Dynamics of Ultracold Quantum Gases and Interferometry with Coherent Matter Waves

Abstract

In this thesis, we study the dynamics of ultracold quantum gases with respect to micro-gravity experiments, discuss interferometric applications and aspects on collective scattering. We describe the dynamics of an ultracold quantum gas in a long-distance free-fall experiment, which is of relevance for the present QUANTUS experiment. We develop the quantum field theoretical description of a trapped, interacting degenerate quantum gas in a drop experiment in an inertial frame, the corotating frame of the Earth and the comoving frame of the drop capsule. This formalism provides us with an efficient description of the experiment, especially for numerical studies. Moreover, we review the ideas of gravitational sensing with the help of an interferometric setup. We show that in case of a spatially quasi-homogeneous condensate the same results as in single-atom interferometry can be obtained even in the presence of a nonlinear time evolution. A decline of the contrast in an interferogram is found, though. In addition, we propose a rotational sensor based on a superposition of a non-rotating state and a quantized vortex in a Bose-Einstein condensate. As an application for an interferometric experiment in a micro-gravity environment, we establish a number filter for matter waves. Our number filter allows for a number stabilization, i.e. after passing the filter, the number uncertainty is less than before. This can be achieved by using a nonlinear matter wave interferometer for a two-component BEC. An asymmetric splitting is required in order to observe the effect. Finally, we examine the collective scattering of a superfluid droplet impinging on a two-component Bose-Einstein condensate. We demonstrate that this mesoscopic scenario matches the microscopic setup for Feshbach scattering of two particles. We obtain resonant scattering phase shifts from a linear response theory. We find an energy-dependent transmission coefficient that is controllable between 0 and 100%.