Numerical Simulations of Cooling and Topological Excitations of Quantum Gases

This thesis describes the numerical investigation of the production of ultra-cold particle ensembles and the manipulation of Bose-Einstein condensate (BEC) clouds. Ultra-cold particle ensembles are commonly obtained by several cooling steps, the last and most effective of which is the evaporation of particles from a trap. A simulation program has been developed for the simulation of the evaporative cooling process, paying particular attention to the intricacies and problems encountered in the trapping and cooling processes of molecular oxygen. Additionally, for the purpose of calculating improved elastic and inelastic collision data, needed in the evaporative cooling simulation program, a potential energy surface (PES) for the molecular O2-O2 collision problem has been computed using methods of quantum chemistry. In these computations, individual molecules are treated as rigid rotators and a full ab-initio approach is used to numerically derive the PES as a function of total molecular spin, intermolecular distance and the orientation of the molecules. For the evaporative cooling simulation program several algorithms had to be adapted and improved in order to correctly simulate the physical system under investigation. In particular, large fractional particle loss from the magnetic trap, very strong density inhomogeneities and a large particle energy range must be consistently controlled. The program is used to investigate cooling in harmonic traps and in quadrupole linear magnetic traps. For the investigation of topological excitations, such as vortices and solitons in BEC clouds near the absolute temperature, we developed a simulation program, which allows a three-dimensional numerical time propagation of the quantum mechanical macroscopic matter-wavefunctions on modern workstation computers. The physical description of the BEC is given by the nonlinear Gross-Pitaevskii equation. In cooperation with two experimental workgroups in Oxford/UK and Konstanz, a number of different problems are modelled. One application is the simulation of a central vortex state in a BEC cloud, reacting to external perturbations. The dependence of collective cloud excitation energies on the presence of vortices is investigated and the resonant excitation of Kelvin wave excitation modes of a central vortex core is demonstrated. Additionally, the dependence of BEC cloud expansion in strongly confined spatial dimensions on the decay of residual optical and magnetic trap confinement fields is demonstrated. This is of practical interest, because BEC cloud expansion is heavily used as a common procedure in experimental destructive imaging techniques.