Atomic diffraction is the central concept of matter-wave interferometers, which provide the opportunity of high-precision rotation and acceleration sensing. Ultracold atoms are the ultimate quantum sensors for this purpose. Transferring photon momentum from two counterpropagating laser beams to atomic wavepackets prepares coherent superpositions in the momentum space, realising atomic beamsplitters and mirrors.
Like classical optical systems, these matter-wave devices require exact specifications and ubiquitous imperfections need to be quantified. Therefore, in this thesis, the performance of (3+1)D atomic beamsplitters in the quasi-Bragg regime is studied numerically as well as analytically and is confirmed by experimental data [1]. Ideally, the incoming wavepacket can be split exactly into two parts or reflected perfectly with unit response, independent of its spatial and velocity distribution. However, the velocity selectivity of the Bragg diffraction, as well as losses into undesired diffraction orders in the quasi-Bragg regime, constitute aberrations, which cannot be neglected. The non-ideal behaviour due to spatial variations of the laser beam profiles and wavefront curvatures, regarding realistic Laguerre-Gaussian laser beams instead of ideal plane waves, reduces the diffraction efficiency and leads to rogue momentum components, just like misaligned lasers. In contrast, smooth temporal envelopes improve the beamsplitter performance. Different pulse shapes are taken into account, where some are amenable for closed analytical solutions.
The realistic modelling and exhausting aberration studies characterises in detail atomic Bragg beamsplitters and demonstrate pathways for improvements, both required by challenging experiments.
For hot ions in accelerator beams the atomic diffraction is used contrary to generate a velocity filter. Two counterpropagating far-detuned lasers transfer a narrow velocity class of ions from an initially broad distribution via a stimulated Raman transition between the ground states of a Λ-system. This colder subensemble prepares optimal initial conditions for precision collinear laser spectroscopy on fast ion beams. The efficiency of the filter is diminished by aberrations like the spontaneous emission from the two single-photon resonances, as well as the ground-state decoherence induced by laser noise. Spatial intensity variations of the ion and laser beams are considered, whereas wavefront curvature is negligible. A comprehensive master equation leads to conditions for the optimal frequency pair of lasers. The time-resolved population transfer characterises the filter performance and is evaluated numerically as well as analytically. Derived models match the numerical results, keeping the computational effort small.
Taking into account the mentioned aberrations, the possible use of Raman transition as velocity filter for hot ions is demonstrated. Velocity classes with widths as low as 0.2 m/s can be transferred, achieving a significant population proportion from per mill to percent. Applying the analysis to current 40-Ca+ ion experiments, a sensitivity for measuring high ion acceleration voltages on the ppm level or below is substantiated
