Stationäre und dynamische Eigenschaften von dipolaren Bose-Einstein-Kondensaten in verschiedenen Fallenpotentialen

Abstract

This work investigates dipolar Bose-Einstein condensates in several different external potentials with a special emphasis on effects which are caused by the dipolar interaction and which lead to new and interesting insights. For the theoretical description a fully-numerical solution of the Gross-Pitaevskii equation on a three-dimensional grid is applied. To this end, the highly parallelized algorithm is implemented for the usage of the CUDA hardware. Due to this approach, for the first time the systematical study of many properties of Bose-Einstein condensates in various external potentials is possible. The essential progress made by the parallel implementation of the algorithm is that one does not need to use approximations to reduce the time for calculations and that one does not have to execute the algorithm on huge computer clusters. Solving the Gross-Pitaevskii equation with the imaginaryand real-time evolution yields the ground state and the dynamics of the condensate. The latter allows for simulations which are close to a possible experimental setup, e.g. by changing important parameters of the system over time. Due to the usage of a grid it is possible to implement almost arbitrary potentials and one can make far reaching predictions with respect to the properties of dipolar Bose-Einstein condensates in the context of an experiment. Our algorithm is applied to three different physical systems. The first application covers the dynamics of collisions of quasi two-dimensional solitons with respect to different starting parameters as initital momenta, scattering parameters und phase differences. A second investigation focuses on three-well potentials, which are used as a model system for periodic optical lattices. Such potentials allow for the study of effects like self-organization and pattern formation in dipolar systems. Here we present a phase diagram which shows how the ground states depend on relevant parameters of the system and study the dynamics of metastable states. Due to the scaling properties of the systems of units used in this work, the results for both the collision of the solitons and the investigation of the three-well potential are valid for all dipolar systems. They are completed by a comparison with calculations obtained by a variational ansatz. The last investigation focuses on computations for a condensate with dysprosium, which shall assist the group of Professor Pfau from the 5 Institute of Physics of the University of Stuttgart by realizing a condensate with Dy. Here simulations will cover structured ground states, borders of stability and the dynamics of expansion, which are helpful in determining the scattering length of Dy.