Bose - Einstein condensates in PT - symmetric potentials

PT symmetry, alongside its applications and possible realizations, has established itself as a hot topic in recent years. Next to its possible impact on the fundamental nature of quantum physics, it has proved to be useful in the research on open systems of all kind. While PT physics has already been very successful in the field of optics, this thesis presents numerical calculations that show how PT symmetry can be applied to the mean-field theory of ultra-cold gases, where particles are added and removed coherently from a Bose-Einstein condensate. As long as the eigenvalues of a system are continuous functions with respect to such an exchange rate of particles, PT symmetry is preserved for weak perturbations. Therefore, a prediction of these changes for high excitation numbers is incredibly valuable to ensure stable stationary realizations. Not only does the present work test such rigorous estimates with regard to their validity, it also goes beyond analytically accessible regimes and presents numerical estimations for the nonlinear description of interacting particles. With this in mind, only low excited states have to be considered when studying non-trivial modifications to the PT -symmetric double-well potential. Not only do the results at hand show that this simplest implementation of PT -symmetric concepts is extremely stable with respect to experimental inaccuracies, but such modifications give rise to possible applications. Weakening the barrier inside the double well by introducing another particle channel from the gain to the loss well has a non-trivial effect on the net transport: In general, the net current does not profit from this modification, specific configurations even allow its complete suppression. Further, not only static systems, but rotating condensates are considered. It is shown, that the net particle transport is not only possible in the presence of the rotation; the vortices in the rotating wave functions even generate the necessary current by moving in such a way that their circular current adds to the net current.