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arXiv:1107.6006 · The European Physical Journal D

Metastable states of hydrogen: their geometric phases and flux densities

Thomas Gasenzer, Otto Nachtmann, Martin-Isbjörn Trappe

Published May 1, 2012• 2 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2012-20465-2

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Garrison and Wright showed that upon undergoing cyclic quantum evolution a metastable state acquires both a geometric phase and a geometric decay probability. This is described by a complex geometric phase associated with the cyclic evolution of two states and is closely related to the two-state formalism developed by Aharonov et al. Applications of the complex geometric phase to the Born-Oppenheimer approximation and the Aharonov-Bohm effect are considered. A simple experiment based on the optical properties of absorbing birefringent crystals is proposed. \textcopyright{} 1996 The American Physical Society.

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In the present thesis Berry phases for metastable states of hydrogen and helium exposed \nto external electromagnetic fields are investigated. One main goal is the derivation of \na parity-violating observable incorporating the electroweak mixing angle. The study is \ndone in view of an available high-precision atomic beam spin echo interferometer and \nwith respect to the theoretically very well-known structure of hydrogen. We determine \nthe general properties of parity-violating and parity-conserving Berry phases and their \nflux-density vector fields distinguished by their behaviour under proper and improper \nrotations. This allows for extensive analytical investigations and cross-checks of our \nnumerical computations. Regarding hydrogen, we reveal geometry-dependent modifications \nof atomic lifetimes due to parity-conserving imaginary Berry phases. Deriving \nthe evolution of the atomic wave packets, we establish the theoretical description of an \natom interferometer. An analytical expression for the spin echo signal, easily accessible \nin experiment, is presented and numerically evaluated to extract parity-violating \nsignals. We discuss the implications of the computed parity-violating effects on interferometric \nprecision measurements of the proton’s weak charges. Moreover, we outline \nthe concept of Heisenberg-limited atom interferometry to improve the resolution for \nmeasurements of Berry phases. Finally, we present predictions for parity-conserving \nBerry phases of metastable helium states studied in the Heidelberg experiment.
Garrison and Wright showed that upon undergoing cyclic quantum evolution a metastable state acquires both a geometric phase and a geometric decay probability. This is described by a complex geometric phase associated with the cyclic evolution of two states and is closely related to the two-state formalism developed by Aharonov et al. Applications of the complex geometric phase to the Born-Oppenheimer approximation and the Aharonov-Bohm effect are considered. A simple experiment based on the optical properties of absorbing birefringent crystals is proposed. \textcopyright{} 1996 The American Physical Society.