Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, self-similarity, and the presence of non-trivial structure on all scales. The concept of aperiodic order has been extensively studied in mathematics and geometry, exemplified by the celebrated Penrose tiling. However, the understanding of physical quasicrystals (the vast majority of them are intermetallic compounds) is still incomplete owing to their complexity, regarding both growth processes and stability. Ultracold atoms in optical lattices offer an ideal, yet untested environment for investigating quasicrystals. Optical lattices, i.e. standing waves of light, allow the defect-free formation of a large variety of potential landscapes, including quasiperiodic geometries. In recent years, optical lattices have become one of the most successful tools in the large-scale quantum simulation of condensed-matter problems. This study presents the first experimental realisation of a two-dimensional quasicrystalline potential for ultracold atoms, based on an eightfold symmetric optical lattice. It is aimed at bringing together the fields of ultracold atoms and quasicrystals - and the more general concept of aperiodic order. The first part of this thesis introduces the theoretical aspects of aperiodic order and quasicrystalline structure. The second part comprises a detailed account of the newly designed apparatus that has been used to produce quantum-degenerate gases in quasicrystalline lattices. The third and final part summarises the matter-wave diffraction experiments that have been performed in various lattice geometries. These include one- and two-dimensional simple cubic lattices, one-dimensional quasiperiodic lattices, as well as two-dimensional quasicrystalline lattices. The striking self-similarity of this quasicrystalline structure has been directly observed, in close analogy to Shechtman's very first discovery of quasicrystals using electron diffraction. In addition, an in-depth study of the diffraction dynamics reveals the fundamental differences between periodic and quasicrystalline lattices, in excellent agreement with ab initio theory. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. On the one hand, these measurements establish a novel experimental platform for investigating quasicrystals proper. On the other hand, ultracold atoms in quasicrystalline optical lattices are worth studying in their own right: Possible avenues include the observation many-body localisation and Bose glasses, as well as the creation of topologically non-trivial systems in higher dimensions.

Atom chips are devices used to magnetically trap and manipulate ultracold atoms and Bose-Einstein condensates near a surface. In particular, permanent magnetic film atom chips can allow very tight confinement and intricate magnetic field designs while circumventing technical current noise. Research described in this thesis is focused on the development of a magnetic film atom chip, the production of Bose-Einstein condensates near the film surface, the characterisation of the associated magnetic potentials using rf spectroscopy of ultracold atoms and the realisation of a precision sensor based on splitting Bose-Einstein condensates in a double-well potential. The atom chip itself combines the edge of a perpendicularly magnetised GdTbFeCo film with a machined silver wire structure. A mirror magneto-optical trap collects up to 5 x 108 87Rb atoms beneath the chip surface. The current-carrying wires are then used to transfer the cloud of atoms to the magnetic film microtrap and radio frequency evaporative cooling is applied to produce Bose-Einstein condensates consisting of 1 x 105 atoms. We have identified small spatial magnetic field variations near the film surface that fragment the ultracold atom cloud. These variations originate from inhomogeneity in the film magnetisation and are characterised using a novel technique based on spatially resolved radio frequency spectroscopy of the atoms to map the magnetic field landscape over a large area. The observations agree with an analytic model for the spatial decay of random magnetic fields from the film surface. Bose-Einstein condensates in our unique potential landscape have been used as a precision sensor for potential gradients. We transfer the atoms to the central region of the chip which produces a double-well potential. A single BEC is formed far from the surface and is then dynamically split in two by moving the trap closer to the surface. After splitting, the population of atoms in each well is extremely sensitive to the asymmetry of the potential and can be used to sense tiny magnetic field gradients or changes in gravity on a small spatial scale.

<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

Recently a new outlook on dealing with dipolar ultracold fermions based on density functional methods has received attention. A Thomas-Fermi treatment coupled with a variational approach has been developed for a collection of fermions trapped in a harmonic potential interacting via dipole-dipole forces. In this thesis, firstly our alternative formalism for Thomas-Fermi method by performing some calculations based on the Kohn-Sham formalism which is one of the main idea of density functional theory is investigated. Furthermore, density distributions are obtained dependent to the parameters / rescaled interaction strength, dipole-dipole energy and the trap parameter which determine the trap geometry based on this theory. The thesis starts with a brief outline of the density functional theory and theory of our system, continues with calculations based on this theory, which are free of any variational assumptions for the density profile. Moreover, results of density graphics for harmonic trap will be followed by discussion of comparison and contrast with Thomas-Fermi method based on the paper of Goral et al.. These discussions are mainly about the shape of the density distribution, variation of the cloud parameters and energy behaviours according to the rescaled interaction strength. The thesis concludes with an analysis of contribution of density functional theory to this fermionic system.

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.

Neste trabalho nós produzimos um plasma neutro ultrafrio de 85Rb através da fotoionização dos átomos aprisionados em uma armadilha magneto-óptica. Medimos o número de partículas que evaporam do plasma no momento de sua criação usando a técnica de tempo-de-vôo. A partir disto realizamos o estudo da taxa de evaporação com relação a energia cinética inicial do elétron fornecida ao sistema, onde para isto criamos o plasma com diferentes comprimentos de onda do laser de fotoinização. Nossos resultados indicam que conforme fornecemos mais energia ao sistema mais partículas evaporam e constatamos que está de acordo com a literatura. Interpretamos o resultado com um modelo analítico que considera a distribuição de energia de Maxwell-Boltzmann e encontramos a temperatura do plasma com relação a temperatura inicial dos elétrons / In this work we produced an ultracold neutral plasma of 85Rb formed by the photoionization of laser-cooled atoms. We measured the number of particles evaporated from the plasma in the moment of its formation using the time-of-flight technique. After this, we studied the evaporation rate as a function of the initial electron kinetic energy, for this we created the plasma at different wavelengths of the photoinization laser. Our results indicate that as we supplied more energy to the system more particles evaporate and we verified that it is in agreement with the literature. We interpreted the result with an analytic model that considers the Maxwell-Boltzmann energy distribution and we found the plasma temperature as a function initial electron temperature

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京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22824号 / 理博第4634号 / 新制||理||1666(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 高橋 義朗, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

We report new studies on the early-time dynamics of ultracold neutral plasmas. We use fluorescence spectroscopy to probe plasma dynamics on the nanosecond time scale. We determine the rms ion velocity during the initial plasma period. The initial ion acceleration is found as the time derivative of the ion velocity. We compare to a theoretical model. The experimental results agree with the model at low plasma densities. However, the ion acceleration is a factor of ten lower than the model at higher densities. The cause of this discrepancy is currently unknown.

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