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.

Fermionic matter is ubiquitous in nature, from the electrons in metals and semiconductors or the neutrons in the inner crust of neutron stars, to gases of fermionic atoms, like 40K or 6Li that can be created and studied under laboratory conditions. It is especially interesting to study these systems at very low temperatures, where we enter the world of quantum mechanical phenomena. Due to the Fermi-Dirac statistics, a dilute system of spin-polarised fermions exhibits no interactions and can be viewed as an ideal Fermi gas. However, interactions play a crucial role for fermions of several spin species. This thesis addresses several questions concerning interacting Fermi gases, in particular the transition between the normal and the superfluid phase and dynamical properties at higher temperatures. First we will look at the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. This system is particularly interesting as it exhibits universal behaviour. Due to the strong interactions perturbation theory is inapplicable and no exact theoretical description is available. I will describe the Determinant Diagrammatic Monte Carlo algorithm with which the unitary Fermi gas can be studied from first principles. This algorithm fails in the presence of a spin imbalance (unequal number of particles in the two components) due to a sign problem. I will show how to apply reweighting techniques to generalise the algorithm to the imbalanced case, and present results for the critical temperature and other thermodynamic observables at the critical point, namely the chemical potential, the energy per particle and the contact density. These are the first numerical results for the imbalanced unitary Fermi gas at finite temperature. I will also show how temperatures beyond the critical point can be accessed and present results for the equation of state and the temperature dependence of the contact density. At sufficiently high temperatures a semiclassical description captures all relevant physical features of the system. The dynamics of an interacting Fermi gas can then be studied via a numerical simulation of the Boltzmann equation. I will describe such a numerical setup and apply it to study the collision of two spin-polarised fermionic clouds. When the two components are separated in an elongated harmonic trap and then released, they collide and for sufficiently strong interactions can bounce off each other several times. I will discuss the different types of the qualitative behaviour, show how they can be interpreted in terms of the equilibrium properties of the system, and explain how they relate to the coupling between different excitation modes. I will also demonstrate how transport coefficients, for instance the spin drag, can be extracted from the numerical data.

Experimental investigations of liquid helium flows Selected turbulent flows of He II, the superfluid phase of liquid 4 He, are inves- tigated experimentally. The second sound attenuation technique is employed to directly probe the tangle of quantized vortices, thin topological defects within the superfluid, while relatively small particles made of solid hydrogen are dispersed in He II to visualize the overall flow of the liquid via the particle tracking ve- locimetry. Considering the known particle-vortex interaction mechanisms, steady thermal counterflow in a square channel is investigated. Significant inhomogene- ity of the vortex tangle density along the channel height (near the flow-generating heater) is shown to develop. The means of energy transport in turbulent flows of He II are found strikingly different from those taking place in turbulent flows of viscous fluids. Moreover, individual particles in counterflow are observed to intermittently switch between two distinct motion regimes along their trajecto- ries. The regimes are identified and qualitatively described. Steady counterflow jets in He II are realized and the spatial arrangement of the underlying vortex tangle is explored. Finally, macroscopic vortex rings are thermally generated and observed in He II. A method for tracking their...

Bien que représentant plus d’un quart de la distribution en énergie de notre Univers ainsi que la majorité (84\%) de la masse de celui-ci, la nature de la matière noire n’a pas encore été percée à ce jour. Dans cette thèse, il sera supposé que la matière noire est une nouvelle particule élémentaire, stable et dont la connexion (hors interactions gravitationnelles) avec le secteur visible est réalisée grâce à une autre particule, le médiateur. Au sein de ces lignes, la matière noire sera supposée être un fermion de Dirac et le médiateur un boson (vecteur ou scalaire), ce dernier étant choisi comme étant plus léger que la matière noire. Cette thèse propose d’explorer les aspects infrarouges de la production de la matière noire dans l’Univers primordial, le potentiel de détection d’une importante classe de candidats dits \enquote{freeze-in}, caractérisés par de très faibles interactions avec le Modèle Standard, auprès des expériences de détection directe et l’effet des auto-interactions de la matière noire sur son comportement superfluide dans les régions de haute densité de matière noire (halos, capture par des astres compacts) asymétrique. Sous ces hypothèses, premièrement, une étude exhaustive des différents mécanismes de production de la matière noire est réalisée, illustrée dans un modèle où le médiateur est un photon du secteur caché, issu d’un nouveau groupe de jauge U(1)’, qui mélange de façon cinématique avec le photon du Modèle Standard. En particulier, de nouveaux canaux de production sont mis en avant, nommément \textit{freeze-in from mediator} et \textit{sequential freeze-in}. Ceux-ci correspondent à des scénarios où la matière noire est très faiblement couplée au Modèle Standard, n’atteint jamais l’équilibre avec celui-ci dans l’Univers primordial et est produit petit à petit par des annihilations de médiateurs (en équilibre ou non avec le Modèle Standard). Il est ensuite montré que pour l’important et très attractif cas d’une matière noire milli-chargée (ainsi que pour des scénarios où le médiateur n’est pas plus massif que 40 méga-electronvolt), l’expérience de détection indirect Xenon1T contraint aujourd’hui l’espace des paramètres de la phase de freeze-in de ces modèles, et est, dans cette région de l’espace des paramètres, la contrainte la plus importante. Une réinterprétation des limites sur les interactions indépendantes du spin matière noire – nucléon est par ailleurs nécessaire, détaillée et validée. Dans la seconde partie de la thèse, l’effet des auto-interactions dans les scénarios de matière noire asymétrique est exploré. Sous l’hypothèse qu’un halo (galactique ou non) de matière noire atteint l’équilibre thermodynamique à très basse température (comparée à sa masse) et développe donc un potentiel chimique fini, des interactions matière noire – matière noire au voisinage de la surface de Fermi peut entraîner la formation de condensats, de transitions de phase du milieu et dès lors modifier drastiquement l’équation d’état du halo. Un système d’équations auto-consistant pour les condensats est présenté et résolu numériquement. Ensuite, la thermodynamique du système de gaz interagissant est explorée. Finalement, les interactions gravitationnelles sont considérées et les configurations auto-gravitantes, prenant en compte l’ensemble des auto-interactions, sont déterminées et leurs aspects phénoménologiques sont explorés.Even though dark matter represents more than a quarter of the energy budget of our Universe and the majority (84\%) of its mass, the nature of dark matter has not yet been unravelled. In this thesis, it will be assumed that dark matter is a new elementary particle, stable and whose connection (on top of gravitational interactions) with the visible sector is realized through another particle, the mediator. In this thesis, dark matter will be assumed to be a Dirac fermion and the mediator will be a boson (either vector or scalar). This thesis proposes to explore infrared aspects of the production of dark matter in the primeval Universe, aspects of detection of the important class of feebly coupled \enquote{freeze-in} candidates at direct detection experiments and aspects of condensed matter physics such as superfluidity in region of high dark matter density (halos or inside compact objects such as neutron stars). Under these hypothesis, we will first detail an exhaustive study of the possible thermal mechanism of dark matter production, illustrated in a model where the mediator is a dark photon, arising from a new $U\left(1\right)'$ gauge group, which kinematically mixes with the Standard Model photon. In particular, new production channels are put forward, namely the \textit{freeze-in from mediator} and \textit{sequential freeze-in}. They correspond to scenarios where dark matter is very feebly coupled to the Standard Model, do not reach equilibrium with the visible sector thermal bath in the Early Universe and are slowly produced by mediator annihilations (in-equilibrium or not with the Standard Model). It is then showed that for the popular case of a millicharged dark matter ( and for scenarios in which the mediator mass is not bigger than $40$ mega electronvolt), the direct detection experiment XENON1T constrains today the freeze-in parameter space of such models and is the strongest constraint overall for such candidates. A recast of the bounds on spin-independent dark matter$-$nucleon interactions was needed and we validate our procedure against other recast. In the second part of this thesis, the effects of self-interactions in asymmetric dark mater scenarios are explored. Under the hypothesis that a dark matter halo reaches thermodynamic equilibrium at very low temperature (compared to its mass) and develops a finite chemical potential, dark matter$-$ dark matter interactions at the vicinity of the Fermi surface can lead to the formation of condensates, to phase transitions and therefore modify drastically the equation of state of the halo. A self-consistant set of equations for the condensates is presented and solved numerically. The thermodynamics of the interacting dark matter cloud is also explored. Finally, gravitational interactions are considered and self-gravitating configurations of halos, taking into account self-interactions, are determined and their phenomenological aspects is explored. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

The dynamics of low-temperature fluids, such as superfluid helium 4, is an open scientific problem. The experimental study of similarities and differences between quantum (superfluid) and classical (viscous) flows is specifically an active research field, which already led to significant progress in our phenomenological understanding of the underlying physics. It also revealed that a comprehensive theoretical description is still missing, as, for example, in the case of the observed behaviour of moving bodies in quantum flows. The work aim is to derive the existence theory for the weak solution of a relevant system of equations based on the Landau model of superfluid helium 4 and appropriate numerical schemes to solve these equations.

The dynamics of low-temperature fluids, such as superfluid helium 4, is an open scientific problem. The experimental study of similarities and differences between quantum (superfluid) and classical (viscous) flows is specifically an active research field, which already led to significant progress in our phenomenological understanding of the underlying physics. It also revealed that a comprehensive theoretical description is still missing, as, for example, in the case of the observed behaviour of moving bodies in quantum flows. The work aim is to derive the existence theory for the weak ort he strong solution of a relevant system of equations based on the Landau model of superfluid helium 4 and appropriate properties of the solution.

This dissertation deals with the following topics related to the magnetic activity of neutron stars and black holes: (I) Magnetic field evolution of neutron stars: We develop a numerical code which models the internal magnetic field evolution of neutron stars in axisymmetry. Our code includes the Hall drift and Ohmic effects in the crust, and the drift of superconducting flux tubes and superfluid vortices inside the liquid core. We enforce the correct hydromagnetic equilibrium in the core. We also model the elastic deformation of the crust and its feedback on the magnetic field evolution. We find that (i) The Hall attractor found by Gourgouliatos and Cumming in the crust also exists for B-fields which penetrate the core. (ii) If the flux tube drift is fast in the core, the pulsar magnetic fields are depleted on the Ohmic timescale (~150 Myr for hot neutron stars, or ~1.8 Gyr for cold neutron stars such as recycled pulsars, depending on impurity levels). (iii) The outward motion of superfluid vortices during the rapid spin-down of a young highly magnetized pulsar, can partially expel magnetic flux from the core when 𝐵 ≲ 10¹³ G. (II) Neutron star quakes and glitches: We develop a theoretical model to explain the remarkable null pulse coincident with the 2016 glitch in Vela rotation. We propose that a crustal quake associated with the glitch strongly disturbed the Vela magnetosphere and thus interrupted its radio emission. We develop the first numerical code which models the global dynamics of a neutron star quake. Our code resolves the elasto-dynamics of the entire crust and follows the evolution of Alfven waves excited in the magnetosphere. We find that Alfven waves launched by the quake become de-phased in the magnetosphere, and generate strong electric currents, capable of igniting electric discharge. Most likely, the discharge floods the magnetosphere with electron-positron plasma, quenching the pulsar radio emission. The observed ~0.2 s duration of the disturbance indicates that the crust is magnetically coupled to the superconducting core of the neutron star. (III) Pulsar magnetospheres and radio emission: We present an extreme high resolution kinetic plasma simulation of a pulsar magnetosphere using the Pigeon code. The simulation shows from first-principles how and where radio emission can be produced in pulsar magnetospheres. We observe the self-consistent formation of electric gaps which periodically ignite electron-positron discharge. The gaps form above the polar-cap, and in the bulk return-current. Discharge of the gaps excites electromagnetic modes which share several features with the radio emission of real pulsars. We also observe the excitation of plasma waves and charge bunches by streaming instabilities in the outer magnetosphere. (IV) Black hole magnetospheres and no-hair theorem: We explore the evolution of highly magnetized magnetospheres on Kerr black holes by performing general relativistic kinetic plasma simulations with the GRZeltron code, and general relativistic resistive magnetohydrodynamics simulations with the BHAC code. We show that a dipole magnetic field on the event horizon opens into a split-monopole and reconnects in a plasmoid-unstable current-sheet. The plasmoids are ejected from the magnetosphere, or swallowed by the black hole. The no-hair theorem is satisfied, in the sense that all components of the stress-energy tensor decay exponentially in time. We measure the decay time of magnetic flux on the event horizon for plasmoid-dominated reconnection in collisionless and collisional plasma.

A nonlinear second order differential equation related to vortex motion is derived. This equation is analyzed using various numerical and analytical techniques including finding approximate solutions using a perturbative approach.

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.

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.