This thesis covers most of my work in the field of Bose-Einstein condensation. It contains several different topics: quantum kinetic theory for describing Bose-gases at finite temperatures, the Bose-Hubbard model and its realization with neutral atoms in an optical lattice, and different ways for implementing quantum computations with neutral atoms in optical lattices and magnetic microtraps. I did all of those works in collaboration with Prof. Peter Zoller, Prof. Crispin Gardiner, and Prof. Ignacio Cirac. I did most of the work at the University of Innsbruck, during a research visit at the Victoria University of Wellington in New Zealand in the beginning of 1998, and while I was staying at the Institute for Theoretical Physics (ITP) in Santa Barbara in the summer of 1998. During my stay in New Zealand I completed the work on quantum kinetic theory. In Santa Barbara I mainly worked on the Bose-Hubbard model. The thesis is divided into four parts. The first part contains a general brief introduction to the field of Bose-Einstein condensation in dilute gases. I also give a list of references which contain all the details. In the second part I first present the basics of quantum kinetic theory, then a publication mostly dealing with the fluctuations of a condensate in its stationary state is reprinted. In the third part, after a short introduction, I present a publication on the Bose-Hubbard model and its realization using neutral atoms in optical lattices. Some details on the Bose-Hubbard model and on optical lattices that were left out in this publication complete the third part of my thesis. In the fourth part, again after an introduction, three publications are presented. The first shows how neutral atoms in optical lattices may be used to perform quantum computations. The second publication demonstrates how to implement two-qubit gates with magnetic microtraps and in the third publication the ideas of the other two publications are extended. It also shows how parallel quantum computing, error correction schemes and fault-tolerant computing can be implemented. However, some of the contents of the third publication is also contained in one of the preceding two publications. Some details left out in the publications complete the fourth part of my thesis. Each chapter of this thesis has its own bibliography. The abbreviation BEC is used for Bose-Einstein condensate as well as for Bose-Einstein condensation.
created: 02-07-2005, last modified: 05-08-2005