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Classical and Quantum Field Theory of Bose-Einstein Condensates

Sebastian Wüster

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We study the application of Bose-Einstein condensates (BECs) to simulations of phenomena across a number of disciplines in physics, using theoretical and computational methods. ¶ ...
DOI
10.25911/5d7a2c12b9880

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Dilute gas Bose-Einstein condensates (BECs) provide unique and powerful experimental platforms to study fluid turbulence. Some aspects of BEC hydrodynamics are specific to atomic quantum fluids such as quantized vortices and flexible trapping geometries. However, there are features of turbulence that are universal and simpler to understand in such systems. BECs are also of interest in fundamental physics in their own right and a rich synthesis of theory and experiment has yielded powerful numerical methods to simulate and study BEC dynamics. In this dissertation I present two experiments, one conducted and one proposed, describing novel aspects of the generation and detection of vorticity in Bose-Einstein condensates. Models of BEC dynamics at zero temperature are provided by the Gross-Pitaevskii equation. Simple and fast numerical solutions of this equation have yielded a wealth of literature. However, in experimental reality the atomic ensemble exists at a finite temperature and consists of a BEC coexisting with a thermal cloud of non-condensed atoms. The interaction between the condensate and the thermal fraction yields rich and complex physics that require more advanced models. We present an experiment demonstrating the relaxation dynamics of a BEC in a rotating trap perturbed by a repulsive laser barrier. The data provided by this experiment are valuable to further development of theoretical models that incorporate interactions between the BEC and noncondensed atoms. In the field of quantum fluid dynamics, an experimental method to determine the position and circulation of vortices is a highly sought-after capability. Onsager's point-vortex model of turbulence completely determines the kinetic energy spectrum of an incompressible fluid by these degrees of freedom. We present proof-of-principle simulations that describe a new method of spatially sampling the velocity field of a two-dimensional BEC by using an optical lattice analogously to a Shack-Hartmann Wavefront Sensor. Extracting vortex information from the appropriately sampled velocity field can be accomplished either qualitatively or with detection algorithms. This method requires minimal experimental infrastructure and is generally applicable across atomic species. The implications of measuring a condensate velocity field are broad and these initial results provide the first step towards realizing a valuable tool in BEC physics.
In this work, we study phase transitions in dilute Bose-Einstein Condensates theoretically. The Gross-Pitaevskii equation (GPE) is applied to describe the properties of dilute Bose gases near zero temperature for various confining geometries. Then, using the harmonic trap, the Thomas Fermi equation has been investigated. The Bose-Hubbard Model has been also investigated using the mean field approach. It is indicated that Bose-Einstein condensation is a second order phase transition. We also presented an exactly solvable phase transition model in which the phase transition is purely statistically derived. It is found out that the mean field theory can be applied to a number of physical systems so as to study the phenomena of Berezinsky-Kosterlitz- Thouless (BKT) phase transitions. Keywords : Phase Transition, BEC, GPE, Bose-Hubbard Model, Berezinsky-Kosterlitz-Thouless (BKT), Mean Field equation