No description available.

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 advancement in the eld of cold-atoms has generated a lot of interest in the condensed matter community. Cold-atom experiments can simulate clean, disor-der/impurity free systems very easily. In these systems, we have a control over various parameters like tuning the interaction between particles by the Feshbach resonance, tuning the hopping between lattice sites by laser intensity and so on. As a result, these systems can be used to mimic various theoretical models, which was hindered because of various experimental limitations. Thus, we have an ex-perimental tool in which we can start with a simple theoretical model and later tune the model experimentally and theoretically to simulate the real materials. This will be helpful in studying the physics of the real materials as we can control interactions as well as the impurities can also be taken care of. But the advance-ment in the eld of cold atoms has seen a roadblock for the fermions in optical lattices. The super uid and anti-ferromagnetic phases has not been achieved for fermions in optical lattices due to the \cooling problem" (entropy issues). In this thesis, we have addressed the issue of the \cooling problem" for fermions in optical lattice systems and studied the system with determinant quantum Monte Carlo technique. We start by giving a general idea of cold-atoms and optical lat-tice potentials, and a brief review of the experimental work going on in the cold-atomic systems. Experimental limitations like \fermionic cooling problem" have been discussed in some detail. Then we proposed a bilayer band-insulator model to circumvent the \entropy problem" and simultaneously increasing the transi-tion temperature for fermions in optical lattices. We have studied the attractive Hubbard model, which is the minimal model for fermions in optical lattices. The techniques that we have used to study the model are mean- eld theory, Gaussian uctuation theory and determinant quantum Monte Carlo numerical technique. . Chapter-1 : provides a general introduction to the ultra-cold atoms, optical lattice and Feshbach resonance. In this chapter we have discussed about cold-atom experiments in optical lattice systems. Here, we have brie y discussed the control over various parameters in the experiments. The goal of these experiments is to realize or mimic many many-body Hamiltonians in experiments, which until now was just a theoretical tool to describe various many-body physics. In the end we give a brief idea for introducing disorder in the cold-atom experiments discuss the limitations of these experiments in realizing the \interesting" super uid and anti-ferromagnetic phases of fermionic Hubbard model in optical lattices. Chapter-2 : gives a brief idea of \Determinant Quantum Monte-Carlo" (DQM C) technique that has been used to study these systems. In this chapter we will discuss the DQM C algorithm and the observables that can be calculated. We will discuss certain limitation of the DQM C algorithm like numerical instability and sign problem. We will brie y discuss how sign problem doesn't occur in the model we studied. Chapter-3 : discusses the way by which we can bypass the \cooling problem" (high entropy state) to get a fermionic super uid state in the cold atom experi-ments. In this chapter we propose a model whose idea hinges on a low-entropy band-insulator state, which can be tuned to super uid state by tuning the on-site attractive interaction by Feshbach resonance. We show through Gaussian uctua-tion theory that the critical temperature achieved is much higher in our model as compared to the single-band Hubbard model. Through detailed variational Monte Carlo calculations, we have shown that the super uid state is indeed the most stable ground state and there is no other competing order. In the end we give a proposal for its realization in the ultra-cold atom optical lattice systems. Chapter-4 : discusses the DQM C study of the model proposed in chapter- 3. Here we have studied the various single-particle properties like momentum distribution, double occupancies which can be easily measured in cold-atom ex-periments. We also studied the pair-pair and the density-density correlations in detail through DQM C algorithm and mapped out the full T U phase diagram. We show that the proposed model doesn't favor the charge density wave for the interaction strengths we are interested in. Chapter-5 : gives a brief idea of the e ect of adding an on-site random disorder in our proposed bilayer-Hubbard model. We study the e ect of random disorder on various single-particle properties which can be easily veri ed in cold-atom ex-periments. We studied the suppression of the pair-pair correlations as we increase the disorder strength in our proposed model. We nd that the critical value of the interaction doesn't change in the weak-disorder limit. We estimated the critical disorder strength needed to destroy the super uid state and argued that the tran-sition from the super uid to Bose-glass phase in presence of disorder lies in the universality class of (d + 1) XY model. In the end, we give a schematic U V phase diagram for our system. Chapter-6 : We studied the bilayer attractive Hubbard model in different lattice geometry, the bilayer honeycomb lattice, both in presence and in absence of the on-site random disorder. We discussed how the pair-pair and density-density cor-relations behave in the presence and absence of disorder. Through the finite-size scaling analysis we see the co-existence of the super fluid and the charge density wave order at half- lling. An in nitesimal disorder destroys the CDW order com-pletely while the super uid phase found to be robust against weak-disorder. We estimated the critical interaction strength, the critical temperature and the critical disorder strength through nite-size scaling, and provide a putative phase diagram for the system considered.

Les propriétés thermiques exceptionnelles de l’hélium superfluide, ou He-II, sont mises à profit pour la réfrigération cryogénique d'installations de forte puissance, bien que les mécanismes physiques sous-jacents restent mal compris. L’He-II peut être décrit à l’échelle macroscopique comme la superposition de deux fluides en interaction : un fluide normal se comportant comme un liquide ordinaire, et un superfluide sans viscosité. En présence d’une source de chaleur, un contre-courant s’établit naturellement entre ces deux composantes. L’évacuation de la chaleur par ce contre-courant est limitée par l’apparition d’instabilités dans des conditions mal comprises ; la grande dispersion des données expérimentales ne permettant pas de discriminer les différents modèles théoriques. Cette thèse examine à l’aide de simulations numériques le rôle des conditions aux bords et du couplage mutuel entre les deux composantes de l’He-II dans le déclenchement des instabilités de contre-courant.Une approche originale de type Boltzmann sur réseau a été développée pour modéliser à l’échelle mésoscopique l'interaction entre les deux composantes de l’He-II. Un code reproduisant les écoulements de contre-courant en conduite 2d et 3d a été développé et validé. Les résultats obtenus indiquent des effets d’entrée de conduite amplifiés pour la composante superfluide, qui engendrent des pertes de charge anormalement élevées. Le mécanisme responsable de ces effets d’entrée a été étudié et il est montré qu'il peut fausser la détection du seuil de transition dans des conduites trop courtes ; ceci peut expliquer en partie la dispersion des données expérimentales.Pour illustrer la puissance de l'approche dans une géométrie complexe, le sillage d'un obstacle dans un écoulement de contre-courant a été simulé. La présence de zones de recirculation des deux côtés de l’obstacle, déjà observée expérimentalement, est retrouvée et expliquée par un mécanisme original de parois virtuelles. / The exceptional thermal properties of superfluid helium, or He-II, are exploited to the cryogenic refrigeration of high power installations, although the underlying physical mechanisms remain poorly understood. The He-II can be described macroscopically as the superposition of two fluids in interaction: a normal fluid behaves as an ordinary liquid, and a superfluid without viscosity. In the presence of a heat source, a counterflow established between these two components. The heat dissipation by this counterflow is limited by the occurrence of instabilities in misunderstood condition; the wide dispersion of experimental data does not allow to discriminate between the different theoretical models. This thesis examines using numerical simulations the role of boundary conditions and the mutual coupling between the two components of the He-II in triggering instabilities in counterflow.An innovative lattice Boltzmann type approach was developed to model the mesoscopic scale interaction between the two components of the He-II. A code reproducing counterflow in 2D and 3D conducts has been developed and validated. The results obtained indicate amplified entrance effects for superfluid component, which generate abnormally high pressure drops. The head of these entrance effects mechanism has been studied and it is shown that it can distort the detection of the transition threshold in too short pipes; This may partly explain the dispersion of experimental data.To illustrate the power of the approach in a complex geometry, the wake of an obstacle in a counterflow was simulated. The presence of recirculation areas on both sides of the obstacle, already observed experimentally, is found and explained by a new mechanism using "virtual walls".

Ce travail de thèse décrit la première observation directe de particules associées à la déplétion quantique et de premières mesures dans l’espace des impulsions d’un superfluide sur réseau. Ces observations ont été réalisées à partir d'un gaz dégénéré d'Hélium métastable sur un tout nouvel dispositif expérimental, dont la construction a été terminée au cours de cette thèse. Permise par l’Hélium métastable, notre détection électronique sensible à l’atome unique donne accès à la distribution tridimensionnelle dans l’espace des impulsions k.Nous avons d’abord développé une approche hybride pour la réalisation de condensats de Bose-Einstein, qui utilise un piège magnétique comme réservoir du piège dipolaire. Cette méthode permet la production rapide de condensats de Bose-Einstein toutes les 6 secondes sur notre expérience. Nous avons alors pu observer, pour la première fois, les particules excitées hors du condensat à cause des interactions (déplétion quantique). En particulier, nous avons observé la loi de puissance en 1/k4 dans la distribution pour de larges impulsions k, comme attendue dans la théorie de Bogoliubov. Enfin nous avons étudié les distributions de superfluide sur réseau. Il s’agit d’une première mesure de la distribution en impulsion dans un réseau comme le démontre les simulations numériques (Monte-Carlo quantique). Les effets de températures sur les distributions mesurées sont extrêmement visibles, ce qui ouvre la voie à une thermométrie des superfluides sur réseau. / In this thesis, we report the first observation of the particles associated with the quantum depletion and the first measurements of the momentum distribution of correlated superfluid lattice bosons. We performed the experiment with a degenerate metastable Helium gas with a novel experimental setup. Making possible with metastable Helium, our electronic detection allows single-atom detection in momentum space k.Firsly, we have demonstrated a new approach to Bose-Einstein condensation of metastable Helium using a hybrid trap, consisting of a magnetic quadrupole and a crossed optical dipole trap. It results in production of a condensate every 6 seconds. Then we observed the excited particles out of the condensate wavefunction due to presence of the interactions (quantum depletion). We observe atom distributions decaying at large momenta k with the 1/k4 power-law predicted by Bogoliubov theory. Furthermore we studied the three-dimensional far field distribution of correlated superfluid lattice bosons. The momentum distributions of the trapped atoms calculated with an ab-initio Monte-Carlo Worm algorithm for the experimental parameters are in excellent agreement with the measured distributions. The finite temperature effect is not negligible, paving the way for a precise thermometry.

The quantum phase transition between groundstates of a system with correlated disorder near absolute zero is studied. The computations are based on Monte Carlo methods and the worm algorithm which is an effective method to simulate basic models like the Ising and XY model by making use of global Monte Carlo moves given by modified random walks. Random quenched disorder modeled as a correlated distribution of two values of the coupling constant gives rise to an additional phase transition with a not before seen intermediate phase. / Kvantfasövergången mellan grundtillstånd av ett system med korrelerad oordning nära nolltemperaturen studeras. Beräkningarna är baserade på Monte Carlo metoder och worm algoritmen som är en effektiv metod för att simulera grundläggande modeller som Ising och XY modellen genom att använda sig av globala Monte Carlo steg som ges av modifierade slumpmässiga vandringar. Slumpmässig infrusen oordning modellerad som en korrelerad fördelning av två värden på kopplingsstyrkan ger upphov till en ny mellanliggande fas.

No description available.

Cette thèse s'intéresse aux phénomènes électrostatiques émergents dans les modèles magnétiques toroïdaux bi-dimensionnels à symétrie XY, fournissant ainsi un support pour de plus amples recherches dans le domaine de la transition de phase Berezinskii-Kosterlitz-Thouless (BKT).Dans de nombreux systèmes bi-dimensionnels, dont le modèle bi-dimensionnel XY du magnétisme, la transition BKT contrôle la dissociation thermique de paires de défauts topologiques liés. Le modèle XY est analogue au gaz de Coulomb bi-dimensionnel, à ceci près qu'il peut être simulé sans avoir à modéliser les interactions à longue distance du système Coulombien. Cette thèse élucide ce paradoxe en démontrant que l'approximation de Villain appliquée au modèle XY est strictement équivalente au modèle électrostatique de Maggs-Rossetto (MR) appliqué au système Coulombien bi-dimensionnel.Cette équivalence est utilisée pour sonder la transition BKT par l'application de l'algorithme MR au gaz de Coulomb bi-dimensionel. En simulant le système Coulombien, il est prouvé que les fluctuations dans l'organisation des charges autour du tore sont activées à la température de transition BKT. Ces fluctuations du champ électrique indiquent ainsi la phase de haute température de la transition.Il est ensuite montré que l'exposant critique effectif de la théorie de Bramwell-Holdsworth (BH) peut être mesuré dans les films d'hélium 4 superfluide, qui correspondent à des gaz de Coulomb effectifs dans la limite de systèmes de grandes tailles finies. / This thesis addresses the emergent electrostatics of two-dimensional, toroidal magnetic models that possess XY symmetry, providing a platform for novel investigations into the Berezinskii-Kosterlitz-Thouless (BKT) phase transition.The BKT transition drives the thermal dissociation of bound pairs of topological defects in many two-dimensional systems, including the two-dimensional XY model of magnetism. The XY model is closely analogous to the two-dimensional Coulomb gas, but can be simulated without computing the long-range interactions of the Coulombic system. This thesis elucidates this paradox by showing that Villain's approximation to the XY model is strictly equivalent to the Maggs-Rossetto (MR) electrostatic model when applied to the two-dimensional Coulomb gas.The mapping is used to probe the BKT transition through the application of the MR algorithm to the two-dimensional Coulomb gas. By simulating the Coulombic system, fluctuations in the winding of charges around the torus are shown to turn on at the BKT transition temperature. These topological-sector fluctuations in the electric field therefore signal the high-temperature phase of the transition.It is then shown that the effective critical exponent of Bramwell-Holdsworth (BH) theory can be measured in superfluid 4He films, which correspond to effective Coulomb gases in the limit of large but finite system size. With the Coulombic system taken as the base BKT system, it is inferred that BH theory is a general property of BKT systems.