Theorie des longitudinalen Atomstrahl-Spinechos und paritaetsverletzende Berry-Phasen in Atomen

TL;DR

This paper develops a nonrelativistic quantum theory for longitudinal atomic beam spin echo experiments, including the effects of parity-violating Berry phases, providing a comprehensive framework and visualization tools for atomic wave packet evolution.

Contribution

It introduces a matrix-valued Schrödinger equation approach and a series expansion method to analyze atomic wave packets, including parity-violating geometric phases, in spin echo experiments.

Findings

Derived a master formula for wave packet amplitudes.

Proved the existence of a parity-violating geometric phase.

Introduced geometric flux densities for visualization.

Abstract

We present a nonrelativistic theory for the quantum mechanical description of longitudinal atomic beam spin echo experiments, where a beam of neutral atoms is subjected to static electric and magnetic fields. The atomic wave function is the solution of a matrix-valued Schroedinger equation and can be written as superposition of local (atomic) eigenstates of the potential matrix. The position- and time-dependent amplitude function of each eigenstate represents an atomic wave packet and can be calculated in a series expansion with a master formula that we derive. The zeroth order of this series expansion describes the adiabatic limit, whereas the higher order contributions contain the mixing of the eigenstates and the corresponding amplitude functions. We give a tutorial for the theoretical description of longitudinal atomic beam spin echo experiments and for the so-called Fahrplan model, which is a visualisation tool for the propagation of wave packets of different atomic eigenstates. As an example for the application of our theory, we study parity violating geometric (Berry-)phases. In this context, we define geometric flux densities, which for certain field configurations can be used to illustrate geometric phases in a vector diagram. Considering an example with a specific field configuration, we prove the existence of a parity violating geometric phase.