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Les microcavités à semiconducteurs apparaissent aujourd’hui comme une plateforme particulièrement propice à l’étude des fluides quantiques en interactions. Dans ces cavités, la lumière et les excitations électroniques sont confinées dans de petits volumes et leur couplage est rendu si fort que les propriétés optiques sont gouvernées par des quasi-particules hybrides lumière-matière appelées polaritons de cavité. Ces quasi-particules se propagent comme des photons, mais interagissent avec leur environnement via leur partie matière. Elles peuvent occuper massivement un même état quantique et se comporter comme une onde macroscopique cohérente et non-linéaire. On parle alors de fluide quantique de lumière. Dans cette thèse, nous étudions la dynamique de fluides quantiques de polaritons dans différentes microstructures unidimensionnelles. La technologie de gravure de microcavités planaires, développée au C2N, permet de réaliser une ingénierie complète du potentiel dans lequel nous générons ces fluides de polaritons et d’implémenter des géométries complexes. Dans une première partie, nous avons étudié les propriétés de localisation des états propres de réseaux synthétiques quasi-périodes. L’exploration théorique du diagramme de phase de localisation des modes propres a dévoilé une nouvelle transition de type délocalisation-localisation lors d’une déformation originale d’un quasi-cristal, transition que nous avons pu observer expérimentalement. Une deuxième partie de la thèse est consacrée à l’étude de la dynamique non-linéaire de deux fluides contra-propageant dans un canal unidimensionnel. La compétition entre énergie cinétique et énergie d’interactions conduit alors à l’apparition de solitons sombres, dont le nombre discret et la position peuvent être contrôlés optiquement. Nous avons mis en évidence une bistabilité contrôlée par la différence de phase imprimée sur les deux fluides. La dernière partie du travail concerne l’étude des non-linéarités pour un fluide de polaritons occupant une bande plate. L’énergie cinétique du fluide y est nulle, si bien que sa propagation est gelée. Nous observons alors la formation de domaines non-linéaires de taille quantifiée. Ce travail ouvre des perspectives prometteuses, tout particulièrement pour l’exploration de phases topologiques de bosons en interactions. De plus, augmenter les interactions permettrait d’utiliser notre plate-forme comme un simulateur quantique. / Semiconductor microcavities have emerged as a powerful platform for the study of interacting quantum fluids. In these cavities, light and electronic excitations are confined in small volumes, and their coupling is so strongly enhanced that optical properties are governed by hybrid light-matter quasiparticles, known as cavity polaritons. These quasiparticles propagate like photons and interact with their environment via their matter part. They can macroscopically occupy a single quantum state and then behave as an extended coherent nonlinear wave, i.e. as a quantum fluid of light. In this thesis, we study the nonlinear dynamics of polariton quantum fluids in various one-dimensional microstructures. The possibility to etch microstructures out of planar cavities, a technology developed at C2N, allows full engineering of the potential landscape for the polariton fluid, and implementing complex geometries. In a first part, we have studied the localization properties of the eigenstates in synthetic quasiperiodic lattices. Theoretical exploration of the localization phase diagram revealed a novel delocalization-localization transition in an original deformation of a quasicrystal and we have experimentally evidenced this transition. A second part of the thesis is dedicated to the study of the nonlinear dynamics of two counterpropagating polariton fluids in a one-dimensional channel. The interplay between kinetic and interaction energy is responsible for the formation of dark solitons, whose number and position can be controlled by optical means. We have evidenced a bistable behaviour controlled by the phase twist imprinted on the two fluids. The last part of this work addresses the study of nonlinearities for a fluid injected in a flat band. Therein, the kinetic energy of the fluid is quenched, so that propagation is frozen. We then observe the formation of nonlinear domains with quantized size. This work opens us exciting perspectives, specifically towards the exploration of topological phases of interacting bosons. Enhancing interactions would also allow using our platform for quantum simulation.

In this thesis we demonstrate the power of the Gross-Pitaevskii and the time-dependent Ginzburg-Landau equations by numerically solving them for various fundamental problems related to superfluidity and superconductivity. We start by studying the motion of a massive object through a quantum fluid modelled by the Gross-Pitaevskii equation. Below a critical velocity, the object does not exchange momentum or energy with the fluid. This is a manifestation of its superfluid nature. We discuss the effect of applying a constant force to the object and show that for small forces a vortex ring is created to which the object becomes attached. For a larger force the object detaches from the vortex ring and we observe periodic shedding of rings. All energy transfered to the system is contained within the vortex rings and the drag force on the object is due to the recoil of the vortex emission. If we exceed the speed of sound, there is an additional contribution to the drag from sound emission. To make a link to superconductivity, we then discuss vortex states in a rotating system. In the ground state, regular arrays of vortices are observed which, for systems containing many vortices, mimic solid-body rotation. In the second part of the thesis, we initially review solutions to the Ginzburg-Landau equations in an applied magnetic field. For superconducting disks we observe vortex arrays similar to those in rotating superfluids. Finally, we study an electrical current flow along a superconducting wire subject to an external magnetic field. We observe the motion of flux lines, and hence dissipation, due to the Lorentz force. We measure the V – I curve which is analogous to the drag force in a superfluid. With the introduction of impurities, flux lines become pinned which gives rise to an increased critical current.

L’étude des corrélations dans les fluides quantiques est abordée dans cette thèse par le biais de mesures neutroniques de leurs excitations élémentaires. Nos recherches sont motivées par les théories récentes qui permettent désormais de décrire ces excitations jusqu’à des vecteurs d’onde atomiques. Par ailleurs, les nouvelles performances du spectromètre temps de vol IN5 de l’ILL offrent la possibilité de réaliser des mesures précises dans une large gamme d’énergie et de vecteur d’onde. Dans le cas de l’4He, l’isotope bosonique, les mesures de diffusion inélastique ont été réalisées à très basse température, de la pression de vapeur saturante jusqu’à la solidification. Les relations de dispersion des excitations élémentaires correspondantes ont été obtenues avec une grande précision. A des énergies supérieures, nous avons observé dans le facteur de structure dynamique une réponse de multi-excitations très fortement structurée, caractérisée par des seuils correspondant à l’interaction entre les modes élémentaires. En particulier, nous avons observé un phonon “fantôme” associé à l’interaction phonon-phonon. Nos mesures dans l’4He superfluide confirment qualititativement les prédictions de la théorie dynamique à N-corps (2015) et même quantitativement jusqu’à une énergie de 2 meV. Les études effectuées dans le cas de l’3He ont été menées jusqu’à des températures bien inférieures à 100 mK dans une cellule spécialement conçue. Les mesures inélastiques sur cet isotope fermionique ont permis de déterminer avec une grande précision les modes collectifs, zéro-son et paramagnon, ainsi que la bande particule-trou. Couvrant une région encore jamais explorée, elles nous ont permis de confirmer la présence prévue par la théorie d’une excitation de type rotonique dans l’3He liquide massif. Ce mode reste ici confiné dans la bande particule-trou, contrairement au cas de l’3He bidimensionnel. L’ensemble de nos mesures apporte une vision complète du facteur de structure dynamique de ces systèmes modèles pour les bosons et les fermions en interaction, depuis le régime de quasi-particules de Landau et des multi-excitations, jusqu’à la limite des hautes énergies où la dynamique rejoint celle des particules indépendantes. / The effect of correlations in quantum fluids is investigated in the present work by inelastic neutron scattering measurements of their elementary excitations.Recent theories provide us with a detailed description of the dynamics up to atomic wave vectors. In addition, the recent improvement of the time-of-flight IN5 spectrometer at the ILL opens new experimental possibilities in terms of neutron flux and resolution, as well as accessible energy and wave vector ranges. In the case of 4He, the bosonic isotope, the neutron measurements have been performed at very low temperatures, from the saturated vapor pressure up to the melting curve. The dispersion relations of the corresponding elementary excitations have been accurately determined. At higher energies, we observe in the dynamic structure factor a highly structured multi-excitation response, characterized by sharp thresholds due to the coupling of elementary excitations. In particular, we observe a ghost phonon related to phonon-phonon coupling. Our measurements on superfluid 4He confirm the predictions of the dynamic many body theory (2015), the agreement being quantitative up to an energy of 2 meV. The investigations on normal liquid 3He were carried out at temperatures well below 100 mK in a cell specially designed for this purpose. Ourmeasurements on this fermionic isotope yield a high precision determination of the collective modes, zero-sound and paramagnon, as well as the particle-hole band. Since they also cover an unexplored region, we were able to confirm the theoretical prediction of a roton-like excitation in bulk liquid 3He. This mode remains within the particle-hole band, contrarily to the case of two-dimensional 3He. A broad vision of the dynamics of interacting Bose and Fermi systems, going from the Landau quasi-particles and multi-excitations regimes up to the high-energy limit, where the independent particle dynamics is recovered, emerges from our work.

L'4He et l'3He sont des systèmes modèles pour comprendre les propriétés quantiques de la matière fortement corrélée. C'est pour cette raison que plusieurs études ont été consacrées à la compréhension de leur dynamique. A basses températures où les effets quantiques jouent un rôle essentiel, les excitations élémentaires dans l'4He sont décrites par un mode collectif d'excitations: phonon-roton. Par contre pour un système d'3He la description est plus complexe, le spectre d'excitation a deux composantes: un mode collectif (zéro-son) et un continuum d'excitations incohérentes de type particule-trou. Les deux sont bien décrites par la théorie de Landau des liquides de Fermi qui trouve sa validité pour des petits vecteurs d'onde. Jusqu'à présent, on supposait que la dynamique dans les liquides de Fermi à vecteurs d'onde élevés était essentiellement incohérente. Cette thèse porte sur l'exploration, par diffusion inélastique de neutrons, des excitations collectives dans l'3He liquide 2D adsorbé sur un substrat de graphite. Un tel travail expérimental requiert trois ingrédients essentiels : un réfrigérateur à dilution afin de travailler à basses températures, un spectromètre temps de vol afin de mesurer le facteur de structure dynamique du système et un substrat solide (graphite exfolié ZYX) pour la préparation de films d'3He-2D par physisorption. Nos expériences sur ces films d'3He déposés en deuxième couche sur de l'4He solide adsorbé sur le graphite nous ont permis de faire les observations suivantes : à petit vecteur d'onde, le zéro-son est plus proche de la bande particule-trou que celui observé dans le cas de l'3He massif, tandis qu'à fort vecteur d'onde le mode collectif entre dans le continuum et réapparait de l'autre côté. Cette nouvelle branche, observée pour la première fois, est aujourd'hui décrite par la théorie dynamique à N-corps développée par nos collaborateurs de l'université Johannes Kepler de Linz, Autriche. Au cours de ce travail de thèse plusieurs techniques expérimentales ont été développées, en particulier, un réfrigérateur à dilution sans fluide cryogénique robuste adapté à des expériences de diffusion neutronique. Son optimisation a permis de réduire le temps de refroidissement de ce type de réfrigérateurs. / 4He and 3He are model systems for understanding quantum properties of strongly interacting matter. For this reason many studies have been devoted for the understanding of their dynamics. At low temperatures at which quantum effects play an essential role, the elementary excitations in 4He are described by a phonon-roton collective mode. For 3He, the physical description is more complicated, the spectrum has two components: collective excitations (zero-sound) and incoherent particle-hole excitations. Both are described by Landau's theory of Fermi liquids which is valid at low wave vectors. So far, it was thus believed that the dynamics at high wave vectors is essentially incoherent. This thesis is mainly concerned by exploring the collective excitations of a two dimensional 3He film adsorbed on graphite, using inelastic neutron scattering. Such an experiment has three main requirements: a dilution refrigerator in order to work at low temperatures, a time of flight spectrometer for measuring the dynamical structure factor of 3He and a solid substrate (exfoliated graphite ZYX) to obtain a two dimensional film by physical adsorption. Our investigations of the dynamics in two-dimensional 3He adsorbed on graphite preplated with 4He films have revealed important features: At low wave-vectors, the zero-sound mode is considerably depressed compared to bulk 3He. At higher wave vectors, the collective excitations branch enters the particle-hole continuum, and reappears at the lower energy branch of the continuum. This new branch, observed for the first time, is described by the dynamic many-body theory developed by our collaborators from Johannes Kepler University, Linz, Austria. During this work several low temperature techniques have been developed, in particular a robust, cryogen-free dilution refrigerator adapted to the demanding conditions of a neutron scattering experiments. Due to its efficient design, the cooling time has been considerably reduced compared to that of refrigerators of the same type developed in the past.

Abstract The problem of describing a system of many interacting particles is one of the most fundamental questions in physics. One of the central theories used in condensed matter physics to address the problem is the Fermi liquid theory developed by L. D. Landau in the 1956. The theory describes interacting fermions, and can be used to explain transport phenomena of electrons in metals and dynamics of helium three. Even when the theory is not directly applicable, it forms a basis against which other, more sophisticated theories can be compared. this thesis the Fermi liquid theory is applied to 3He-4He-mixtures at temperatures where the bosonic 4He part is superfluid, and the mechanical properties of the system are largely determined by the 3He component, treated as a degenerate normal Fermi liquid. The dynamics of strongly interacting liquid 3He can be described as a collection of quasiparticles, elementary excitations of the system, which interact only weakly. In 3He-4He mixtures the interactions can be continuously tuned by changing the temperature and the concentration of the mixture. The scattering time of quasiparticles depends on temperature, and thus the transition from the hydrodynamic limit of continuous collisions at higher temperatures to the collisionless ballistic limit at low temperatures can be studied. This gives invaluable information on the role of the interactions in the dynamics of the system. In this work, by using the Fermi liquid theory and Boltzmann transport equation, the dynamics of helium mixture disturbed by a mechanical oscillator is described in the full temperature range. The solution necessarily is numeric, but new analytical results in the low temperature limit are obtained as well. The numerical approach enables one to study various boundary conditions thoroughly, and allows application of the theory to a specic geometry. It is shown that in order to explain the experimental observations, it is necessary to take into account the reflection of quasiparticles from the walls of the container. For suitable choice of oscillator frequency and container size, second sound resonances are observed at higher temperatures, while in the ballistic limit quasiparticle interference can be seen. The numerical results are in quantitative agreement with experiments, thus attesting the accuracy of Fermi liquid theory. In particular, the previously observed decrease of inertia of a mechanical oscillator immersed in helium at low temperatures is reproduced in the calculations, and is explained by elasticity of the fluid due to Fermi liquid interactions.

Condensed matter systems undergoing phase transitions rarely allow exact solutions. The presence of disorder renders the situation  even worse but collective Monte Carlo methods and parallel algorithms allow numerical descriptions. This thesis considers classical phase transitions in disordered spin systems in general and in effective models of superfluids with disorder and novel interactions in particular. Quantum phase transitions are considered via a quantum to classical mapping. Central questions are if the presence of defects changes universal properties and what qualitative implications follow for experiments. Common to the cases considered is that the disorder maps out correlated structures. All results are obtained using large-scale Monte Carlo simulations of effective models capturing the relevant degrees of freedom at the transition. Considering a model system for superflow aided by a defect network, we find that the onset properties are significantly altered compared to the $\lambda$-transition in $^{4}$He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario. For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent $z=1.8 \pm 0.05$ contradicting the long standing result $z=d$. Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role. Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations. / <p>QC 20150306</p>

Path integral Monte Carlo (PIMC) is a method suitable for quantum liquid simulations at finite temperature. We present in this thesis a study of PIMC dealing with the theory and algorithms related to it, and then two applications of PIMC to current research problems of quantum fluids in the Bolzmann regime. The first part encompasses a study of the different ingredients of a PIMC code: action, sampling and physical property estimators. Particular attention has been paid to Li-Broughton's higher order approximation to the action. Regarding sampling, several collective movement methods have been derived, including the bisection algorithm, that has been thoroughly tested. We also include a study of estimators for different physical properties, such as, the energy (through the thermodynamic and virial estimators), the pair distribution function, the structure factor, and the momentum distribution. In relation to the momentum distribution, we have developed a novel algorithm for its estimation, the trail method. It surmounts some of the problems exposed by previous approaches, such as the open chain method or McMillan's algorithm.The Richardson extrapolation used within PIMC simulations, is another contribution of this thesis. Up until now, this extrapolation has not been used in this context. We present studies of the energy dependence on the number of "beads", along with the betterment provide by the Richardson extrapolation. Inasmuch as our goal is to perform research of quantum liquids at finite temperature, we have produced a library of codes, written from scratch, that implement most of the features theoretically developed. The most elaborated parts of these codes are included in some of the appendixes.The second part shows two different applications of the algorithms coded. We present results of a PIMC calculation of the momentum distribution of Ne and normal 4He at low temperatures. In the range of temperatures analysed, exchanges can be disregarded and both systems are considered Boltzmann quantum liquids. Their quantum character is well reflected in their momentum distributions witch show clear departures from the classical limit. The PIMC momentum distributions which show clear departures from the classical limit. The PIMC momentum distributions are sampled using the trail method. Kinetic energies of both systems, as a function of temperature and at a fixed density, are also reported. Finally, the solid-liquid neon phase transition along the 35 K isotherm has been characterized.While thermodynamic properties of the solid phase are well known the behaviour of some properties, such as the energy or the dessity, during the trasition presen6 some uncertainties For example, experimental data for the place diagram, which determines solid and liquid boundaries, present sizeable differences. The temperature chosen is high enough so that Bose or Fermi statistics corrections are small, although the system is strongly quantum mechanical. The results obtained show a discontinuity in the kinetic energy during the transition.