangle- ment and phase. We show that, in general, the more entangled a state is, the better its phase resolution. This leads us to consider schemes by which maximally entangled states may be able to be created since these should give the best prac- tical advantages over their classical counterparts. We consider two such states: a number correlated pair of condensates and a Schrodinger cat state. Both schemes are shown to be remarkably robust to loss. A comparison of the merits of these two states, as the inputs to an interferom- eter, reveals very different behaviours. In particular, the number correlated state performs significantly better than the cat state in the presence of loss, which means that it might be useful in interferometry and frequency standard schemes where phase resolution is of the utmost importance. Finally, we propose a scheme for concentrating the entanglement between con- densates, which is an important step in quantum communication protocols. This, along with the ability to manipulate phase and entanglement, suggests that the future for condensates holds not only academic interest but great potential for practical applications.

Bose-Einstein condensation is a collective quantum phenomenon where a macroscopic number of bosons occupies the lowest quantum state. For fixed temperature, bosons condense above a critical particle density. This phenomenon is a consequence of the Bose-Einstein distribution which dictates that excited states can host only a finite number of particles so that all remaining particles must form a condensate in the ground state. This reasoning applies to thermal equilibrium. We investigate the fate of Bose condensation in nonisolated systems of noninteracting Bose gases driven far away from equilibrium. An example of such a driven-dissipative scenario is a Floquet system coupled to a heat bath. In these time-periodically driven systems, the particles are distributed among the Floquet states, which are the solutions of the Schrödinger equation that are time periodic up to a phase factor. The absence of the definition of a ground state in Floquet systems raises the question, whether Bose condensation survives far from equilibrium. We show that Bose condensation generalizes to an unambiguous selection of multiple states each acquiring a large occupation proportional to the total particle number. In contrast, the occupation numbers of nonselected states are bounded from above. We observe this phenomenon not only in various Floquet systems, i.a. time-periodically-driven quartic oscillators and tight-binding chains, but also in systems coupled to two baths where the population of one bath is inverted. In many cases, the occupation numbers of the selected states are macroscopic such that a fragmented condensation is formed according to the Penrose-Onsager criterion. We propose to control the heat conductivity through a chain by switching between a single and several selected states. Furthermore, the number of selected states is always odd except for fine-tuning. We provide a criterion, whether a single state (e.g., Bose condensation) or several states are selected. In open systems, which exchange also particles with their environment, the nonequilibrium steady state is determined by the interplay between the particle-number-conserving intermode kinetics and particle-number-changing pumping and loss processes. For a large class of model systems, we find the following generic sequence when increasing the pumping: For small pumping, no state is selected. The first threshold, where the stimulated emission from the gain medium exceeds the loss in a state, is equivalent to the classical lasing threshold. Due to the competition between gain, loss and intermode kinetics, further transitions may occur. At each transition, a single state becomes either selected or deselected. Counterintuitively, at sufficiently strong pumping, the set of selected states is independent of the details of the gain and loss. Instead, it is solely determined by the intermode kinetics like in closed systems. This implies equilibrium condensation when the intermode kinetics is caused by a thermal environment. These findings agree well with observations of exciton-polariton gases in microcavities. In a collaboration with experimentalists, we observe and explain the pump-power-driven mode switching in a bimodal quantum-dot micropillar cavity
Die Bose-Einstein-Kondensation ist ein Quantenphänomen, bei dem eine makroskopische Zahl von Bosonen den tiefsten Quantenzustand besetzt. Die Teilchen kondensieren, wenn bei konstanter Temperatur die Teilchendichte einen kritischen Wert übersteigt. Da die Besetzungen von angeregten Zuständen nach der Bose-Einstein-Statistik begrenzt sind, bilden alle verbleibenden Teilchen ein Kondensat im Grundzustand. Diese Argumentation ist im thermischen Gleichgewicht gültig. In dieser Arbeit untersuchen wir, ob die Bose-Einstein-Kondensation in nicht wechselwirkenden Gasen fern des Gleichgewichtes überlebt. Diese Frage stellt sich beispielsweise in Floquet-Systemen, welche Energie mit einer thermischen Umgebung austauschen. In diesen zeitperiodisch getriebenen Systemen verteilen sich die Teilchen auf Floquet-Zustände, die bis auf einen Phasenfaktor zeitperiodischen Lösungen der Schrödinger-Gleichung. Die fehlende Definition eines Grundzustandes wirft die Frage nach der Existenz eines Bose-Kondensates auf. Wir finden eine Generalisierung der Bose-Kondensation in Form einer Selektion mehrerer Zustände. Die Besetzung in jedem selektierten Zustand ist proportional zur Gesamtteilchenzahl, während die Besetzung aller übrigen Zustände begrenzt bleibt. Wir beobachten diesen Effekt nicht nur in Floquet-Systemen, z.B. getriebenen quartischen Fallen, sondern auch in Systemen die an zwei Wärmebäder gekoppelt sind, wobei die Besetzung des einen invertiert ist. In vielen Fällen ist die Teilchenzahl in den selektierten Zuständen makroskopisch, sodass nach dem Penrose-Onsager Kriterium ein fragmentiertes Kondensat vorliegt. Die Wärmeleitfähigkeit des Systems kann durch den Wechsel zwischen einem und mehreren selektierten Zuständen kontrolliert werden. Die Anzahl der selektierten Zustände ist stets ungerade, außer im Falle von Feintuning. Wir beschreiben ein Kriterium, welches bestimmt, ob es nur einen selektierten Zustand (z.B. Bose-Kondensation) oder viele selektierte Zustände gibt. In offenen Systemen, die auch Teilchen mit der Umgebung austauschen, ist der stationäre Nichtgleichgewichtszustand durch ein Wechselspiel zwischen der (Teilchenzahl-erhaltenden) Intermodenkinetik und den (Teilchenzahl-ändernden) Pump- und Verlustprozessen bestimmt. Für eine Vielzahl an Modellsystemen zeigen wir folgendes typisches Verhalten mit steigender Pumpleistung: Zunächst ist kein Zustand selektiert. Die erste Schwelle tritt auf, wenn der Gewinn den Verlust in einer Mode ausgleicht und entspricht der klassischen Laserschwelle. Bei stärkerem Pumpen treten weitere Übergänge auf, an denen je ein einzelner Zustand entweder selektiert oder deselektiert wird. Schließlich ist die Selektion überraschenderweise unabhängig von der Charakteristik des Pumpens und der Verlustprozesse. Die Selektion ist vielmehr ausschließlich durch die Intermodenkinetik bestimmt und entspricht damit den oben beschriebenen geschlossenen Systemen. Ist die Kinetik durch ein thermisches Bad hervorgerufen, tritt wie im Gleichgewicht eine Grundzustands-Kondensation auf. Unsere Theorie ist in Übereinstimmung mit experimentellen Beobachtungen von Exziton-Polariton-Gasen in Mikrokavitäten. In einer Kooperation mit experimentellen Gruppen konnten wir den Modenwechsel in einem bimodalen Quantenpunkt-Mikrolaser erklären

In this thesis regimes of quantum degeneracy of electrons and holes in semiconductor quantum wells in a strong magnetic field are studied theoretically. The coherent pairing of electrons and holes results in the formation of Bose-Einstein condensate of magnetic excitons in a single-particle state with wave vector K. We show that correlation effects due to coherent excitations drastically change the properties of excitonic gas, making possible the formation of a novel metastable state of dielectric liquid phase with positive compressibility consisting of condensed magnetoexcitons with finite momentum. On the other hand, virtual transitions to excited Landau levels cause a repulsive interaction between excitons with zero momentum, and the ground state of the system in this case is a Bose condensed gas of weakly repulsive excitons. We introduce explicitly the damping rate of the exciton level and show that three different phases can be realized in a single quantum well depending on the exciton density: excitonic dielectric liquid surrounded by weakly interacting gas of condensed excitons versus metallic electron-hole liquid. In the double quantum well system the phase transition from the excitonic dielectric liquid phase to the crystalline state of electrons and holes is predicted with the increase of the interwell separation and damping rate.

We used a framework of Green's function to investigate the collective elementary excitations of the system in the presence of Bose-Einstein condensate, introducing "anomalous" two-particle Green's functions and symmetry breaking terms into the Hamiltonian. The analytical solution of secular equation was obtained in the Hartree-Fock approximation and energy spectra were calculated. The Coulomb interactions in the system results in a multiple-branch structure of the collective excitations energy spectrum. Systematic classification of the branches is proposed, and the condition of the stability of the condensed excitonic phase is discussed.

The concept of coherent states for a quantum system has been generalized in many different ways. One elegant way is the dynamical group approach. The subject of this thesis is the physical application of some dynamical group methods in quantum optics and Bose-Einstein Condensation(BEC) and their use in generalizing some quantum optical states and BEC states. We start by generalizing squeezed coherent states to the displaced squeezed phase number states and studying the signal-to-quantum noise ratio for these states. Following a review of the properties of Kerr states and the basic theory of the deformation of the boson algebra, we present an algebraic approach to Kerr states and generalize them to the squeezed states of the q-parametrized harmonic oscillator. Using the eigenstates of a nonlinear density-dependent annihilation operator of the deformed boson algebra, we propose general time covariant coherent states for any time-independent quantum system. Using the ladder operator approach similar to that of binomial states, we construct interpolating number-coherent states, intermediate states which are generalizations of some fundamental states in quantum optics. Salient statistical properties and non-classical features of these interpolating numbercoherent states are investigated and the interaction with an atomic system in the framework of the Jaynes-Cummings model and the scheme to produce these states are also studied in detail. After briefly reviewing the realization of Bose-Einstein Condensates and relevant theoretical research using mean-field theory, we present a dynamical group approach to Bose-Einstein condensation and the atomic tunnelling between two condensates which interact via a minimal coupling term. First we consider the spectrum of one Bose-Einstein condensate and show that the mean-field dynamics is characterised by the semi-direct product of the 8U(1,1) and Heisenberg-Weyl groups. We then construct a generalized version of the BEC ground states and weakly excited states. It is shown that our states for BEC provide better fits to the experimental results. Then we investigate the tunnelling between the excitations in two condensates which interact via a minimal coupling term. The dynamics of the two interacting Bose systems is characterised by the 80(3,2) group, which leads to an exactly solvable model. Further we describe the dynamics of the tunnelling of the two coupled condensates in terms of the semi-direct product of 80(3,2) and two independent Heisenberg-Weyl groups. From this we obtain the energy spectrum and eigenstates for the two interacting Bose-Einstein condensates, as well as the Josephson current between the two coupled condensates.

Thesis (Ph.D) -- Australian National University, 2007.
DVD contains movies in .mov (macintosh quicktime) and .mpg formats, providing additional visualisation of the material discussed in the thesis. It also contains the source files for figures within the thesis as well as sample numerical code that was used for the research. The accompanying .txt files provide a brief description of the movie and a link to the relevant part of the thesis. Also contains some files in pdf format.

Several microscopic theories point out that Bose-Einstein condensation (BEC), i.e., a macroscopic occupation of the lowest energy single particle state in many-boson systems, may appear also in quantum fluids and solids and that it is at the origin of the phenomenon of superfluidity. Nevertheless, the connection between BEC and superfluidity is still matter of debate, since the experimental evidences indicating a non zero condensate fraction in superfluid helium are only indirect. In the theoretical study of BEC in quantum fluids and solids, perturbative approaches are useless because of the strong correlations between the atoms, arising both from the interatomic potential and from the quantum nature of the system. Microscopic Quantum Monte Carlo simulations provide a reliable description of these systems. In particular, the Path Integral Monte Carlo (PIMC) method is very suitable for this purpose. This method is able to provide exact results for the properties of the quantum system, both at zero and finite temperature, only with the definition of the Hamiltonian and of the symmetry properties of the system, giving an easy picture for superfluidity and BEC in many-boson systems. In this thesis, we apply PIMC methods to the study of several quantum fluids and solids. We describe in detail all the features of PIMC, from the sampling methods to the estimators of the physical properties. We present also the most recent techniques, such as the high-order approximations for the thermal density matrix and the worm algorithm, used in PIMC to provide reliable simulations. We study the liquid phase of condensed 4He, providing unbiased estimations of the one-body density matrix g1(r). We analyze the model for g1(r) used to fit the experimental data, highlighting its merits and its faults. In particular we see that, even if it presents some difficulties in the description of the overall behavior of g1(r), it can provide an accurate estimation of the kinetic energy K and of the condensate fraction n0 of the system. Furthermore, we show that our results for n0 as a function of the pressure are in a good agreement with the most recent experimental results. The study of the solid phase of 4He is the most significant part of this thesis. The recent observation of non classical rotational inertia (NCRI) effects in solid helium has generated big interest in the study of an eventual supersolid phase, characterized at the same time by crystalline order and superfluidity. Nevertheless, until now it has been impossible to give a theoretical model able to describe all the experimental evidences. In this work, we perform PIMC simulations of 4He at high densities, according to different microscopic configurations of the atoms. In commensurate crystals we see that BEC does not appear, our model being able to reproduce the momentum distribution obtained form neutron scattering experiments. In a crystal with vacancies, we have been able to see a transition to a superfluid phase at temperatures in agreement with experimental results if the vacancy concentration is low enough. In amorphous solids, superfluid effects are enhanced but appear at temperatures higher than the experimental estimation for the transition temperature. Finally, we study also metastable disordered configurations in molecular para-hydrogen at low temperature. The aim of this study is to investigate if a Bose liquid other than helium can display superfluidity. Choosing accurately a ¿quantum liquid¿ initial configuration and the dimensions of the simulation box, we have been able to frustrate the formation of the crystal and to calculate the temperature dependence of the superfluid density, showing a transition to a superfluid phase at temperatures close to 1 K.

In this work we study a Bose-Einstein condensate of 87Rb under the effects of an oscillatory excitation. The condensate is produced through forced evaporative cooling by radio-frequency in a harmonic magnetic trap. The excitation is generated by an oscillatory quadrupole field superimposed on the trapping potential. For a fixed value of the frequency of the excitation we observe the production of different regimes in the condensate as a function of two parameters of the excitation: the time and the amplitude. For the lowest values of these parameters we observe a bending of the main axis of the condensate. This demonstrates that the excitation is able to transfer angular momentum into the sample. By increasing the time or the amplitude of the excitation we observe the nucleation of an increasing number of quantized vortices. If the value of the parameters of the excitation is increased even further the vortices evolve into a different regime which we have identified as quantum turbulence. In this regime, the vortices are tangled among each other, generating a highly irregular array. For the highest values of the excitation the condensate breaks into pieces surrounded by a thermal cloud. This constitutes a different regime which we have identified as granulation. We present numerical simulations together with other theoretical considerations which allow us to interpret our observations. In this thesis we also describe the construction of a second experimental setup whose objective is to study magnetic properties of a Bose-Einstein condensate of 87Rb. In this new system the condensate is produced in a hybrid trap which combines a magnetic trap with an optical dipole trap. Bose-Einstein condensation has been already achieved in the new apparatus; experiments will be performed in the near future.
Neste trabalho, estudamos um condensado de Bose-Einstein de átomos de 87Rb sob os efeitos de uma excitação oscilatória. O condensado é produzido por meio de resfriamento evaporativo por radiofreqüência em uma armadilha magnética harmônica. A excitação é gerada por um campo quadrupolar oscilatório sobreposto ao potencial de aprisionamento. Para um valor fixo da freqüência de excitação, observamos a produção de diferentes regimes no condensado como função de dois parâmetros da excitação, a saber, o tempo e a amplitude. Para os valores mais baixos destes parâmetros observamos a inclinação do eixo principal do condensado, isto demonstra que a excitação transfere momento angular à amostra. Ao aumentar o tempo ou a amplitude da excitação observamos a nucleação de um número crescente de vórtices quantizados. Se incrementarmos ainda mais o valor dos parâmetros da excitação, os vórtices evoluem para um novo regime que identificamos como turbulência quântica. Neste regime, os vórtices se encontram emaranhados entre si, dando origem a um arranjo altamente irregular. Para os valores mais altos da excitação o condensado se quebra em pedaços rodeados por uma nuvem térmica. Isto constitui um novo regime que identificamos como a granulação do condensado. Apresentamos simulações numéricas junto com outras considerações teóricas que nos permitem interpretar as nossas observações. Nesta tese, apresentamos ainda a descrição da montagem de um segundo sistema experimental cujo objetivo é o de estudar propriedades magnéticas de um condensado de Bose-Einstein de 87Rb. Neste novo sistema o condensado é produzido em uma armadilha híbrida composta por uma armadilha magnética junto com uma armadilha óptica de dipolo. A condensação de Bose-Einstein foi já observada neste novo sistema, os experimentos serão realizados no futuro próximo.

Orientador: Marcos Cesar de Oliveira
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
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Resumo: Óptica atômica e em particular a física de ondas de matéria ultrafrias tiveram um grande desenvolvimento teórico e experimental em muito devido à realização experimental da condensação de Bose-Einstein em vapores atômicos. A gama de interesse nesses sistemas é muito ampla já que eles proporcionam reais aplicações práticas de assuntos inovadores em física fundamental de sistemas de muitos corpos com parâmetros altamente controláveis e até mesmo na implementação de computação quântica, teleporte e lasers atômicos. Com efeito, demonstramos numa formulação completamente quântica que a colisão cruzada entre átomos aprisionados num potencial de poço duplo pode aumentar significativamente a taxa de tunelamento atômico em configurações específicas da armadilha, levando a um regime de oscilação Rabi da população dos poços do potencial. Ainda, mostramos que os fenômenos de colapso e ressurgimento do condensado são suprimidos devido à competição entre autocolisão e colisão cruzada intermediada pelo tunelamento. Um aspecto da condensação de Bose-Einstein que tem atraído muita discussão teórica é a idéia de fase. Nesse sentido, o modelo de poço duplo aqui discutido pode resultar em condições ideais para esquemas de detecção homódina atômica de fase. Propomos uma técnica de medição não destrutiva para monitorar oscilações do tipo Josephson entre dois condensados de Bose-Einstein de átomos neutros espacialmente separados. Um condensado é disposto em uma cavidade óptica, fortemente dirigida por um campo coerente. O sinal de saída é monitorado lançando-se mão de um esquema de detecção homódina balanceada. O campo da cavidade é escolhido de forma que esteja muito fora de sintonia com quaisquer transições atômicas. Assim, esse campo ganha uma fase proporcional ao número de átomos na cavidade devido à interação dispersiva entre os campos atômico e fotônico. A corrente detectada é então modulada pela corrente de oscilação devida ao tunelamento dos modos condensados. De fato, mesmo quando ambos os poços estão igualmente populados, uma fase é estabelecida pelo processo de medição e oscilações do tipo Josephson acabam ocorrendo. Nesse contexto, mostramos que a presença de colisão cruzada aprimora as condições necessárias para se adquirir informações sobre a fase quântica relativa de um condensado de Bose-Einstein num potencial de poço duplo
Abstract: Recently, atom optics and the physics of ultracold matter waves have witnessed rapid theoretical and experimental progress due to the achievement of atomic vapor Bose-Einstein condensation (BEC). The interest in such systems is quite wide ranged since it opens new applicative frontiers such as investigations on fundamental many-body physics in model systems with highly controllable parameters and even quantum computation, teleportation and atom-lasers besides several other ground breaking subjects. Henceforth, we demonstrate in an exact quantum formulation that cross-collisions between atoms trapped in a double well can significantly increase the atom tunnelling rate for special trap configurations leading to an effective linear Rabi regime of population oscillation between the trap wells. Typical collapse and revival of the condensate are suppressed as well as due to cross- and self-collision competition intermediated by tunnelling. One aspect of BECs that has attracted much theoretical work is the idea of phase. In this sense if we face this double-well BEC model as a temporal atomic beam splitter it may result in optimal conditions for homodyne atomic detection schemes. A nondestructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates is investigated. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from any atomic resonance and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunnelling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop. Hence we show that the presence of cross-collisions enhances the possibility of acquiring information about the relative quantum phase of a double-well Bose-Einstein condensate
Mestrado
Física da Matéria Condensada
Mestre em Física

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.

In this thesis, we present the generation and studies of a 87Rb Bose-Einstein condensate (BEC) perturbed by an oscillatory excitation. The atoms are trapped in a harmonic magnetic trap where, after an evaporative cooling process, we produce the BEC. In order to study the effect caused by oscillatory excitations, a quadrupole magnetic field time oscillatory is superimposed to the trapping potential. Through this perturbation, collective modes were observed. The dipole mode is excited even for low excitation amplitudes. However, a minimum excitation energy is needed to excite the condensate quadrupole mode. Observing the excited cloud in TOF expansion, we note that for excitation amplitude in which the quadrupole mode is excited, the cloud expands without invert its aspect ratio. By looking these clouds, after long time-of-flight, it was possible to see vortices and, sometimes, a turbulent state in the condensed cloud. We calculated the momentum distribution of the perturbed BECs and a power law behavior, like the law to Kolmogorov turbulence, was observed. Furthermore, we show that using the method that we have developed to calculate the momentum distribution, the distribution curve (including the power law exponent) exhibits a dependence on the quadrupole mode oscillation of the cloud. The randomness distribution of peaks and depletions in density distribution image of an expanded turbulent BEC, remind us to the intensity profile of a speckle light beam. The analogy between matter-wave speckle and light speckle is justified by showing the similarities in the spatial propagation (or time expansion) of the waves. In addition, the second order correlation function is evaluated and the same dependence with distance was observed for the both waves. This creates the possibility to understand the properties of quantum matter in a disordered state. The propagation of a three-dimensional speckle field (as the matter-wave speckle described here) creates an opportunity to investigate the speckle phenomenon existing in dimensions higher than 2D (the case of light speckle).
Nesta tese, descrevemos a produção e os estudos de condensados de Bose-Einstein, em átomos de 87Rb, perturbados através de excitações oscilatórias. Os átomos aprisionados são aprisionados em uma armadilha magnética harmônica onde produzimos o condensado de Bose-Einstein após o processo de resfriamento evaporativo. Com o objetivo de estudar o efeito de excitações oscilatórias, um campo magnético quadrupolar temporalmente oscilanteé superposto ao campo de aprisionamento. Através dessa perturbação, podemos observar a excitação de modos coletivos no condensado. Mesmo para baixas amplitudes de excitação, o modo dipolar é facilmente excitado. Porém, observamos que para excitar o modo quadrupolar no condensado é necessária uma energia mínima. Através da expansão em tempo de voo da nuvem excitada, identificamos que, para amplitude de excitação na quail o modo quadrupolar é excitado, a nuvem expande sem inverter o aspect ratio. Analisando essas nuvens por longos tempos de voo, foi possível observar alguns vórtices e, às vezes, um estado turbulento na nuvem condensada. Calculamos a distribuição de momento dessas nuvens e notamos que ela exibe um comportamento de lei de potência, parecido com a lei de Kolmogorov para turbulência. Além disso, mostramos que pelo nosso método que desenvolvemos para calcular a distribuição de momento, a forma da curva dessa distribuição (inclusive o expoente da lei de potência) exibe uma dependência com o modo quadrupolar de oscilação da nuvem. A distribuição desordenada de picos e depleções, na imagem da distribuição de densidade do condensado turbulento expandido, assemelha-se ao perfil de intensidade de um feixe de luz com speckle. A analogia entre speckle de onda de matéria e de luz é fundamentada através das semelhanças entre a propagação (ou expansão) dessas duas ondas. Além disso, a função de correlação de segunda ordem foi calculada e a mesma dependência com a distância foi observada para as duas ondas. Isto cria a possibilidade de entender melhor as propriedades da matéria quântica em um estado de desordem. A propagação de um campo de speckle tridimensional (como é o caso do speckle de onda de matéria aqui descrito) cria uma oportunidade de investigar o fenômeno de speckle em dimensões maiores que 2D (o caso do speckle de luz).

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.

The processing of information based on the generation of common quantum optical states (e.g. coherent states) and the measurement of the quadrature components of the light field (e.g. homodyne detection) is often referred to as continuous-variable quantum information processing. It is a very fertile field of investigation, at a crossroads between quantum optics and information theory, with notable successes such as unconditional continuous-variable quantum teleportation or Gaussian quantum key distribution. In quantum optics, the states of the light field are conveniently characterized using a phase-space representation (e.g. Wigner function), and the common optical components effect simple affine transformations in phase space (e.g. rotations). In quantum information theory, one often needs to determine entropic characteristics of quantum states and operations, since the von Neuman entropy is the quantity at the heart of entanglement measures or channel capacities. Computing entropies of quantum optical states requires instead turning to a state-space representation of the light field, which formally is the Fock space of a bosonic mode.

This interplay between phase-space and state-space representations does not represent a particular problem as long as Gaussian states (e.g. coherent, squeezed, or thermal states) and Gaussian operations (e.g. beam splitters or squeezers) are concerned. Indeed, Gaussian states are fully characterized by the first- and second-order moments of mode operators, while Gaussian operations are defined via their actions on these moments. The so-called symplectic formalism can be used to treat all Gaussian transformations on Gaussian states, including mixed states of an arbitrary number of modes, and the entropies of Gaussian states are directly linked to their symplectic eigenvalues.

This thesis is concerned with the Gaussian transformations applied onto arbitrary states of light, in which case the symplectic formalism is unapplicable and this phase-to-state space interplay becomes highly non trivial. A first motivation to consider arbitrary (non-Gaussian) states of light results from various Gaussian no-go theorems in continuous-variable quantum information theory. For instance, universal quantum computing, quantum entanglement concentration, or quantum error correction are known to be impossible when restricted to the Gaussian realm. A second motivation comes from the fact that several fundamental quantities, such as the entanglement of formation of a Gaussian state or the communication capacity of a Gaussian channel, rely on an optimization over all states, including non-Gaussian states even though the considered state or channel is Gaussian. This thesis is therefore devoted to developing new tools in order to compute state-space properties (e.g. entropies) of transformations defined in phase-space or conversely to computing phase-space properties (e.g. mean-field amplitudes) of transformations defined in state space. Remarkably, even some basic questions such as the entanglement generation of optical squeezers or beam splitters were unsolved, which gave us a nice work-bench to investigate this interplay.

In the first part of this thesis (Chapter 3), we considered a recently discovered Gaussian probabilistic transformation called the noiseless optical amplifier. More specifically, this is a process enabling the amplification of a quantum state without introducing noise. As it has long been known, when amplifing a quantum signal, the arising of noise is inevitable due to the unitary evolution that governs quantum mechanics. It was recently realized, however, that one can drop the unitarity of the amplification procedure and trade it for a noiseless, albeit probabilistic (heralded) transformation. The fact that the transformation is probabilistic is mathematically reflected in the fact that it is non trace-preserving. This quantum device has gained much interest during the last years because it can be used to compensate losses in a quantum channel, for entanglement distillation, probabilistic quantum cloning, or quantum error correction. Several experimental demonstrations of this device have already been carried out. Our contribution to this topic has been to derive the action of this device on squeezed states and to prove that it acts quite surprisingly as a universal (phase-insensitive) optical squeezer, conserving the signal-to-noise ratio just as a phase-sensitive optical amplifier but for all quadratures at the same time. This also brought into surface a paradoxical effect, namely that such a device could seemingly lead to instantaneous signaling by circumventing the quantum no-cloning theorem. This paradox was discussed and resolved in our work.

In a second step, the action of the noiseless optical amplifier and it dual operation (i.e. heralded noiseless attenuator) on non-Gaussian states has been examined. We have observed that the mean-field amplitude may decrease in the process of noiseless amplification (or may increase in the process of noiseless attenuation), a very counterintuitive effect that Gaussian states cannot exhibit. This work illustrates the above-mentioned phase-to-state space interplay since these devices are defined as simple filtering operations in state space but inferring their action on phase-space quantities such as the mean-field amplitude is not straightforward. It also illustrates the difficulty of dealing with non-Gaussian states in Gaussian transformations (these noiseless devices are probabilistic but Gaussian). Furthermore, we have exhibited an experimental proposal that could be used to test this counterintuitive feature. The proposed set-up is feasible with current technology and robust against usual inefficiencies that occur in optical experiment.

Noiseless amplification and attenuation represent new important tools, which may offer interesting perspectives in quantum optical communications. Therefore, further understanding of these transformations is both of fundamental interest and important for the development and analysis of protocols exploiting these tools. Our work provides a better understanding of these transformations and reveals that the intuition based on ordinary (deterministic phase-insensitive) amplifiers and losses is not always applicable to the noiseless amplifiers and attenuators.

In the last part of this thesis, we have considered the entropic characterization of some of the most fundamental Gaussian transformations in quantum optics, namely a beam splitter and two-mode squeezer. A beam splitter effects a simple rotation in phase space, while a two-mode squeezer produces a Bogoliubov transformation. Thus, there is a well-known phase-space characterization in terms of symplectic transformations, but the difficulty originates from that one must return to state space in order to access quantum entropies or entanglement. This is again a hard problem, linked to the above-mentioned interplay in the reverse direction this time. As soon as non-Gaussian states are concerned, there is no way of calculating the entropy produced by such Gaussian transformations. We have investigated two novel tools in order to treat non-Gaussian states under Gaussian transformations, namely majorization theory and the replica method.

In Chapter 4, we have started by analyzing the entanglement generated by a beam splitter that is fed with a photon-number state, and have shown that the entanglement monotones can be neatly combined with majorization theory in this context. Majorization theory provides a preorder relation between bipartite pure quantum states, and gives a necessary and sufficient condition for the existence of a deterministic LOCC (local operations and classical communication) transformation from one state to another. We have shown that the state resulting from n photons impinging on a beam splitter majorizes the corresponding state with any larger photon number n’ > n, implying that the entanglement monotonically grows with n, as expected. In contrast, we have proven that such a seemingly simple optical component may have a rather surprising behavior when it comes to majorization theory: it does not necessarily lead to states that obey a majorization relation if one varies the transmittance (moving towards a balanced beam splitter). These results are significant for entanglement manipulation, giving rise in particular to a catalysis effect.

Moving forward, in Chapter 5, we took the step of introducing the replica method in quantum optics, with the goal of achieving an entropic characterization of general Gaussian operations on a bosonic quantum field. The replica method, a tool borrowed from statistical physics, can also be used to calculate the von Neumann entropy and is the last line of defense when the usual definition is not practical, which is often the case in quantum optics since the definition involves calculating the eigenvalues of some (infinite-dimensional) density matrix. With this method, the entropy produced by a two-mode squeezer (or parametric optical amplifier) with non-trivial input states has been studied. As an application, we have determined the entropy generated by amplifying a binary superposition of the vacuum and an arbitrary Fock state, which yields a surprisingly simple, yet unknown analytical expression. Finally, we have turned to the replica method in the context of field theory, and have examined the behavior of a bosonic field with finite temperature when the temperature decreases. To this end, information theoretical tools were used, such as the geometric entropy and the mutual information, and interesting connection between phase transitions and informational quantities were found. More specifically, dividing the field in two spatial regions and calculating the mutual information between these two regions, it turns out that the mutual information is non-differentiable exactly at the critical temperature for the formation of the Bose-Einstein condensate.

The replica method provides a new angle of attack to access quantum entropies in fundamental Gaussian bosonic transformations, that is quadratic interactions between bosonic mode operators such as Bogoliubov transformations. The difficulty of accessing entropies produced when transforming non-Gaussian states is also linked to several currently unproven entropic conjectures on Gaussian optimality in the context of bosonic channels. Notably, determining the capacity of a multiple-access or broadcast Gaussian bosonic channel is pending on being able to access entropies. We anticipate that the replica method may become an invaluable tool in order to reach a complete entropic characterization of Gaussian bosonic transformations, or perhaps even solve some of these pending conjectures on Gaussian bosonic channels.

Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

We report experimentally results on the low temperature properties of two classes of materials with a special emphasizes near the QCP induced by substitution and magnetic 1.field: (1) the HF systems YbRh2(Si0.95Ge0.05)2, Yb1-yLayRh2Si2 (y = 0.05, 0.1),and YbIr2Si2 with tetragonal structures and CeIn3-xSnx (x = 0.55, 0.6, 0.65, 0.7, 0.8) with cubic structure; (2) the quantum spin systems: Cs2CuCl4 and Cs2CoCl4. In all the HF compounds we have observed NFL behavior in zero magnetic field close to the QCP. The La substituted system does not show an antiferromagnetic (AFM) transition down to the lowest accessible temperature (0.03 K) while in YbRh2(Si1-xGex)2 with x = 0 and x = 0.05 AFM transitions occur at TN =0.07 K and 0.02 K, respectively. For Yb0.9La0.1Rh2Si2 we observe below 0.07 K saturation of DeltaC/T indicating clearly a LFL state for this concentration. For YbIr2Si2, DeltaC/T saturates below 0.5 K. In contrast to the Yb based compounds in the vicinity of the QCP, CeIn3-xSnx shows no evidence of a divergence in Delta C/T, with B or with x. Furthermore, we used specic heat measurements in the mK temperature range and at high fields (up to 12 T) to probe the phase diagrams in the low dimensional quantum antiferromagnets Cs2CuCl4 and Cs2CoCl4. In applied magnetic field, we have presented experimental evidence that in Cs2CuCl4 the field dependence of the critical temperature Tc(B) ~ (Bc-B)^1-Phi close to the critical field Bc = 8.51 T is well described with Phi=1.5. This is in very good agreement with the exponent expected in the mean-field approximation and support the notion of a Bose-Einstein condensation of magnons in Cs2CuCl4.

In dieser Dissertation werden das Anregungsspektrum und das Phasendiagramm wechselwirkender Fermi- und Bosegase untersucht. Zu diesem Zweck wird eine neuartige renormierte Kadanoff-Martin-Näherung vorgestellt, die Selbstwechselwirkung von Teilchen vermeidet und somit eine einheitliche Beschreibung sowohl der normalen als auch der kondensierten Phase ermöglicht. Für Fermionen findet man den BCS-Zustand, benannt nach Bardeen, Cooper und Schrieffer, welcher entscheidend ist für das Phänomen der Supraleitung. Charakteristisch für diesen Zustand ist eine Energielücke im Anregungsspektrum an der Fermi-Energie. Weiterhin tritt für Bosonen eine Bose-Einstein-Kondensation (BEC) auf, bei der das Anregungsspektrum für kleine Impulse linear ist. Letzteres führt zum Phänomen der Suprafluidität. Über die bereits bekannten Phänomene hinaus findet man eine dem BCS-Zustand ähnliche Kondensation von Zweiteilchenbindungszuständen, sowohl für Fermionen als auch für Bosonen. Für Fermionen tritt ein Übergang zwischen der Kondensation von Bindungszuständen und dem BCS-Zustand auf, der sogenannte BEC-BCS-Übergang. Die Untersuchung der Zustandsgleichung zeigt, dass im Gegensatz zu Fermi-Gasen und Bose-Gasen mit abstoßender Wechselwirkung Bose-Gase mit anziehender Wechselwirkung zu einer Flüssigkeit kondensieren oder sich verfestigen, bevor es zur Kondensation von Bindungszuständen oder zur Bose-Einstein-Kondensation kommt. Daher können diese Phänomene voraussichtlich nicht in der Gasphase beobachtet werden. Zusammenfassend lässt sich sagen, dass das vorgestellte Näherungsverfahren sehr gut geeignet ist, die erwähnten Phänomene im Zusammenhang mit der Bose-Einstein-Kondensation zu beschreiben.

Neste trabalho estudamos a interação entre dois sólitons em condensados de Bose-Einstein diluídos submetidos a perturbações temporais nos potencias de armadilhamento e interação entre as partículas. Em condensados de Bose-Einstein densos estudamos a inserção do termo cinético indo além da aproximação de Thomas-Fermi e seu efeito na velocidade crítica para a formação de vórtices no condensado.
In this work we studied the soliton interactions between two solitons under time dependent perturbations in a trap potential and interparticule potential. In a dense Bose-Einstein condensate we studied the insertion of kinetic term going beyond the Thomas-Fermi approximation and its effect in critical frequency of vortices formation.

We directly model the quantum many particle dynamics during the transition of a gas of N indistinguishable bosons into a Bose-Einstein condensate. To this end, we develop a quantitative quantum master equation theory, which takes into account two body interaction processes, and in particular describes the particle number fluctuations characteristic for the Bose-Einstein phase transition. Within the Markovian dynamics assumption, we analytically prove and numerically verify the Boltzmann ergodicity conjecture for a dilute, weakly interacting Bose-Einstein condensate. The new physical bottom line of our theory is the direct microscopic monitoring of the Bose-Einstein distribution during condensate formation in real-time, after a sudden quench of the non-condensate atomic density above the critical density for Bose-Einstein condensation.

In this thesis, we will study the superfluidity of condensed atomic and photonic systems, through the manipulation of rotational states, such as vortices or persistent currents. We will study Bose-Einstein condensates both in the strongly-correlated regime, where models based on second quantization, like Bose-Hubbard model, will be required; and in weakly-interacting systems, where mean-field approximations will be accurate enough, and the system is described by means of the Gross-Pitaevskii equation. We will start with the analysis of the fundamental properties of Bose gases trapped in few-site lattices, such as the phase diagram, the condensed fractions and the entanglement. Concerning the phases, we will study the properties of the transitions between them and, in particular, their characteristic critical exponents. Afterwards, we will consider the sites of a lattice constituting a ring geometry and study the effect of manipulating the tunnelling rate between two of the wells. This kind of tunable link is called weak link, and we will analyze what happens in the mean-field approximation, in comparison with the strongly-correlated case. In both regimes we will observe that the weak link behaves as a key element in the system in order to generate superpositions of flow states. Moreover, in the mean-field case, we can identify an energy barrier that separates two current states (also known as winding number states), where solitonic states, i.e. states characterized by the presence of topological singularities, live. Such a barrier will be the origin of the appearance of a hysteresis cicle in processes of transfer between different winding number curves, called phase slips. After that, we will study two coherently-coupled components of a toroidally-trapped Bose-Einstein condensate. We will see that when we imprint a persistent current in one of the components, there is an angular momentum transfer between both components. This transfer can be identified as a phase slip event, and the tunability of the system allows it to behave as a robust qubit, due to the fact that states supported by currents are less fragile. In two-component condensates, it is possible to find a particular solitonic state called Josephson vortex. This state is characterized by a density depletion around a point with nonzero currents. Moreover, these states are energetically more favourable than dark soliton states, whose main difference with respect to Josephson vortices is the fact that dark solitons do not present currents. However, when spin-orbit coupling is added, dark soliton states are no longer possible, but Josephson vortices persist. In this thesis, we will see that these states decay through transversal excitations (i.e. snake instability), producing vortex-antivortex pairs, and their subsequent dynamical evolution depends on the initial orientation of the Josephson vortex. Finally, we will move to the field of polariton condensates. Polaritons are quasiparticles product of the coupling between photons and excitons (which are electron-hole excitations) in semiconductor microcavities. These particles can constitute an out-of-equilibrium (due to the short lifetime of polaritons) Bose-Einstein condensate described by the Gross-Pitaevskii-like equation for two components, because of the two polarization components inherent to the photonic nature of polaritons. The cavities where these condensates are created generate a spin-orbit coupling between the two polariton components, in such a way that current states with different orbital angular momentum are coupled. This yields to a phenomenon of spin-to-orbital angular momentum conversion that we will study in ring-trapped polariton condensates. At the end of this thesis, we will probe the superfluid properties of polariton condensates, by analyzing the response of the generated currents against the presence of disorder.
En aquesta tesi estudiarem fenòmens relacionats amb la superfluïdesa de sistemes atòmics i fotònics condensats, a través de la manipulació d'estats rotacionals, com poden ser vòrtexs i corrents persistents. Estudiarem condensats de Bose-Einstein tant en sistemes fortament correlacionats, on models basats en la segona quantització com el model de Bose-Hubbard seran necessaris per a estudiar aquest tipus de sistemes, com en sistemes feblement interactuants, on les aproximacions de camp mig resultaran prou acurades, i on el sistema pot ser descrit per l'equació de Gross-Pitaevskii. Començarem amb l'anàlisi de les propietats fonamentals de sistemes de gasos bosònics atrapats en xarxes constituïdes per pocs pous. Per exemple, el diagrama de fases, les fraccions condensades, i l'entrellaçament. Pel que respecta a les fases, estudiarem les propietats de les transicions entre aquestes, i en particular, els exponents crítics que les caracteritzen. Més endavant, adaptarem la geometria del sistema com un sistema de pous formant un anell, i estudiarem l'efecte de manipular la junció que uneix dos d'ells. Aquest tipus d'unió manipulable és el que s'anomena weak link, i analitzarem què succeeix en l'aproximació de camp mig, en comparació amb el cas fortament correlacionat. En tots dos casos observarem que el weak link resulta ser un element crucial en el sistema, per a realitzar superposicions d'estats de corrent. A més a més, en el cas de camp mig, podrem identificar una barrera energètica que separa els dos estats de corrent, on hi habiten estats de tipus solitònic, és a dir, estats caracteritzats per la presència de singularitats topològiques. Aquesta barrera serà la causant de la presència d'un cicle d'histèresi, en processos de trànsit entre diferents corbes de corrent, anomenats phase slips. A continuació, estudiarem el cas de dues components d'un condensat de Bose-Einstein acoblades de manera coherent i atrapades en un potencial de tipus toroidal. Veurem que quan imprimim un corrent persistent en una de les components, hi ha una transferència de moment angular entre les dues components. Aquesta transferència pot ser identificada com esdeveniments de tipus phase slip. Investigarem com aquests sistemes són prou robusts com per a fer-se servir com qubits, donat que els estats de corrent són menys fràgils. En condensats de dues components acoblades de manera coherent, és possible trobar un tipus d'estat solitònic anomenat Josephson vortex. Aquest estat ve caracteritzat per una depressió de densitat entorn d'un punt on les corrents són no nul·les. A més a més, aquests estats són energèticament més favorables que els estats de tipus dark soliton, els quals es diferencien en el fet de que no presenten corrents. En el cas en el qual afegim acoblament de tipus spí-òrbita en el sistema, els estats de tipus dark soliton ja no són possibles, i només es poden trobar estats de tipus Josephson vortex. En aquesta tesi veurem que aquests estats decauen a causa d'excitacions transversals, produint parelles de vòrtex-antivòrtex, llur evolució dinàmica dependrà de la orientació inicial del Josephson vortex. Per acabar, concluïrem l'estudi en el camp de condensats de polaritons, els quals són quasipartícules producte de l'acoblament de fotons i excitons (que són acoblaments electró-forat) en cavitats semiconductores. Els polaritons poden formar un condensat de Bose-Einstein fora d'equilibri, degut a la curta vida dels polaritons. A més a més, poden ser descrits per una equació de tipus Gross-Pitaevskii però per a dues components, donades les components de polarització inherent de la naturalesa fotònica dels polaritons. Les cavitats on es formen aquests condensats generen un acoblament de tipus espín-òrbita entre les dues components, que permet acoblar estats de diferent moment angular entre les dues components. Això dóna lloc a un fenomen de conversió de moment angular d'espín en moment angular orbital que estudiarem en polaritons confinats en forma d'anell, i finalment provarem la superfluïdesa dels condensats polaritònics, analitzant la resposta dels corrents generats davant la presència de desordre.

Neste trabalho nós apresentamos detalhadamente todo o desenvolvimento experimental realizado em São Carlos para produção e estudo de gases quânticos, visando principalmente à produção do condensado de Bose-Einstein em átomos de Na-23. Para isso projetamos, construímos e integramos todo um complexo sistema experimental que reúne a maioria das técnicas desenvolvidas na área de átomos frios nas últimas décadas: desaceleração de feixes atômicos, aprisionamento magnético e magneto-óptico de átomos neutros, resfriamento sub-Doppler, resfriamento evaporativo induzido por radiofreqüência, manipulação de altos campos magnéticos e o processamento de imagens de amostras próximas do zero absoluto. Com isso realizamos o primeiro e mais importante passo, também o mais difícil, do nosso projeto de estudo de gases quânticos, que foi o desenvolvimento e operacionalização de todo o aparato experimental. Ainda assim, este trabalho não se resume apenas ao desenvolvimento de instrumentação, pois ao longo do caminho também fizemos contribuições cientificas originais e importantes para o desenvolvimento da área de átomos frios, como um todo. Essas contribuições resultaram em várias publicações que estão anexadas no apêndice III, mas não constituem o foco deste trabalho, cujo principal objetivo é o estudo de gases quânticos macroscopicamente degenerados.
We present here all the experimental development obtained in São Carlos to produce and study quantum degenerate gases, aiming specially the realization of Bose-Einstein Condensation (BEC) in sodium (Na-23) atoms. In order to do that we designed, built and completely integrated a complex experimental setup which conjugates most of the techniques developed along the last decades to produce cold atoms: atomic beam slowing, magnetic and magneto-optical trapping, optical sub-Doppler cooling, forced evaporative cooling induced by radio-frequency (RF), controlling of high gradient and curvature magnetic fields for atom trapping and the image acquisition and processing of atomic samples near absolute zero temperatures. During this period we did the first and most important step, also the most difficult, of our current project to study quantum gases, which was the development and realization of all the experimental apparatus. However, this work is not just about instrumentation, and along the way we also did important scientific contributions to the cold atom field, as whole. These contributions resulted in several publications, listed in appendix III, but they do not constitute the focus of this work, which main goal is the study of macroscopically quantum degenerate gases.

From almost one century, Bose-Einstein condensation has become progressively more important especially due to its connection with superfluidity, superconductivity and manybody physics. Nowadays quantum gases are powerful experimental tools to discover new physics and to emulate systems in condensed matter due to their versatility and very high control. Despite the increasing use of quantum gases as platforms for studying many problems in physics, their comprehension is very limited if we consider systems that are out-of-equilibrium due to the lack of experimental controllability of all the parameters involved in these systems. Another limitation in the understanding of this kind of systems comes from the limitation of the theoretical frameworks used to understand non-equilibrium dynamics, although many efforts have been made in this direction. Hence, many interesting phenomena in non-equilibrium quantum systems have not yet been discovered or well understood from a theoretical and experimental point of view, and thus its physics have not been the focus of much attention, although this situation has recently changed due to the rapid development of experimental techniques which enables a better control of parameters of these systems. Motivated by this progress, we study non-equilibrium Bose gases in the search of turbulence using an oscillatory excitation performed in a Bose-Einstein condensate of 87Rb atoms. In this thesis, we describe these experiments and characterize our non-equilibrium quantum system through some quantifiers. One of these quantifiers is a dimensionless value that represent the exponent γ obtained from the cascade of the transverse momentum distribution ñ(k). ñ(k) is obtained from absorption images of atoms in expansion using the time-of-flight technique in a well defined range of momenta. We analyze the dependence of γ with the amount of the pumped energy, and we found a steady-value which describe a well-established non-equilibrium regime. Also, it is analyzed the viability of using the fluctuations statistics in order to extract some quantifier from the power-spectrum of the fluctuations assuming that it represents an analog to the energy spectrum, due to the consideration of the time-of-flight technique. From the powerspectrum it is extracted an exponent, in the same range as for ñ(k), and compared with γ 2, that will be the exponent for the pseudo-energy spectrum in the kinetic dominated regime. Finally, we consider, again with the time-of-flight technique, the continuous Shannon entropy as quantifier that measure the disorder of the excited clouds and study their dependence with the pumped energy. These studies show us that there is an out-ofequilibrium regime that takes place when we inject a fixed quantity of energy into the system.
Desde há quase um século a condensação de Bose-Einstein vem se tornando cada vez mais importante, especialmente devido à sua forte conexão com superfluidez, supercondutividade e física de muitos corpos. Hoje em dia, os gases quânticos são poderosas ferramentas experimentais para descobrir-se nova física e para emular sistemas em matéria condensada devido à sua grande versatilidade e altíssimo controle. Apesar do uso crescente de gases quânticos como plataformas para se estudar diversos problemas na física, sua compreensão é muito limitada se considerarmos sistemas que estão fora de equilíbrio, devido à falta de controle experimental de todos os parâmetros envolvidos deste tipo de situações. Outra limitação na compreensão deste tipo de sistemas vem da limitação das abordagens teóricas usadas para entender a dinâmica em regimes de não equilíbrio, embora muitos esforços tem sido feitos nessa direção. Assim, muitos fenômenos interessantes em sistemas quânticos fora do equilíbrio ainda não foram descobertos ou bem compreendidos do ponto de vista teórico e experimental, e portanto, sua física não tem sido foco de muita atenção, embora esta situação tenha mudado recentemente devido ao rápido desenvolvimento de técnicas experimentais que permitem um melhor controle dos parâmetros destes sistemas. Motivados por estes progressos, estudamos aqui gases de Bose fora do equilíbrio, na busca de turbulência, através de excitações oscilatórias em um condensado de Bose-Einstein de átomos de 87Rb. Nesta tese, descrevemos estes experimentos e caracterizamos o nosso sistema quântico fora do equilíbrio através de alguns quantificadores. Um desses quantificadores é o valor adimensional que representa o expoente γ obtido da de cascata na distribuição de momento transversal ñ(k). ñ(k) é obtido da imagem de absorção da nuvem atômica em expansão usando a técnica de tempo de voo em um intervalo de momento bem definido. É analisada a dependência de γ com energia bombeada e encontramos um valor constante o qual descreve um regime de não equilíbrio bem estabelecido. Analisamos também a viabilidade do uso da estatística das flutuações para extrair algum quantificador do espectro de potências das flutuações, supondo que ele representa um análogo ao espectro de energia, devido à consideração da técnica de tempo de voo. Do espectro de potências é extraído outro expoente, no mesmo intervalo que para ñ(k), e este é comparado com γ 2, que por sua vez, pode ser considerado como o expoente do espectro de pseudo-energia no regime cinético dominado. Finalmente, consideramos, novamente com a técnica do tempo de voo, a entropia continua de Shannon como quantificador que mede a desordem das nuvens excitadas e estuda sua dependência com a energia bombeada. Estes estudos mostram que há um regime do fora de equilíbrio bem definido que acontece quando injetamos uma quantidade fixa de energia no sistema.

Ce mémoire de thèse étudie diverses méthodes d'amélioration des interféromètres atomiques. Dans la première partie du manuscrit, nous analysons comment une détection non-destructive, au sens où elle préserve la cohérence entre les états internes de l'ensemble atomique, permet d'améliorer la sensibilité des interféromètres. Nous montrons tout d'abord, grâce à une étude théorique, que la projection du vecteur d'onde engendrée par la mesure permet de préparer des états comprimés de spin. Nous présentons ensuite la mise en œuvre de cette méthode à l'aide d'une détection reposant sur la spectroscopie par modulation de fréquence. Finalement, nous exposons quelques premières applications de cette détection non-destructive, plus précisément nous présentons la réalisation du rétroaction quantique qui protège l'état atomique contre la décohérence induite par un basculement du spin collectif, nous montrons aussi comment réaliser une boucle à verrouillage de phase où les atomes servent de référence de phase. Dans la seconde partie du manuscrit, nous présentons la réalisation tout-optique d'un condensat de Bose-Einstein dans une cavité de haute finesse, exploitant les technologies développées pour les télécommunications optiques. Nous commençons par une analyse du résonateur et des méthodes d'asservissement, nous introduisons notamment une méthode d'asservissement originale exploitant la modulation serrodyne. Enfin, nous montrons comment un condensat est obtenu par évaporation dans le mode optique de la cavité
In this thesis, we study several methods to improve atom interferometers. In the first part of the manuscript, we analyze how a nondestructive detection, that preserves the coherence between the internal degrees of freedom in an atomic ensemble, can be used to increase the sensitivity of interferometers. We first theoretically show how the projection of the wave-function induced by the measurement prepares spin-squeezed states. We then present the implementation of this method with a detection based on the frequency modulation spectroscopy. Finally, some first applications are described, more explicitly we show how to implement a quantum feedback that preserve the atomic state against the decoherence induced by a random collective flip, we also introduce a phase-locked loop where the atomic sample is used as the phase reference. In the second part of the manuscript, we present the all-optical realization of a Bose-Einstein condensate in a high-finesse cavity using a laser system based on standard telecoms technologies. We first describe the resonator and the frequency lock of the laser on the resonance, in particular, we introduce a new stabilization method based of the serrodyne modulation. Finally, we show how the condensate is obtained from the evaporation in the cavity mode

Cette thèse est dédiée à l’étude des phénomènes non-linéaires dans deux fluides quantiques qui partagent de nombreuses similitudes : les condensats de Bose-Einstein et les “fluides de lumière”. Dans une première partie, nous étudions les analogues soniques des trous noirs. Il est possible de créer une configuration stationnaire d’un condensat de Bose-Einstein en écoulement d’une région subsonique vers une région supersonique. Ce fluide transsonique joue alors le rôle d’un trou noir puisque les ondes sonores ne peuvent s’échapper de la région supersonique. En outre, en quantifiant le champ sonore, il est possible de montrer qu’un rayonnement de Hawking analogue émerge des fluctuations quantiques du vide. Dans cette thèse, nous montrons que la prise en compte des “modes zéros” – omis jusqu’alors dans le contexte de la gravité analogue – est essentielle pour obtenir une description précise du processus de Hawking, menant alors à un excellent accord avec les résultats expérimentaux. Enfin, nous étudions l’intrication entre les différentes excitations quantiques et montrons que notre système crée de l’intrication tripartite. Dans un second temps, nous étudions la propagation des fluides non-linéaires grâce à une approche hydrodynamique et à des méthodes mathématiques développées par Riemann et Whitham. Nous étudions la structure oscillante et la dynamique des ondes de chocs dispersives qui se forment à la suite d’un déferlement. Notre approche permet de trouver des expressions analytiques simples qui décrivent les propriétés asymptotiques du choc. Cela donne accès à des paramètres d’intérêt expérimental, comme le temps de déferlement, la vitesse de l’onde de choc ou encore le contraste de ses franges
This thesis is dedicated to the study of nonlinear-driven phenomena in two quantum gases which bear important similarities: Bose-Einstein condensates of ultracold atomic vapors and “fluids of light”. In a first part, we study sonic analogues of black holes. In a Bose-Einstein condensate, it is possible to implement a stationary configuration with a current flowing from a subsonic region to a supersonic one. This mimics a black hole, since sonic excitations cannot escape the supersonic region. Besides, quantizing the phonon field leads to a sonic analogue of Hawking radiation. In this thesis, we show that a correct account of “zero modes” – overlooked so far in the context of analogue gravity – is essential for an accurate description of the Hawking process, and results in a excellent comparison with recent experimental data. In addition, we characterize the entanglement shared among quantum excitations and show that they exhibit tripartite entanglement. In a second part, we investigate the short and long time propagation of nonlinear fluids within a hydrodynamic framework and by means of mathematical methods developed by Riemann and Whitham. In particular, we study the oscillating structure and the dynamics of dispersive shock waves which arise after a wave breaking event. We obtain a weak shock theory, from which we can extract a quantitative description of experimentally relevant parameters, such as the wave breaking time, the velocity of the solitonic edge of the shock or the contrast of its fringes

A turbulência clássica é um fenômeno de natureza caótica, mas de difícil estudo por ser constituída pela fusão e superposição de vórtices aleatórios, dificultando sua descrição matemática. A turbulência quântica (TQ), embora também caótica, é composta por vórtices quantizados, que favorecem o controle experimental e sua definição teórica. Embora a evidência experimental da TQ tenha sido obtida em sistemas de He líquido, sua caracterização em condensados de Bose-Einstein (BEC) ainda não foi totalmente realizada. Neste trabalho, estudamos a distribuição de momento em BECs expandidos em tempo de voo, nos regimes convencional e turbulento. Para a produção experimental da amostra quanticamente degenerada, utilizamos a técnica do resfriamento evaporativo em átomos de 87Rb, previamente resfriados em uma armadilha puramente magnética do tipo QUIC. A turbulência quântica foi produzida no sistema através de um par de bobinas de excitação capaz de produzir uma perturbação oscilatória na nuvem previamente condensada. O diagnóstico da amostra aprisionada é feito por imagem de absorção durante expansão livre da nuvem. Durante a expansão, tanto a nuvem condensada quanto a turbulenta, alcançaram um valor assintótico no aspect ratio, indicando uma evolução isotrópica. A partir deste resultado, elaboramos um método teórico capaz de determinar a projeção isotrópica da distribuição de momento, baseado na imagem produzida experimentalmente. Através de argumentos de simetria e de uma transformada integral, recuperamos a densidade de momento tridimensional da projeção, para então determinar o espectro de energia cinética da nuvem, observando uma lei de escala para um estreito intervalo de momento. A lei de escala já foi prevista teoricamente para sistemas quânticos e medida para o He superfluido, mas pela primeira vez foi evidenciada em um BEC. Desta forma, os resultados corroboram a existência da turbulência quântica em uma amostra quanticamente degenerada, introduzindo os BECs como candidatos alternativos ao He líquido superfluido no estudo deste fenômeno.
Classical turbulence is a chaotic phenomenon that requires labored work, because of its merging and overlapping of random vortices nature, which hinders its mathematical description. Quantum turbulence (QT), although chaotic, is comprised of quantized vortices that favor the experimental control and its theoretical definition. Although experimental evidence of QT has been proved in liquid helium systems, its characterization in Bose-Einstein condensates (BEC) has not been fully accomplished. In this work, we studied the momentum distribution of expanding turbulent and non-turbulent BEC. For experimental achievement of the quantum degenerated sample, we used evaporative cooling in rubidium atoms, previously cooled in a QUIC trap. Quantum turbulence was produced through a pair of excitation coils capable of producing an oscillatory perturbation in the cloud previously condensed. The diagnosis of the trapped sample is done by absorption image during free expansion of the cloud. During the expansion, both clouds achieved a asymptotic value of the aspect ratio, indicating an isotropic evolution. From this result, we have developed a theoretical method able to determine the projection of the isotropic distribution of momentum, based on the image produced experimentally. Through symmetry arguments and an integral transformation, we recovered the tridimensional momentum distribution of the projection and then determined the kinetic energy spectrum of the cloud, observing a scaling power law for a narrow range of momenta. The scaling law has been theoretically predicted for quantum systems and has been proved to liquid helium superfluid, but, in this work, was for the first time evidenced in a BEC. Thus, the results support the existence of quantum turbulence in our quantum degenerated sample, introducing the BECs as potential candidates besides liquid helium superfluid for the study of this phenomenon.

The work presented in this thesis revolves around spectral inequalities and their applications in quantum mechanics. In Paper A, the ground state energy of an atom confined to two dimensions is analyzed in the limit when the charge of the nucleus Z becomes very large. The main result is a two-term asymptotic expansion of the ground state energy in terms of Z. Paper B deals with Hardy inequalities for the kinetic energy of a particle in the presence of an external magnetic field. If the magnetic field has a non-trivial radial component, we show that Hardy’s classical lower bound can be improved by an extra term depending on the magnetic field. In Paper C we study interacting Bose gases and prove Lieb-Thirring type estimates for several types of interaction potentials, such as the hard-sphere interaction in three dimensions, the hard-disk interaction in two dimensions as well as homogeneous potentials.

QC 20140520

Dans ce manuscrit, nous présentons une étude expérimentale d'un gaz de Bose de spin 1 avec des interactions antiferromagnétiques avec des atomes de sodium ultra-froids dans l'état hyperfin F=1. Les trois composantes Zeeman sont piégées simultanément dans des pièges dipolaires optiques. Nous obtenons un condensat de Bose-Einstein spineur par refroidissement évaporatif et nous étudions ses propriétés magnétiques. Il y a deux types d’interactions dans le système: des interactions de contact qui ne changent pas les populations des composantes Zeeman et des interactions d'échange de spin qui les modifient. Une compétition entre l'énergie Zeeman et l'énergie d'échange impose l'ordre magnétique dans le système.Nous étudions dans un premier temps les phases magnétiques de condensats de Bose-Einstein spineurs a température quasi nulle. L'état fondamental comporte deux phases qui sont observées en variant le champ magnétique (donc l'énergie Zeeman quadratique) et la magnétisation de l'échantillon. Dans la phase antiferromagnétique, le spin de l'échantillon est simplement selon l'axe du champ magnétique. Dans la phase polaire, une composante transverse apparait pour minimiser l'énergie Zeeman. Pour une magnétisation nulle, le condensat spineur forme un nématique de spin. Cet état, nommé par analogie avec la phase nématique dans les cristaux liquides, est caractérisée par des fluctuations de spin orthogonales à un axe particulier, mais sans préférer une des deux direction sur cet axe. Dans chacune des deux phases, l'ordre nématique se manifeste par un minimisation de la longueur du spin transverse en imposant une valeur particulière ($pi$) de la phase relative des composantes Zeeman ${theta = phi_{+1} + phi_{-1} - 2 phi_{0}}$. Nous mesurons la longueur du spin transverse en analysant le bruit de spin après une rotation.Dans un second temps, nous étudions la thermodynamique d'un gaz de Bose de spin 1 près de la température critique pour la condensation de Bose-Einstein. Nous mesurons plusieurs scénarios de condensation séquentiels en fonction de la magnétisation et du champ magnétique. La température critique mesurée révèle que les interactions ont un effet important quand la condensation d'une composante se fait en présence d'un condensat dans une autre composante. Nous utilisons une théorie d'Hartree-Fock simplifiée, en négligeant les interactions d’échange de spin. Nous constatons que les résultats expérimentaux sont en bon accord. Cependant, pour de bas champs magnétiques, le diagramme de phase thermodynamique est largement modifié par les interactions d'échange de spin, ce qui pose de nouvelles questions sur leur rôle a température finie
In this manuscript, we present an experimental study of a Spin 1 Bose gas with antiferromagnetic interactions with ultracold sodium atoms in the F=1 manifold. The three Zeeman components are trapped simultaneously in optical dipole traps. By performing evaporative cooling, we obtain quasi-pure spinor Bose-Einstein condensates of which we study the magnetic properties. There are two types of interactions between the constituents of the system: Contact interactions that do not change the Zeeman populations and spin-exchange contact interactions that do. A competition between Zeeman energy and the spin-exchange energy sets the magnetic ordering in the system.We first study the magnetic phases of spinor Bose-Einstein condensates near zero temperature. The ground state present two phases that are observed by varying the magnetic field (hence the quadratic Zeeman energy) and the magnetization of the sample. In the antiferromagnetic phase, the spin of the sample is purely along the direction of the magnetic field. In the broken-axisymmetry phase, a transverse component appears in order to minimize the Zeeman energy. For zero magnetization, the spinor condensate forms a spin nematic. This state, named in analogy with the liquid crystal nematic phase, is characterized by spin fluctuations orthogonal to a particular axis, with no preferred direction along that axis. In both phases, spin nematic order manifests as a minimization of the transverse spin length that is realized by enforcing a particular value ($pi$) of the relative phase of the Zeeman components $theta = phi_{+1} + phi_{-1} - 2 phi_0$. We measure the transverse spin length by analyzing spin noise after a spin rotation.Second, we study the thermodynamics of an antiferromagnetic spin 1 Bose gas next to the critical temperature for Bose-Einstein condensation. We measure several sequential condensation scenarii depending on the magnetization and the magnetic field. The measured critical temperatures reveal a large effect of interactions when one of the Zeeman component condenses in presence of a condensate in another component. We use a simplified Hartree-Fock theory, neglecting the spin exchange interactions and note a good agreement with our data. However, for low magnetic fields, the thermodynamic phase diagram is strongly modified which raises new open questions about the role of spin exchange interactions at finite temperatures

Neste trabalho descrevemos a produção e estudo de excitações topológicas em um condensado de Bose-Einstein em átomos de Rubídio-87. O condensado é produzido através de resfriamento evaporativo forçado por rádio-freqüência em uma armadilha puramente magnética do tipo QUIC. A armadilha magnética é carregada por um sistema de duplo-MOT. A temperatura de transição é de cerca de 150nK. Condensados puros com 1 - 2 × 10^5 átomos de Rb-87 são observados. Realizamos uma caracterização da amostra em relação às suas características fundamentais. Fração condensada, expansão anisotrópica, distribuição espacial e efeitos de temperatura finita são descritos. Com o objetivo de observar excitações coerentes do condensado entre os estados da armadilha, adicionamos um campo magnético do tipo quadrupolo esférico oscilante no tempo. Observamos, no entanto, a transferência de momento angular para a amostra com a formação de vórtices e arranjos de vórtices. Definimos regiões de amplitude que geram números de vórtices crescentes. Observamos a formação de estruturas de três vórtices não convencionais donde supusemos a possibilidade de excitação conjunta de vórtices e anti-vórtices. Observamos evidência de turbulência quântica, um estado onde os arranjos dos vórtices não são regulares nem as linhas de vórtices têm um eixo de rotação comum.
In this work we describe the production and investigation of topological excitations in a Bose-Einstein condensate in Rubidium-87 atoms. The condensate is produced through forced evaporative cooling by radio-frequency in a QUIC-type purely magnetic trap. The magnetic trap is loaded from a double-MOT system. Transition temperature is about 150nK. Pure condensates containing 1-2×105 87Rb atoms are observed. We performed the characterization of the sample in relation to its fundamental aspects. Condensed fraction, anisotropic expansion, spacial distribution and finite temperature effects are described. Aiming to observe coherent topological excitations of the condensate between two states of the trap, we added a spherical quadrupole magnetic fields oscillating in time. We observe, instead, angular momentum tranference to the sample and the formation of vortices and arrays of vortices. We define amplitude regions where an increasing number of vortices are observed. We observe the formation of non-usual three-vortex structures from which we infer the existence of vortices and anti-vortices together in the sample. We observe evidence of quantum turbulence, a state where non-regular vortex arrays appear as well as vortex lines have no preferred direction to form.

Dans cette thèse nous étudions expérimentalement les propriétés magnétiques de condensats de sodium de spin 1 à l'équilibre. Dans ce système les atomes peuvent occuper chacun des trois états Zeeman caractérisés par la projection de leur spin sur l'axe de quantification m=+1,0,-1. Nous mesurons l'état de spin à N particules du système en fonction du champ magnétique appliqué et et de la magnétisation (différence entre les populations des états m=+1 et m=-1) du nuage atomique. Nos mesures sont en très bon accord avec la prédiction de la théorie de champ moyen, et nous identifions deux phases magnétiques résultant de la compétition entre les interactions de spin antiferromagnétiques et l'effet du champ magnétique. Nous décrivons ces deux phases en terme d'un ordre nématique de spin caractérisant la symétrie de l'état de spin à N particules. Dans une seconde partie nous nous concentrons sur les propriétés du condensat à très faible magnétisation et soumis à un faible champ magnétique. Dans ces conditions, la symétrie du système se manifeste à travers de très grandes fluctuations de spin. Ce phénomène n'est pas explicable par une théorie de champs moyen naïve, et nous développons une approche statistique plus élaborée pour décrire l'état de spin du condensat. Nous mesurons les fluctuations de spin et nous sommes capables de déduire de leur analyse la température caractérisant le degré de liberté de spin du condensat. Nous trouvons que cette température diffère de celle décrivant les atomes thermiques entourant le condensat. Nous interprétons cette différence comme une conséquence du faible couplage entre ces deux systèmes
In this thesis we study experimentally the magnetic properties of spin-1 Bose-Einstein condensate of Sodium at equilibrium. In this system the atoms can occupy any of the three Zeeman states characterized by their spin projection on the quantization axis m=+1,0,-1. We measure the many-body spin state of the system as a function of the applied magnetic field and of the magnetization (difference between the populations of the spin states m=+1 and m=-1) of the atomic sample. We find that our measurements reproduce very well the mean-field prediction, and we identify two magnetic phases expressing the competition between the antiferromagnetic inter-particle interactions and the effect of the magnetic field. We describe these phases in terms of a spin nematic order characterizing the symmetry of the many-body spin state. In a second part we focus on the properties of condensates of very low magnetization under a weak magnetic field. In these conditions, the symmetry of the system manifests itself in huge spin fluctuations. This phenomenon is not explainable by a naive mean-field theory and we develop a more elaborate statistical approach to describe the spin state of the condensate. We measure the spin fluctuations and are able from their analysis to infer the temperature characterizing the spin degree of freedom of the condensate. We find that this temperature differs from the temperature of the thermal fraction surrounding the condensate. We interpret this difference as a consequence of the weak coupling between these two systems

Les travaux présentés dans ce manuscrit de thèse portent sur la construction d’un nouveau dispositif pour atomes froids de strontium 84. Les expériences réalisées sur ce montage porteront sur la dynamique de relaxation de gaz quantiques hors équilibre. Cette dynamique est étudiée pour des gaz bidimensionnels sur réseau. Ce manuscrit de thèse s'attache à décrire la conception des systèmes optiques utilisés pour piéger et manipuler les gaz lors des expériences. En particulier, le montage optique utilisé pour le transport des atomes entre deux positions de l'enceinte à vide est présenté. La solution choisie pour la réalisation du piège bidimensionnel est elle aussi détaillée. Enfin, un microscope à gaz quantiques est mis en place afin de mesurer in situ les fonctions de corrélation spatiales à partir de la répartition des atomes dans le piège bidimensionnel. Une caractérisation du microscope est présentée dans ce manuscrit. Bien que la conception des différents systèmes optiques soit terminée dans sa première version, il nous reste quelques étapes de construction avant d'achever le montage de notre dispositif expérimental
This manuscript presents the construction of a new quantum ultracold atom experiment using strontium 84. The aim of this experiment is to study the relaxation dynamics of quantum gases initially prepared in an out-of-equilibrium state. We will investigate bidimensional gases on a lattice. This manuscript aims to describe the optical systems designed for trapping and manipulating the atoms during the experiment. Specifically, we present our optical solution to transport the atoms between locations in the vacuum chamber. We also discuss the choices we made to create the bidimensional lattice. Lastly, a quantum gas microscope is implemented to measure the spatial correlation functions from the atoms’ distribution in the lattice. A characterization of the microscope is laid out in this manuscript. Though we determined a first version of our optical systems, there are still a few steps needed to complete the experimental setup

Neste projeto de doutorado estudamos dois aspectos em condensados de Bose-Einstein de gases alcalinos diluídos: (i) a expansão auto-similar de um superfluido turbulento, e (ii) a física dos pólarons no contexto de misturas de superfluidos e redes de vórtices. Ambas as análises estão relacionadas com nossas tendências experimentais em átomos frios. Na primeira etapa generalizamos as equações hidrodinâmicas dos superfluidos para descrever a expansão anômala de uma nuvem condensada turbulenta. A física por detrás dessa assinatura característica da natureza turbulenta da nuvem pôde ser compreendida através das equações derivadas em nosso modelo, que considerou a energia cinética advinda de uma configuração de vórtices enovelados. Na segunda parte do trabalho abordamos a física do pólaron, analisando as propriedades de uma impureza neutra acoplada com os modos Tkachenkos de um condensado de Bose-Einstein contendo uma rede de vórtices. Através da função espectral da impureza, pudemos acompanhar a evolução das propriedades de quase-partícula em função da magnitude do parâmetro de interação, à medida que caminhávamos em direção ao regime de baixas energias do sistema. A função espectral apresentou inicialmente um alargamento do seu perfil Lorentziano para baixos valores dos momentos da impureza e das excitações, mesmo a temperatura zero. Ao atingir a proximidade de um ponto fixo de baixas energias, porém, o espectro passa a adquirir um perfil de decaimento com lei de potência. Trata-se de uma assinatura do fenômeno da catástrofe de ortogonalidade, com a quebra da natureza de quase-particula do sistema. Aplicamos uma transformação canônica com operadores unitários e técnicas de grupo de renormalização para avaliar o fluxo das constantes da teoria à medida que diminuíamos as escalas de energia características do nosso sistema. Na etapa final apresentamos alguns resultados preliminares sobre o sistema de duas espécies de condensado sobrepostas, uma delas contendo a rede de vórtices. Por meio de uma analogia com superfluidos em redes ópticas, mapeamos nosso Hamiltoniano em um modelo Bose-Hubbard e variamos o comprimento de espalhamento atômico das espécies envolvidas para induzir a transição de fase quântica naquela aprisionada na rede. Mostramos que essa nossa nova configuração quântica de rede permite investigações que vão além daquelas estudadas com redes ópticas estáticas.
In this thesis we studied two aspects of Bose-Einstein condensation in dilute gases: (i) the self-similar expansion of a turbulent superfluidity, and (ii) the polaron physics in the context of the superfluid mixtures and vortex lattices. Both analyses are closely related to our experimental trends. Concerning the first subject, we generalized the superfluid hydrodynamic equations to describe the anomalous expansion of a turbulent condensate cloud. The physics behind this characteristic signature of the turbulence could be clarified through the expressions derived in our model, that considered the kinetic energy associated with a tangled vortex configuration. As for the second item, we present the polaron physics of a neutral impurity coupled with the Tkachenko modes of a vortex lattice Bose-Einstein condensate. Through the impurity spectral function, we tracked how the quasiparticle properties varied as a function of the interaction strength toward the lower energy regimes. The spectral function exhibits a Lorentzian broadening for small wave vectors, even at zero temperature, until it starts to reach the low energy fixed point, where it acquires a power law decay. That is the signature of orthogonality catastrophe phenomena, with the breakdown of the quasiparticle picture. We applied canonical unitary transform and renormalization group equations to evaluate the flow of the theory parameters as we go further down in the characteristic energy scales. Finally, we provide preliminary results on the calculation of a system composed of two condensate species, one immersed in a second containing an array of vortices. Making an analogy with superfluids in an optical lattice, we map our Hamiltonian onto a Bose-Hubbard type model and tune the atomic scattering length of the two species to induce a quantum phase transition in the confined cloud. This is a new quantum system which allows investigation beyond the present studies with static optical lattices.

La dimensionnalité d’un système affecte fortement ses propriétés physiques ; les transitions de phasequi s’y déroulent ainsi que le type d’ordre qui y apparaît dépendent de la dimension. Dans les systèmesde basse dimension, la cohérence s’avère plus difficile à établir car les fluctuations thermiques etquantiques y jouent un rôle plus important. Le fluide de Bose à deux dimensions est particulièrementintéressant car, même si un ordre total est exclu, un ordre résiduel à « quasi-longue » portée s’établit àbasse température. Deux ingrédients ont un effet significatif sur l’état du système : (i) la taille finie d’unsystème réel permet de retrouver une occupation macroscopique d’un état à une particule ; (ii) les interactionsentre particules conduisent à l’apparition d’un type non-conventionnel de transition de phasevers un état superfluide.Dans cette thèse, nous présentons une étude expérimentale du gaz de Bose bidimensionnel (2D) utilisantdeux types de paysages énergétiques pour piéger nos atomes. Dans la première partie, nous utilisonsla dépendance spatiale de certaines propriétés locales d’un gaz inhomogène pour caractériser l’étatdu système homogène équivalent. Nous extrayons son équation d’état des profils de densité et noustestons son comportement superfluide en mesurant le chauffage induit par le mouvement d’une perturbationlocale. Dans la deuxième partie, nous observons et caractérisons l’émergence d’une cohérencede phase étendue dans un gaz 2D homogène, en particulier via le passage de trois dimensions à deux(croisement dimensionnel). Nous étudions l’établissement dynamique de la cohérence par un passagerapide du croisement dimensionnel et nous observons des défauts topologiques dans l’état superfluidefinal. Nous comparons nos résultats avec les prédictions du mécanisme de Kibble–Zurek
The dimensionality of a system strongly affects its physical properties; the phase transitions that takeplace and the type of order that arises depend on the dimension. In low dimensional systems phasecoherence proves more difficult to achieve as both thermal and quantum fluctuations play a strongerrole. The two-dimensional Bose fluid is of particular interest as even if full order is precluded, a residual"quasi-long" range order arises at low temperatures. Then two ingredients have a significant effecton the state of the system: (i) the finite size of a real system enables one to recover of a macroscopicoccupation of a single-particle state; (ii) the interactions between particles lead to the emergence of anon-conventional type of phase transition toward a superfluid state.In this thesis, we present an experimental study of the two-dimensional (2D) Bose gas using two differentenergy landscapes to trap our atoms. In the first part, we use the spatial dependence of somelocal properties of an inhomogeneous gas to characterize the state of the equivalent homogeneous system.We extract its equation of state with a high accuracy from the gas density profiles and test itssuperfluid behavior by measuring the heating induced by a moving local perturbation. In the secondpart, we observe and characterize the emergence of an extended phase coherence in a 2D homogeneousgas in particular via a 3D-to-2D dimensional crossover. We investigate the dynamical establishment ofthe coherence via a rapid crossing of the dimensional crossover and observe topological defects in thefinal superfluid state. We compare our findings with the predictions for the Kibble–Zurek mechanism

For ninety years we have known that our universe is in expansion. Cosmological data favor an unknown form of intrinsic and fundamental uniform energy contributing approximately 68% of the total energy budget in the current epoch. The simplest proposal in accordance with observations is the standard cosmological model consisting of a small but positive cosmological constant producing a gravitational repulsive effect driving the accelerated expansion. In standard cosmology general relativity is assumed as the theory for gravity, which in turn predicts that a sufficiently compact mass can deform spacetime and form a black hole. At a mathematical level, these objects are considered vacuum solutions described by very few parameters. For instance, a stationary black hole solution is completely described by its mass, angular momentum, and electric charge; and two black holes that share the same values for these parameters, are indistinguishable from one another. On the basis of the usual metrics describing black holes, it is generally believed that all contained matter is localized in the center or, if rotating, on an infinitely thin ring. Recent approaches challenge this unintuitive assumption and consider matter just spread throughout the interior. Clearly, this begs for a quantum description in curved space. In past years, a novel approach established a new bridge between quantum information and the physics of black holes when an intriguing proposal was made: black holes could possibly be understood as Bose—Einstein condensates of soft interacting but densely packed gravitons. The aim of this thesis is to discuss how to construct a graviton condensate structure on top of a classical gravitational field describing black holes. A necessary parameter to be introduced for this analogy is a chemical potential which we discuss how to incorporate within general relativity. Next we search for solutions and, employing some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. These results can be extended easily to a Reissner—Nordström black hole. In fact, we find that the phenomenon seems to be rather generic and is associated with the presence of a horizon, acting as a confining potential. In order to see whether a Bose— Einstein condensate is preferred, we use the Brown—York quasilocal energy, finding that a condensate is energetically favourable in all cases in the classically forbidden region. The Brown—York quasilocal energy also allows us to derive a quasilocal potential, whose consequences allow us to suggest a possible mechanism to generate a graviton condensate in black holes. On the contrary, this is not the case for any kind of horizons; for instance, this mechanism appears not to be feasible in order to generate a quantum condensate behind the cosmological de Sitter horizon. Furthermore, when a pair of black holes merge, an immense amount of energy should be given off as gravitational waves. Their wave forms have been recently confirmed to be perfectly described by general relativity. We discuss why for low frequency gravitational waves aimed to be detected by astrophysical PTA observations the fact that propagation should take place over an expanding (approximately globally de Sitter) spacetime should be taken into account. In this manner, harmonic waves produced in such mergers would become anharmonic when measured by cosmological observers. This effect is tiny but appears to be observable for gravitational waves to which PTA are sensitive. Therefore we have characterized modifications to the expected signal, and how it is related to the source and pulsar characteristics that are employed by the IPTA collaboration. If the cosmological constant were an intrinsic property, this experiment would be capable of confirming the relevance of lambda at redshift z < 1.
El objetivo de la presente tesis es profundizar en diversos aspectos de la física de los agujeros negros. Tanto en lo que respecta a sus características constitutivas fundamentales, su "estructura" interna, como a la posibilidad de observar o detectar mediante observaciones astrofísicas ciertos efectos producto de su dinámica. Por un lado, hemos seguido las ideas de Dvali, Gómez et al. quienes han sugerido la posibilidad de que un agujero negro sea un condensado de Bose—Einstein de gravitones débilmente interactuantes. En nuestro caso hemos estudiado la existencia de este tipo de soluciones sobre diferentes métricas de agujero negro (Schwarzschild y Reissner— Nordström) que actuarían como potencial confinante para dichos condensados. Un parámetro necesario para ello, es el equivalente a un potencial químico que debe ser incorporado a la relatividad general. Cabe destacar que la solución encontrada puede ser interpretada como la función de campo medio del condensado. Además resulta fuertemente ligada a la estructura clásica de la métrica que la sustenta. Por otro lado, es bien sabido que la aceleración de cuerpos muy masivos producen perturbaciones de tipo onda en el espaciotiempo. Son de nuestro interés las ondas gravitatorias de baja frecuencia, provenientes de la colisión de agujeros negros supermasivos y que deberían poder ser detectadas mediante sistemas de púlsares (Pulsar Timing Arrays). De acuerdo a una línea de investigación desarrollada por Espriu et al. la presencian de una constante cosmológica podría tener un efecto en la propagación y por lo tanto en la detección por parte de la colaboración IPTA de estas ondas. En la presente tesis hemos generalizado el método para incluir diferentes tipos de materia (relativista y no relativista) además de la constante cosmológica. Del análisis se deriva que el efecto depende sensiblemente del valor de la constante de Hubble (que engloba todos los tipos de materia presentes). Continuando dicha línea, hemos caracterizado detalladamente el efecto en su dependencia con los parámetros cosmológicas y las distancias involucradas, y cómo podría ser hallado. Esperamos que nuestros resultados puedan contribuir a una definitiva detección por IPTA.

The quantum properties of matter waves, in particular quantum correlations and entanglement are an important frontier in atom optics with applications in quantum metrology and quantum information. In this thesis, we report the first observation of sub-Poissonian fluctuations in the magnetization of a spinor 87Rb condensate. The fluctuations in the magnetization are reduced up to 10 dB below the classical shot noise limit. This relative number squeezing is indicative of the predicted pair-correlations in a spinor condensate and lay the foundation for future experiments involving spin-squeezing and entanglement measurements. We have investigated the limits of the imaging techniques used in our lab, absorption and fluorescence imaging, and have developed the capability to measure atoms numbers with an uncertainly < 10 atoms. Condensates as small as ≈ 10 atoms were imaged and the measured fluctuations agree well with the theoretical predictions. Furthermore, we implement a reliable calibration method of our imaging system based on quantum projection noise measurements. We have resolved the individual lattice sites of a standing-wave potential created by a CO2 laser, which has a lattice spacing of 5.3 µm. Using microwaves, we site-selectively address and manipulate the condensate and therefore demonstrate the ability to perturb the lattice condensate of a local level. Interference between condensates in adjacent lattice sites and lattice sites separated by a lattice site are observed.

Ce manuscrit présente mes travaux de recherche depuis la fin de ma thèse début 2005. J'essaye en particulier de replacer mes recherches dans leur contexte, et d'expliquer mes choix scientifiques de façon chronologique. Les principaux résultats ont donne lieu a des publications. Celles-ci ont été écrites avec soin et c'est pourquoi, j'ai choisi de ne décrire les résultats principaux que de fa con succincte. Pour avoir plus de détails et pour retrouver les gures expérimentales, mes articles sont reproduits a la n de chaque chapitre et cites à l'endroit adéquat. J'ajoute parfois des parties plus techniques qui ne sont pas explicitées dans les publications. Le Chapitre 2 est une courte introduction au domaine des atomes ultrafroids, s'adressant a un lecteur non spécialiste. Cela permet de présenter mon domaine de recherche, c'est a dire l'utilisation des gaz d'atomes ultra-froids en tant que systèmes modèles pour l'étude des propriétés quantiques des systèmes a N-corps. Le chapitre 3 est consacre a mes recherches durant mon séjour postdoctoral de deux ans dans le groupe de T. Esslinger a l'ETH Zurich. J'ai participé a une série d'expériences utilisant une cavité de haute nesse pour détecter individuellement les atomes issus d'un gaz ultra-froids. J'explique la théorie de ce système quantique ouvert et sa résolution numérique qui permet de comprendre quantitativement le processus de mesure de la présence d'un atome dans la cavit e. Experimentalement, nous avons mis en œuvre une technique consistant a extraire deux faisceaux d'atomes en deux points distincts du nuage d'atomes pour avoir accès a la fonction de corrélation g1 en perturbant peu le système. Nous avons ainsi étudie la dynamique de la transition de Bose-Einstein de fa con beaucoup plus ne que cela n'avait et e 15 fait auparavant. Nous avons pu comparer la dynamique de croissance de la densite a la dynamique d'apparition de la cohérence. Nous avons ensuite observe le comportement de la fonction g1 dans le régime critique tr es proche de la condensation et extrait une valeur expérimentale de l'exposant critique associe a la longueur de cohérence. En n, nous avons mis en place un ascenseur a atomes constitue de deux lasers contra-propageants contrôles en phase. Le condensat de Bose-Einstein a ainsi et e transport e vers la cavite de haute nesse pour créer un système quantique couple atome-rayonnement dans un régime de couplage extrême et nouveau. Le chapitre 4 est d edi e a mes trois premières années (2007-2009) au laboratoire Charles Fabry de l'Institut d'Optique dans le groupe d'optique atomique. J'explique d'abord le d em enagement du syst eme exp erimental a Palaiseau ainsi que les differentes ameliorations apportees au piege magn etooptique 2D. Nous avons realise un condensat de Bose-Einstein de rubidium par une methode entierement optique. Notre laser de piegeage est un laser a bre dop ee erbium de puissance a 1565 nm. Cette longueur d'onde n'avait jamais et e utilisee auparavant dans des experiences avec des atomes ultrafroids. Nous avons utilise les specifcites de ce laser, et notamment le fort decalage lumineux de la transition optique pour demontrer une technique de tomographie du champ lumineux vu par les atomes. Cette compr ehension des d ecalages lumineux nous a guide vers une melasse tres fortement decalee (environ 200 MHz) pour charger les atomes le plus e cacement possible dans le piege optique. Nous avons montre qu'une nouvelle geometrie permet de contrôler independamment la profondeur du piege et sa raideur, et ainsi d'optimiser l' evaporation dans le piege optique. En n, nous avons utilise notre dispositif pour une premiere application qui consiste a faire rebondir les atomes sur une onde stationnaire dans le but d'allonger le temps d'interrogation dans les interferometres o u les atomes sont en chute libre. Le trampoline a atomes peut fonctionner dans un r egime quantique o u les interferences entre chemins quantiques permettent d'allonger le temps de levitation. Le chapitre 5 est consacre a mes recherches sur les gaz 2D et desordonnes qui se poursuivent encore aujourd'hui. Lorsque les interactions entre atomes sont negligeables, la physique est a un corps. Le phenomene de diffusion a et e mis en evidence et caracteris e pour la premi ere fois avec des atomes ultra-froids dans un potentiel conservatif. En allant vers le regime quantique ou la longueur d'onde de DeBroglie des atomes devient de l'ordre de la taille caracteristique des grains de desordre, on s'attend alors a voir des effets de localisation d'Anderson, li es aux interferences entre ondes de mati ere. Les conditions necessaires pour observer la localisation d'Anderson dans un gaz en expansion sont detaillees. Pour des gaz pieges, les interactions jouent un r^ole predominant a 2D et la transition de Bose-Einstein est alors rem- 16 placee par une transition super uide de type Berezinskii-Kosterliz-Thouless. Exp erimentalement, nous avons etudie cette transition via la distribution en impulsion qui permet de caract eriser les propri et es de coherence du gaz. Ensuite, nous avons observe quantitativement l'in uence du d esordre sur la transition super uide. Nous formons alors un systeme quantique complexe pour lequel il n'y a pas de pr ediction th eorique pr ecise et dont la physique est liee a celle de certains materiaux de matiere condensee. J'insiste sur le rôle de la longueur de correlation du desordre en la comparant aux longueurs caracteristiques du gaz. Dans le regime d'un desordre correle a longue portee, l'approximation de densite locale est valable dans le desordre et alors des predictions quantitatives sur le diagramme de phase du systeme sont possibles. En n, je propose des directions pour nos recherches futures. Le refroidissement du potassium par un m ethode enti erement optique est un d e experimental mais permettra d'avoir acces a des resonances de Feshbach larges et ainsi de controler la force des interactions. De plus, un champ magnetique effectif donnera un parametre de controle suppl ementaire sur le syst eme. Ces deux outils seront utiles non seulement pour l' etude de la physique a un corps mais aussi pour une etude plus pr ecise du gaz de Bose 2D en pr esence de d esordre et d'interactions. On cherchera notamment a mettre en evidence le diagramme de phase et a observer une phase isolante exotique, le verre de Bose.

In this thesis, we report experimental evidence of a "gray" condensate of excitons, as predicted theoretically by M. Combescot et al. Most importantly, the condensate is characterized by the macroscopic population of dark excitons coherently coupled to a weak population of bright excitons through fermion exchanges. Such quantum condensation results from the excitons internal structure, with a dark i.e. optically inactive ground state. It is actually very similar to what occurs in the phases of superfluid 3He or in the more recent spinor condensates of ultracold atomic Bose gases. While it is our belief that such a "gray" condensate will eventually be observed in other excitonic systems, our study focus on its appearance together with the macroscopic auto-organization of dipolar excitons. Precisely we emphasize fragmented exciton rings in an electrically biased GaAs single quantum well. This very striking pattern was first observed independently by the groups of L. Butov and D. Snoke. It was interpreted as the result of an ambipolar diffusion of carriers in the quantum wells. The fragmentation of the macrosopic ring observed at low temperature by Butov and coworkers, and the subsequent evidence for long-range spatial coherence together with complex pattern of polarization, led Butov et al. to interpret the fragmentation as an evidence for the transition to a quantum regime where coherent exciton transport dominates. Our experiments led us to a very different interpretation. Indeed, we show that for our sample the formation of the fragmented ring is dominated by the diffusion of dipolar excitons in an optically induced electrostatic landscape. This potential landscape arises from the modulation of the internal electric field by excess charges injected in the QW by the same excitation beam which induces the ring. Dipolar excitons then explore a potential landscape characterized by a wide anti-trap inside the ring and more strikingly by microscopic traps distributed along the circumference of the ring. There, i.e. in the outside vicinity of the ring, a confining potential is responsible for the formation of "islands" where the population of dark excitons is dominant. Due to the low energy splitting between the bright and dark excitonic states in our sample, the observation of a dominant population of dark excitons signals that excitons condense in the low-lying dark states. To confirm this interpretation we show that the weak photoluminescence emitted in the outer vicinity exhibits macroscopic spatial coherence, up to 10 times larger than the de Broglie wavelength. Islands of extended coherence are in fact identified and quickly disappear upon increase of the bath temperature. This leads to an evolution of the coherence length strongly dependent on the temperature. Finally, we show that the photoluminescence emitted in the vicinity of the fragmented ring is dominantly linearly polarized and also organized in islands outside the ring. All these observations confirm the predicted signatures of a "gray" condensate, as formulated by M. and R. Combescot.
En aquesta tesis, mostrem evidència experimental d'un condensat "gris" d'excitons, tal com prediu la teoria de M. Combescot et al. En particular, el condensat està caracteritzat per la població macroscòpica d'excitons foscos acoblats coherentment a una població baixa d'excitons brillants a través d'intercanvis fermiònics. Aquesta condensació quàntica es dóna com a resultat de l'estructura interna dels excitons, amb un estat fonamental fosc i.e. òpticament inactiu. És de fet molt similar al que passa en les fases de 3He superfluid o en els més recents condensats d'espinors de gasos atòmics ultrafreds de Bose. Encara que nosaltres creiem que un condensat "gris" serà eventualment observat en altres sistemes excitònics, el nostre estudi es focalitza en la seva manifestació juntament amb l'auto-organització macroscòpica d'excitons dipolars. Precisament, ens centrem en els anells excitònics fragmentats en un sol pou quàntic elèctricament polaritzat. Aquest sorprenent patró va ser observat independentment per primer cop pels grups de L. Butanov i D. Snoke. Va ser interpretat com el resultat d'una difusió ambipolar de portadors en pous quàntics. La fragmentació de l'anell macroscòpic observada a baixes temperatures per Butov i els seus col.laboradors, i la posterior evidència de coherència espacial de llarg abast juntament amb un patró de polarització complex, va portar a Butov et al. a interpretar la fragmentació com una evidència de la transició cap al règim quàntic en el que domina el transport coherent d'excitons. El nostre experiment ens va portar cap una interpretació molt diferent. En efecte, mostrem que per la nostra mostra la formació d'anells fragmentats és dominada per la difusió d'excitacions dipolars en un perfil electrostàtic òpticament induït. Aquest perfil de potencial sorgeix de la modulació del camp elèctric intern per un excés de càrregues injectades en el PQ pel mateix feix d'excitació que indueix l'anell. Les excitacions dipolars exploren per tant un perfil de potencial caracteritzat per una anti-trampa ampla dins de l'anell i més sorprenentment per trampes microscòpiques distribuïdes al llarg de la circumferència de l'anell. Allà, i.e. en la proximitat exterior de l'anell, un potencial de confinament és el responsable de la formació d'"illes" on la població d'excitons foscos és dominant. Degut a la baixa separació energètica entre els estats excitònics brillant i fosc en la nostra mostra, l'observació d'una població dominant d'excitons foscos senyala que els excitons es condensen en els estats foscos de més baixa energia. Per tal de confirmar aquesta interpretació, mostrem que la dèbil fotoluminescència emesa en la proximitat exterior exhibeix coherència espacial macroscòpica, fins a 10 vegades major que la longitud d'ona de de Broglie. Illes de coherència ampliada són de fet identificades i desapareixen ràpidament en incrementar la temperatura del focus. Això porta cap a una evolució de la longitud de coherència que depèn fortament de la temperatura. Finalment, mostrem que la fotoluminescència emesa en la proximitat de l'anell fragmentat està dominantment polaritzada linealment i organitzada també en illes fora de l'anell. Totes les observacions confirmen les senyals característiques previstes per un condensat "gris", tal com està formulat en la teoria desenvolupada per M. i R. Combescot

In the mid-1920s, the great Albert Einstein proposed that at extremely low temperatures, a gas of bosonic particles will enter a new phase where a large fraction of them occupy the same quantum state. This state would bring many of the peculiar features of quantum mechanics, previously reserved for small samples consisting only of a few atoms or molecules, up to a macroscopic scale. This is what we today call a Bose-Einstein condensate. It would take physicists almost 70 years to realize Einstein's idea, but in 1995 this was finally achieved. The research on Bose-Einstein condensates has since taken many directions, one of the most exciting being to study their behavior when they are placed in optical lattices generated by laser beams. This has already produced a number of fascinating results, but it has also proven to be an ideal test-ground for predictions from certain nonlinear lattice models. Because on the other hand, nonlinear science, the study of generic nonlinear phenomena, has in the last half century grown out to a research field in its own right, influencing almost all areas of science and physics. Nonlinear localization is one of these phenomena, where localized structures, such as solitons and discrete breathers, can appear even in translationally invariant systems. Another one is the (in)famous chaos, where deterministic systems can be so sensitive to perturbations that they in practice become completely unpredictable. Related to this is the study of different types of instabilities; what their behavior are and how they arise. In this thesis we compare classical and quantum mechanical nonlinear lattice models which can be applied to BECs in optical lattices, and also examine how classical nonlinear concepts, such as localization, chaos and instabilities, can be transfered to the quantum world.

In this doctoral thesis, we theoretically investigate the propagation of sound waves in dilute Bose gases, in both the collisionless and hydrodynamic regimes. The study of sound wave is a topic of high relevance for the understanding of dynamical properties of any fluid, classical or quantum, and further provides insightful information about the equation of state of the system. In our work, we focus in particular on the two-dimensional (2D) Bose gas, in which the sound wave is predicted to give useful information about the nature of the superfluid phase transition. Recently, experimental measurement of sound wave in a uniform 2D Bose gas has become available, and we show that the measured data are quantitatively well explained by our collisionless theory. Finally, we study the mixtures of weakly interacting Bose gases, by developing a beyond mean-field theory, which includes the effects of thermal and quantum fluctuations in both the density and spin channels. Our new theory allows for the investigation of sound dynamics, as well as the fundamental problem of phase- separation.

The primary study of this thesis is the experimental realization of the non-equilibrium dynamics of a quantum inverted pendulum as examined in the collective spin dynamics of a spin-1 Bose-Einstein condensate. In order to compare experimental results with the simulation past the low depletion limit, current simulation techniques needed to be extended to model atomic loss. These extensions show that traditional measurements of the system evolution (e.g. measuring the mean and standard deviation of the evolving quantity) were insufficient in capturing the quantum nature of the evolution. It became necessary to look at higher order moments and cumulants of the distributions in order to capture the quantum fluctuations. Extending the implications of the loss model further, it is possible that the system evolves in a way previously unpredicted. Spin-mixing from a hyperbolic fixed point in the phase space and low noise atom counting form the core of the experiment to measure the evolution of the distributions of the spin populations. The evolution of the system is also compared to its classical analogue, the momentum-shortened inverted pendulum. The other experimental study in this thesis is mapping the mean-field phase space. The mean-field phase space consists of different energy contours that are divided into both phase-winding trajectories and closed orbits. These two regions are divided by a separatrix whose orbit has infinite period. Coherent states can be created fairly accurately within the phase space and allowed to evolve freely. The nature of their subsequent evolution provides the shape of the phase space orbit at that initial condition. From this analysis a prediction of the nature of the entire phase space is possible.