Thesis advisor: Kevin S. Bedell / Landau Fermi-liquid theory was first introduced by L. D. Landau in the effort of understanding the normal state of Fermi systems, where the application of the concept of elementary excitations to the Fermi systems has proved very fruitful in clarifying the physics of strongly correlated quantum systems at low temperatures. In this thesis, I use Landau Fermi-liquid theory to study the transport phenomena of two different correlated quantum liquids: the strongly interacting ultracold Fermi gases and the ferromagnet/normal metal (F/N) junctions. The detailed work is presented in chapter II and chapter III of this thesis, respectively. Chapter I holds the introductory part and the background knowledge of this thesis. In chapter II, I study the transport properties of a Fermi gas with strong attractive interactions close to the unitary limit. In particular, I compute the transport lifetimes of the Fermi gas due to superfluid fluctuations above the BCS transition temperature Tc. To calculate the transport lifetimes I need the scattering amplitudes. The scattering amplitudes are dominated by the superfluid fluctuations at temperatures just above Tc. The normal scattering amplitudes are calculated from the Landau parameters. These Landau parameters are obtained from the local version of the induced interaction model for computing Landau parameters. I also calculate the leading order finite temperature corrections to the various transport lifetimes. A calculation of the spin diffusion coefficient is presented in comparison to the experimental findings. Upon choosing a proper value of F0a, I am able to present a good match between the theoretical result and the experimental measurement, which indicates the presence of the superfluid fluctuations near Tc. Calculations of the viscosity, the viscosity/entropy ratio and the thermal conductivity are also shown in support of the appearance of the superfluid fluctuations. In chapter III, I study the spin transport in the low temperature regime (often referred to as the precession-dominated regime) between a ferromagnetic Fermi liquid (FFL) and a normal metal metallic Fermi liquid (NFL), also known as the (F/N) junction, which is considered as one of the most basic spintronic devices. In particular, I explore the propagation of spin waves and transport of magnetization through the interface of the F/N junction where nonequilibrium spin polarization is created on the normal metal side of the junction by electrical spin injection. I calculate the probable spin wave modes in the precession-dominated regime on both sides of the junction especially on the NFL side where the system is out of equilibrium. Proper boundary conditions at the interface are introduced to establish the transport of the spin properties through the F/N junction. A possible transmission conduction electron spin resonance (CESR) experiment is suggested on the F/N junction to see if the predicted spin wave modes could indeed propagate through the junction. Potential applications based on this novel spin transport feature of the F/N junction are proposed in the end. / Thesis (PhD) — Boston College, 2016. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

L’exploration de systèmes quantiques à N corps fortement corrélés représente l’un des domaines de recherche les plus stimulants de la physique contemporaine. Au cours des trente dernières années, les vapeurs diluées d’atomes neutres en suspension dans le vide et contrôlées par un laser sont devenues une plate-forme polyvalente et formidable pour l’étude de tels systèmes. L’intérêt principal réside dans la capacité d’ajuster arbitrairement la force de l’interaction atomique au moyen de résonances de Feshbach induites magnétiquement, ainsi que la possibilité de créer une large gamme de potentiels via des champs optiques précisément adaptés. Cette thèse présente les résultats récents de l’expérience FerMix, consacrée à l’étude des systèmes quantiques à plusieurs corps fermioniques à des températures ultra-basses utilisant les atomes alcalins 40K et 6Li. Les principaux résultats présentés dans ce texte sont doubles. Premièrement, nous rapportons la caractérisation expérimentale d’une nouvelle résonance de Feshbach (s,d)-wave du 40K, dont les résultats sont comparés aux prédictions théoriques correspondantes. En particulier, le spectre du taux de perte inélastique est déterminé pour différentes températures et profondeurs de piège, ce qui nous permet d’identifier les pertes en tant que processus à deux corps. De plus, il est confirmé que le canal d’entrée dominant est de type s-wave. À l’aide de modèles d’équation de taux, nous analysons le réchauffement observé de l’ensemble atomique et trouvons que le comportement est cohérent avec l’état lié prévu L = 2 présent dans le canal de sortie. Enfin, nous étudions expérimentalement la dynamique des populations de spin induite par les collisions inélastiques renforcées par résonance dans l’onde d, en observant un bon accord avec nos modèles numériques. En second lieu, nous résumons nos progrès dans l’étude des croisements dimensionnels entre le liquide de Tomonaga-Luttinger en 1D et le liquide de Landau-Fermi en 3D en utilisant les gaz de Fermi de 40K confinés dans un réseau optique à grand pas. Cela inclut à la fois les considérations de conception fondamentales et l’installation du matériel expérimental requis. / The exploration of strongly correlated quantum many-body systems represents one of the most challenging fields of research of contemporary physics. Over the past thirty years, dilute vapors of neutral atoms suspended in vacuum and controlled with laser light have become a versatile and powerful platform for the study of such systems. At the very heart lies the ability to arbitrarily tune the interaction strength by means of magnetically induced Feshbach resonances as well as the possibility to create a wide range of potential landscapes via precisely tailored optical fields. This thesis reports on the recent results of the FerMix experiment, which is dedicated to the study of fermionic quantum many-body-systems at ultralow temperatures using the Alkali atoms 40K and 6Li. The main results presented in this text are twofold. First, we report on the experimental characterization of a novel (s,d)-wave Feshbach resonance in 6Li, the results of which are compared to the corresponding theoretical predictions. In particular, the spectrum of the inelastic loss rate is determined for different temperatures and trap depths, which enables us to identify the losses as two-body processes. Moreover, the dominant entrance channel is confirmed to be s-wave in nature. Using rate equation models we analyze the observed heating of the atomic ensemble and find the behavior to be consistent with the predicted L = 2 bound state present in the exit channel. Finally, we investigate experimentally the dynamics of the spin populations driven by resonantly enhanced inelastic collisions in dwave, observing good agreement with our numerical models. Second, we summarize our progress towards the study of dimensional crossovers between the Tomonaga-Luttinger liquid in 1D and the Landau-Fermi liquid in 3D using Fermi gases of 40K confined in a large spacing optical lattice. This includes both the fundamental design considerations as well as the implementation of the required experimental hardware.