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Universiẗat, Diss., 2001--München.

Techn. Universiẗat, Diss., 2000--Darmstadt.

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.

<p>This dissertation presents the first experiments on radio frequency (rf) spectroscopy of a quasi-two dimensional strongly interacting ultracold atomic Fermi gas. A 50-50 mixture of spin-up and spin-down atoms is confined in a series of pancake-shaped traps produced using an optical standing-wave. To make the system quasi-two dimensional, I adjust the Fermi energy in the weakly confined direction to be comparable to the harmonic oscillator energy level spacing in the tightly confined direction.</p><p>For a perfectly two dimensional system, at low enough temperature, spin-up and spin-down atoms should form dimers in the ground state of the tightly confined direction. However, in our quasi-two dimensional system I find that the simple dimer theory does not agree with the measured radio-frequency spectra. Instead, the data can be explained by polaron to polaron transitions, which is a many-body effect. Here, a polaron is a spin-down impurity surrounded by a cloud of particle-hole pairs in a spin-up Fermi sea. With this unique strongly interacting quasi-two dimensional system, I am able to study the interplay between confinement induced two-body pairing and many-body physics in confined mesoscopic systems of several hundred atoms, which has not been previously explored and offers new challenges for predictions.</p> / Dissertation

In this Thesis we discussed ultracold Fermi gas with an s-wave interaction and synthetic spin-orbit coupling under a variety of conditions. We considered the system in both three and two spatial dimensions, with equal-Rashba-Dresselhaus type or Rashba-only type of spin-orbit-coupling, and with or without an artificial Zeeman field. We found competing effects on Fermionic superfluidity from spin-orbit coupling and Zeeman fields, and topologically non-trivial states in the presence of both fields. We gave an outlook on the many-body physics in the last.

Made available in DSpace on 2014-06-11T19:23:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-03-01Bitstream added on 2014-06-13T18:09:47Z : No. of bitstreams: 1 silva_ley_me_ift.pdf: 1027482 bytes, checksum: 33786f51e1c264a391590d7d9fd221a5 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho consideramos um gás diluído de átomos de Fermi a baixas temperaturas, com igual numero de átomos de espin para acima (↑) e espin para abaixo (↓) formando um conjunto de N pares de átomos fermiônicos prisioneiros pela ação de uma armadilha com diferentes simetrias, nos distintos limites: de interação fraca, no limite da unitariedade, e no chamado crossover BEC-unitariedade, empregando uma equação de funcional densidade cujas soluções descrevem adequadamente as características principais do superfluido, como são: a densidade de partículas, o tamanho médio, o potencial químico e a energia do sistema / In this work we considered a Fermi gas diluted at low temperatures, to equal number of atoms with spin up (↑) and spin down (↓) into a system of N fermion pairs prisoners for the action of a trap with different symmetries, in different limits: weak-coupling, unitarity limit, and the call crossover BEC-unitarity, using a densityfunctional equation whose solutions describe some characteristics of the superfluid appropriately, for example: density profiles of particles, radius, chemical potential and the energy of the system

Interacting Fermi gases are one of the chief paradigms of condensed matter physics. They have been studied since the beginning of the development of quantum mechanics, but continue to produce surprises today. Recent experimental developments in the field of ultracold atomic gases, as well as conventional solid state materials, have produced new and exotic forms of Fermi gases, the theoretical understanding of which is still in its infancy. This Thesis aims to provide updated tools and additional insights into some of these systems, through the application of both numerical and analytical techniques. The first Part of this Thesis is concerned with the development of improved numerical tools for the study of interacting Fermi gases. These tools take the form of accurate model potentials for the dipolar and contact interactions, as found in various ultracold atomic gas experiments, and a new form of Jastrow correlation factor that interpolates between the radial symmetry of the inter-electron Coulomb potential at short inter-particle distances, and the symmetry of the numerical simulation cell at large separation. These methods are designed primarily for use in quantum Monte Carlo numerical calculations, and provide high accuracy along with considerable acceleration of simulations. The second Part shifts focus to an analytical analysis of spin-imbalanced Fermi gases with an attractive contact interaction. The spin-imbalanced Fermi gas is shown to be unstable to the formation of multi-particle instabilities, generalisations of a Cooper pair containing more than two fermions, and then a theory of superconductivity is built from these instabilities. This multi-particle superconductivity is shown to be energetically favourable over conventional superconducting phases in spin-imbalanced Fermi gases, and its unusual experimental consequences are discussed.

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