No description available.

Esta tesis es un trabajo teórico, en el que estudiamos la física de los átomos dipolares bosónicos ultrafríos en retículos ópticos. Éstos gases consisten de átomos o moléculas bosónicas, enfriados bajo la temperatura de degeneración cuántica, típicamente del orden de nK. En éstas condiciones, en una trampa armónica tridimensional (3D), los bosones que interaccionan débilmente condensan y forman un Condensado de Bose Einstein (BEC). Cuando se carga un BEC en un retículo óptico producido por ondas estacionarias de luz láser, se producen nuevos fenómenos físicos. Estos sistemas entonces realizan modelos de tipo Hubbard y pueden ser llevados a regimenes fuertemente correlacionados.En 1989, M. Fisher et. al. predecían que el modelo de Bose-Hubbard homogéneo (BH) presenta la transición de fase cuántica Superfluid-Mott insulator (SF-MI). En 2002, la transición entre éstas dos fases fue observada experimentalmente por primera vez en el grupo de T. Esslinger e I. Bloch. La realización experimental de un BEC dipolar de cromo en el grupo de T. Pfau, y los progresos recientes en las técnicas de enfriamiento y atrapamiento de moléculas dipolares en los grupos de D. Jin e J. Ye, han abierto el camino hacia los gases cuánticos ultra-fríos dominados por la interacción dipolar. La evolución natural, y el reto de hoy en día por parte experimental, es de cargar BEC dipolares en retículos ópticos y estudiar los gases dipolares fuertemente correlacionados.Antes de éste trabajo de doctorado, estudios sobre modelos de BH con interacciones extendidas a los primeros vecinos mostraron la evidencia de nuevas fases cuánticas, como el supersólido (SS) y la fase checkerboard (CB). Debido al carácter de largo alcance de la interacción dipolo-dipolo, que decae con la potencia cúbica inversa de la distancia, es necesario incluir más de un primer vecino para obtener una descripción fiel y cuantitativa de los sistemas dipolares. De hecho, al incluir más vecinos se permiten y se estabilizan aún más nuevas fases.En esta tesis estudiamos modelos de BH con interacciones dipolares, investigando más allá del estado fundamental. Estudiamos un retículo bidimensional (2D) donde los dipolos están polarizados en dirección perpendicular al plano 2D, dando lugar a una interacción dipolar repulsiva e isotrópica. Utilizamos aproximaciones de campo-medio y un ansatz Gutzwiller, que son suficientemente correctos y adecuados para describir este sistema. Encontramos que los gases dipolares en 2D presentan una multitud de estados metaestables de tipo MI, que compiten con el estado fundamental, de modo parecido a sistemas desordenados. Estudiamos en detalle el destino de estos estados metaestables: como pueden ser preparados de manera controlada, como pueden ser detectados, cual es su tiempo de vida debido al tunnelling, y cual es su rol en los procesos de enfriamiento. Además, encontramos que el estado fundamental está caracterizado por estados MI de tipo checkerboard con coeficiente de ocupación n fraccionario (numero medio de partículas por sitio) que depende del cut-off utilizado en el radio de alcance de la interacción. Confirmamos esta predicción estudiando el mismo sistema con métodos Quantum Monte Carlo (worm algorithm). En este caso no utilizamos ningún cut-off en el radio de alcance de la interacción, y encontramos pruebas de una "Devil's staircase" en el estado fundamental, i.e. donde las fases MI aparecen en todos los n racionales del retículo subyacente. Encontramos además, regiones de los parámetros donde el estado fundamental es supersólido, obtenido drogando los sólidos con partículas o con agujeros.En este trabajo, investigamos también como cambia la estructura precedente en 3D. Nos focalizamos en el retículo 3D más sencillo compuesto de dos planos 2D, en el cual los dipolos están polarizados perpendicularmente a los planos; la interacción dipolar es entonces repulsiva por partículas del mismo plano, mientras es atractiva por partículas en el mismo sitio de dos planos diferentes. En cambio suprimimos el tunnelling entre los planos, lo cual hace el sistema equivalente a una mezcla bosónica en un retículo 2D. Nuestros cálculos muestran que las partículas se juntan en parejas, y demostramos la existencia de la nueva fase cuántica Pair Super Solid (PSS).Actualmente estamos estudiando un retículo 2D donde los dipolos están libres de apuntar en ambas direcciones perpendicularmente al plano, lo cual resulta en una interacción a primeros vecinos repulsiva (atractiva) por dipolos alineados (anti-alineados). Encontramos regiones de parámetros donde el estado fundamental es ferromagnético u anti-ferromagnético, y encontramos pruebas de la existencia de la fase cuántica Counterflow Super Solid (CSS).Las nuestras predicciones tienen directas consecuencias experimentales, y esperamos que vengan pronto controladas en experimentos con gases dipolares atómicos y moleculares ultra-fríos. / This thesis is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules, cooled below the quantum degeneracy temperature, typically in the nK range. In such conditions, in a three-dimensional (3D) harmonic trap, weakly interacting bosons condense and form a Bose-Einstein Condensate (BEC). When a BEC is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur.These systems realize then Hubbard-type models and can be brought to a strongly correlated regime. In 1989, M. Fisher et. al. predicted that the homogeneous Bose-Hubbard model (BH) exhibits the Superfluid-Mott insulator (SF-MI) quantum phase transition. In 2002 the transition between these two phases were observed experimentally for the first time in the group of T. Esslinger and I. Bloch. The experimental realisation of a dipolar BEC of Chromium by the group of T. Pfau, and the recent progresses in trapping and cooling of dipolar molecules by the groups of D. Jin and J. Ye, have opened the path towards ultra-cold quantum gases with dominant dipole interactions. A natural evolution and present challenge, on the experimental side is then to load dipolar BECs into optical lattices and study strongly correlated ultracold dipolar lattice gases.Before this PhD work, studies of BH models with interactions extended to nearest neighbours had pointed out that novel quantum phases, like supersolid (SS) and checkerboard phases (CB) are expected. Due to the long-range character of the dipole-dipole interaction, which decays as the inverse cubic power of the distance, it is necessary to include more than one nearest neighbour to have a faithful quantitative description of dipolar systems. In fact, longer-range interactions tend to allow for and stabilize more novel phases.In this thesis we study BH models with dipolar interactions, going beyond the ground state search. We consider a two-dimensional (2D) lattice where the dipoles are polarized perpendicularly to the 2D plane, resulting in an isotropic repulsive interaction. We use the mean-field approximations and a Gutzwiller ansatz which are quite accurate and suitable to describe this system. We find that dipolar bosonic gas in 2D exhibits a multitude of insulating metastable states, often competing with the ground state, similarly as in a disordered system. We study in detail the fate of these metastable states: how can they be prepared on demand, how they can be detected, what is their lifetime due to tunnelling, and what is their role in various cooling schemes. Moreover, we find that the ground state is characterized by insulating checkerboard-like states with fractional filling factors v(average number of particles per site) that depend on the cut-off used for the interaction range. We confirm this prediction by studying the same system with Quantum Monte Carlo methods (the worm algorithm). In this case no cut-off is used, and we find evidence for a Devil's staircase in the ground state, i.e. where insulating phases appear at all rational of the underlying lattice. We also find regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies.In this work, we also investigate how the previous scenario changes in 3D. We focus on the simplest 3D lattice composed of two 2D layers in which the dipoles are polarized perpendicularly to the planes; the dipolar interaction is then repulsive for particles laying on the same plane, while it is attractive for particles at the same lattice site on different layers. Instead we consider inter-layer tunnelling to be suppressed, which makes the system analogous to a bosonic mixture in a 2D lattice. Our calculations show that particles pair into composites, and demonstrate the existence of the novel Pair Super Solid (PSS) quantum phase.Currently we are studying a 2D lattice where the dipoles are free to point in both directions perpendicularly to the plane, which results in a nearest neighbour repulsive (attractive) interaction for aligned (antialigned) dipoles. We find regions of parameters where the ground state is ferromagnetic or antiferromagnetic, and find evidences for the existence of a Counterflow Super Solid (CSS) quantum phase.Our predictions have direct experimental consequences, and we hope that they will be soon checked in experiments with ultracold dipolar atomic and molecular gases.

We examine a phase transition in a model of random spatial permutations which originates in a study of the interacting Bose gas. Permutations are weighted according to point positions; the low-temperature onset of the appearance of arbitrarily long cycles is connected to the phase transition of Bose-Einstein condensates. In our simplified model, point positions are held fixed on the fully occupied cubic lattice and interactions are expressed as Ewens-type weights on cycle lengths of permutations. The critical temperature of the transition to long cycles depends on an interaction-strength parameter α. For weak interactions, the shift in critical temperature is expected to be linear in α with constant of linearity c. Using Markov chain Monte Carlo methods and finite-size scaling, we find c = 0.618 ± 0.086. This finding matches a similar analytical result of Ueltschi and Betz. We also examine the mean longest cycle length as a fraction of the number of sites in long cycles, recovering an earlier result of Shepp and Lloyd for non-spatial permutations. The plan of this paper is as follows. We begin with a non-technical discussion of the historical context of the project, along with a mention of alternative approaches. Relevant previous works are cited, thus annotating the bibliography. The random-cycle approach to the BEC problem requires a model of spatial permutations. This model it is of its own probabilistic interest; it is developed mathematically, without reference to the Bose gas. Our Markov-chain Monte Carlo algorithms for sampling from the random-cycle distribution - the swap-only, swap-and-reverse, band-update, and worm algorithms - are presented, compared, and contrasted. Finite-size scaling techniques are used to obtain information about infinite-volume quantities from finite-volume computational data.

The Hartree-Fock-Bogoliubov theory of homogeneous boson systems at finite temperatures is rederived using, a free energy variational principle. It is shown that a t-matrix naturally emerges in the theory. Phenomenological modifications are made (1) to remove the energy gap at zero momentum, and (2) to eliminate the Hartree-Fock-like terms, which dress the kinetic energy of the particle. A numerical calculation of the energy spectrum is made over a temperature range of 0.00 to 3.14 K using the Morse dipole-dipole-2 potential and the Frost-Musulin potential. The energy spectrum of the elementary excitations is calculated self-consistently. It has a phonon behavior at low momentum and a roton behavior at higher momentum, so it is in qualitative agreement with the observed energy spectrum of liquid He II. However, the temperature dependence of the spectrum is incorrectly given. At the observed density of 0.0219 atoms A-3, the depletion of the zero-momentum state at zero temperature is 40.5% for the Morse dipole-dipole-2potential, and 43.2% for the Frost- Musulin potential. The depletion increases gradually until at 3.14 K the zero momentum density becomes zero discontinuously, which indicates a transition to the ideal Bose gas.

Ce travail de thèse est consacrée à l'étude des interractions de gaz de Bose de polaritons avec leurs environnements dans le but de déterminer l'impact de la densité, de la dimmensinalité du confinement, du potentiel ressentis par le gaz et du bain de phonons sur les propriétés du gaz de Bose.Le premier chapitre présente un condensat de polaritons unidimensionel au sein de microfils d'oxyde de zinc qui présente d'une nature quasi excitonique.En déterminant les propriétés de corrélation spatiale du gaz et en utilisant un modèle champ moyen nous déterminons l'influence combinée de la nature quasi-excitonique, du potentiel confinant et de la densité sur les propriétés de cohérence du gaz. La fin du chapitre décrit une application de ces polaritons très excitoniques à une nouvelle technique d'imagerie de Sub-longueur d'onde basée sur le concept lentilles solides à immersion.Dans la deuxième partie, nous abordons les interactions du champ de polaritons avec une caractéristique intrinsèque de l'environnement à l'état solide : les excitations thermiques du réseau appelées phonons.Dans cette partie, nous utilisons la spectroscopie Raman résolue en angle pour étudier la Fluorescence Anti-Stokes qui consiste en l'absorption d'un phonon par un état excité pour refroidir la microcavité étudiée.L'étude réalisée a exploité la fluorescence anti Stokes de polaritons en exploitant respectivement leur très courte durée de vie et leur très faible masse pour accéder à une dynamique de refroidissement extrêmement rapide rapide et une gamme d'énergie allant de 150K à 4K. / This work is devoted to the study of the interaction of a Bose gas of polariton with its environment it aims to determine the impact of the gas density, the dimensionality of the confinement, the experienced potential and the surrounding phonon bath on the polariton Bose gas characteristics.In the first chapter, we study a one dimensional polariton condensate in Zinc Oxide microwires that features a quasi excitonic nature.By determining the spatial correlation properties of the gas, and using a mean field driven dissipative model developed by our colleagues of the Laboratoire de Physique et de Mod'elisation des Milieux Condens'es we were able to determine the influence of the combined quasi excitonic nature, disordered one dimensional confining potential and density on the coherence properties of the gas. The end of the chapter describes an application of those highly excitonic polaritons to a novel subwavelength imaging technic based on the Solid Immersion Lens concept.In the second part we address the interactions of the polariton field with an intrinsic characteristic of the solid state environment : the thermal excitations of the lattice called phonons.In this part, we use angle resolved Raman spectroscopy to study Anti-Stokes Fluorescence (ASF) which consists in the the absorption of a phonon by an excited states to cool down the studied microcavity. The state of the art technics are using ion doped materials or bare excitons in semiconductors as emitters.The study performed exploited the polaritons as emitters, using respectively their very short lifetime and their very light mass to access a faster cooling dynamics and an energy range going from 150K to 4K.

In this thesis, the properties of the Bose-Einstein condensation (BEC) in low dimensions are reviewed. Three dimensional weakly interacting Bose systems are examined by the variational method. The effects of both the attractive and the repulsive interatomic forces are studied. Thomas-Fermi approximation is applied to find the ground state energy and the chemical potential. The occurrence of the BEC in low dimensional systems, is studied for ideal gases confined by both harmonic and power-law potentials. The properties of BEC in highly anisotropic trap are investigated and the conditions for reduced dimensionality are derived.

The quantum dynamics and grand canonical thermodynamics of many-mode (one-, two-, and three-dimensional) interacting Bose gases are simulated from first principles. The model uses a lattice Hamiltonian based on a continuum second-quantized model with two-particle interactions, external potential, and interactions with an environment, with no further approximations. The interparticle potential can be either an (effective) delta function as in Bose-Hubbard models, or extended with a shape resolved by the lattice. Simulations are of a set of stochastic equations that in the limit of many realizations correspond exactly to the full quantum evolution of the many-body systems. These equations describe the evolution of samples of the gauge P distribution of the quantum state, details of which are developed. Conditions under which general quantum phase-space representations can be used to derive stochastic simulation methods are investigated in detail, given the criteria: 1) The simulation corresponds exactly to quantum mechanics in the limit of many trajectories. 2) The number of equations scales linearly with system size, to allow the possibility of efficient first-principles quantum mesoscopic simulations. 3) All observables can be calculated from one simulation. 4) Each stochastic realization is independent to allow straightforward use of parallel algorithms. Special emphasis is placed on allowing for simulation of open systems. In contrast to typical Monte Carlo techniques based on path integrals, the phase-space representation approach can also be used for dynamical calculations. Two major (and related) known technical stumbling blocks with such stochastic simulations are instabilities in the stochastic equations, and pathological trajectory distributions as the boundaries of phase space are approached. These can (and often do) lead to systematic biases in the calculated observables. The nature of these problems are investigated in detail. Many phase-space distributions have, however, more phase-space freedoms than the minimum required for exact correspondence to quantum mechanics, and these freedoms can in many cases be exploited to overcome the instability and boundary term problems, recovering an unbiased simulation. The stochastic gauge technique, which achieves this in a systematic way, is derived and heuristic guidelines for its use are developed. The gauge P representation is an extension of the positive P distribution, which uses coherent basis states, but allows a variety of useful stochastic gauges that are used to overcome the stability problems. Its properties are investigated, and the resulting equations to be simulated for the open interacting Bose gas system are derived. The dynamics of the following many-mode systems are simulated as examples: 1) Uniform one-dimensional and two-dimensional Bose gases after the rapid appearance of significant two-body collisions (e.g. after entering a Feshbach resonance). 2) Trapped bosons, where the size of the trap is of the same order as the range of the interparticle potential. 3) Stimulated Bose enhancement of scattered atom modes during the collision of two Bose-Einstein condensates. The grand canonical thermodynamics of uniform one-dimensional Bose gases is also calculated for a variety of temperatures and collision strengths. Observables calculated include first to third order spatial correlation functions (including at finite interparticle separation) and momentum distributions. The predicted phenomena are discussed. Improvements over the positive P distribution and other methods are discussed, and simulation times are analyzed for Bose-Hubbard lattice models from a general perspective. To understand the behavior of the equations, and subsequently optimize the gauges for the interacting Bose gas, single- and coupled two-mode dynamical and thermodynamical models of interacting Bose gases are investigated in detail. Directions in which future progress can be expected are considered. Lastly, safeguards are necessary to avoid biased averages when exponentials of Gaussian-like trajectory distributions are used (as here), and these are investigated.

The quantum dynamics and grand canonical thermodynamics of many-mode (one-, two-, and three-dimensional) interacting Bose gases are simulated from first principles. The model uses a lattice Hamiltonian based on a continuum second-quantized model with two-particle interactions, external potential, and interactions with an environment, with no further approximations. The interparticle potential can be either an (effective) delta function as in Bose-Hubbard models, or extended with a shape resolved by the lattice. Simulations are of a set of stochastic equations that in the limit of many realizations correspond exactly to the full quantum evolution of the many-body systems. These equations describe the evolution of samples of the gauge P distribution of the quantum state, details of which are developed. Conditions under which general quantum phase-space representations can be used to derive stochastic simulation methods are investigated in detail, given the criteria: 1) The simulation corresponds exactly to quantum mechanics in the limit of many trajectories. 2) The number of equations scales linearly with system size, to allow the possibility of efficient first-principles quantum mesoscopic simulations. 3) All observables can be calculated from one simulation. 4) Each stochastic realization is independent to allow straightforward use of parallel algorithms. Special emphasis is placed on allowing for simulation of open systems. In contrast to typical Monte Carlo techniques based on path integrals, the phase-space representation approach can also be used for dynamical calculations. Two major (and related) known technical stumbling blocks with such stochastic simulations are instabilities in the stochastic equations, and pathological trajectory distributions as the boundaries of phase space are approached. These can (and often do) lead to systematic biases in the calculated observables. The nature of these problems are investigated in detail. Many phase-space distributions have, however, more phase-space freedoms than the minimum required for exact correspondence to quantum mechanics, and these freedoms can in many cases be exploited to overcome the instability and boundary term problems, recovering an unbiased simulation. The stochastic gauge technique, which achieves this in a systematic way, is derived and heuristic guidelines for its use are developed. The gauge P representation is an extension of the positive P distribution, which uses coherent basis states, but allows a variety of useful stochastic gauges that are used to overcome the stability problems. Its properties are investigated, and the resulting equations to be simulated for the open interacting Bose gas system are derived. The dynamics of the following many-mode systems are simulated as examples: 1) Uniform one-dimensional and two-dimensional Bose gases after the rapid appearance of significant two-body collisions (e.g. after entering a Feshbach resonance). 2) Trapped bosons, where the size of the trap is of the same order as the range of the interparticle potential. 3) Stimulated Bose enhancement of scattered atom modes during the collision of two Bose-Einstein condensates. The grand canonical thermodynamics of uniform one-dimensional Bose gases is also calculated for a variety of temperatures and collision strengths. Observables calculated include first to third order spatial correlation functions (including at finite interparticle separation) and momentum distributions. The predicted phenomena are discussed. Improvements over the positive P distribution and other methods are discussed, and simulation times are analyzed for Bose-Hubbard lattice models from a general perspective. To understand the behavior of the equations, and subsequently optimize the gauges for the interacting Bose gas, single- and coupled two-mode dynamical and thermodynamical models of interacting Bose gases are investigated in detail. Directions in which future progress can be expected are considered. Lastly, safeguards are necessary to avoid biased averages when exponentials of Gaussian-like trajectory distributions are used (as here), and these are investigated.

Ces dernières années d'importantes avancées techniques dans la manipulation des gaz atomiques ultrafroids ont ouvert la voie à la réalisation de fluides quantiques mésoscopiques de basse dimension. L'objet de cette thèse est l'étude théorique de certains systèmes mésoscopiques réalisables avec un gaz de Bose unidimensionel. Ces systèmes présentent des phénomènes quantiques intéressants, et sont potentiellement utiles en vue d'applications technologiques. Nous étudions le phénomène des courants permanents induits dans un gaz confiné sur un anneau par la rotation d'une barrière de potentiel, nous examinons la faisabilité d'un qubit fondé sur la superposition d'états de courant dans un réseau en forme d'anneau traversé par un champ de jauge et contenant un 'weak-link', ainsi que l'excitation dipolaire du gaz dans un 'split-trap' induit par le déplacement hors équilibre du potentiel externe. Dans tous ces cas, nous combinons diverses approches analytiques et numériques, qui permettent de couvrir l'ensemble des régimes d'interactions. Nous mettons en lumière un régime jusque-là inconnu, d'écrantage maximal des barrières de potentiel par le fluide, dû à une competition entre les effets des interactions et des fluctuations quantiques. Ces résultats ont des conséquences significatives sur le comportement de tels systèmes et, de ce fait, sont importants pour les réalisations en cours et à venir de dispositifs à gaz d'atomes ultrafroids. / Thanks to the experimental breakthrough of the last years in the manipulation of ultra cold atomic gases, it has become possible to realize low-dimensional and mesoscopic quantum fluids. The object of this thesis is the theoretical investigation of a few mesoscopic systems that can be realized with a one-dimensional Bose gas. These systems exhibit interesting quantum phenomena, and are potentially relevant for technological applications. We study the phenomenon of persistent currents induced by stirring the gas confined on a ring with a potential barrier, we examine the feasibility of a qubit based on the superposition of current states in a ring lattice threaded by a gauge field in the presence of a weak-link, and we investigate the dipole excitation of the gas in a split trap induced by an out-of-equilibrium displacement of the external potential. In all these cases, we apply a combination of analytical and numerical approaches that allow to cover all the interaction regimes. As a recurring theme, we disclose a so-far unknown regime of maximal screening of the barrier potential by the fluid, arising from the interplay of effects due to interactions and quantum fluctuations. These results have significant consequences for the behaviour of such systems and are important for the ongoing and future realization of ultracold atomic gases devices.

No description available.