Dynamics of Bose-Einstein condensates in novel optical potentials

Matter wave interferometry offers a novel approach for high precision measurements, such as the determination of physical constants like the local gravity constant g or the fine-structure constant. Since its early demonstration, it has become an important tool in the fields of fundamental and applied physics. The present work covers the implementation of matter wave interferometers as well as the creation of novel guiding potentials for ultra-cold ensembles of atoms and Bose-Einstein condensates for this purpose. In addition, novel techniques for the manipulation of atoms with Bragg lattices are presented, serving as elements for interferometry. The measurements in this work are performed with a Bose-Einstein condensate of 25000 87 rubidium atoms created in a crossed optical dipole trap. The crossed optical dipole trap is loaded from a magneto-optical trap and allows a measurement every 25 s. This work introduces the novel technique of double Bragg diffraction as a tool for atom optics for the first time experimentally. The creation of beamsplitters and mirrors for advanced interferometric measurements is characterized. An in depth discussion on the momentum distribution of atomic clouds and its influence on double Bragg diffraction is given. Additionally experimental results for higher-order Bragg diffraction are explained and double Bragg diffraction is used to implement a full Ramsey-type interferometer. A second central result of this work is the implementation of novel guiding structures for ultra-cold atoms. These structures are created with conical refraction, an effect that occurs when light is guided along one of the optical axis of a bi-axial crystal. The conical refraction crystal used to operate the novel trapping geometries is a KGd(WO4)2 crystal that has been specifically cut orthogonal to one of the optical axis. Two regimes are discussed in detail: the creation of a toroidal matter wave guide and the implementation of a three-dimensional dark focus. Additional geometries accessible with conical refraction are introduced and possible applications are shown. The first regime characterized in detail is the creation of a toroidal wave guide for ultra-cold atoms and Bose-Einstein condensates. With the aid of a lightsheet potential atoms are trapped in a quasi two-dimensional ring geometry. Inside of the geometry atoms are accelerated, decelerated and held for extended storage times of up to two seconds. First attempts for the implementation of a Mach-Zehnder-type interferometer in a toroidal trap are presented. The second regime shown is the creation of a three-dimensional dark focus that is used to trap atoms in a repulsive confinement of light. The parameters of the dark focus are investigated in detail. Future application of a two-dimensional array of dark foci is shown by demonstrating the respective light field