Dynamical Stability of an Ion in a Linear Trap as a Solid-State Problem of Electron Localization

When an ion confined in a linear ion trap interacts with a coherent laser field, the internal degrees of freedom, related to the electron transitions, couple to the vibrational degree of freedom of the ion. As a result of this interaction, quantum dynamics of the vibrational degree of freedom become...

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Bibliographic Details
Published in:arXiv.org 2000-12
Main Authors: Berman, G P, Bishop, A R, James, D F V, Hughes, R J, Kamenev, D I
Format: Article
Language:English
Subjects:
Degrees of freedom
Dynamic stability
Electron transitions
Electrons
Ion dynamics
Localization
Perturbation methods
Perturbation theory
Solid state
Strong interactions (field theory)
Time dependence
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Summary:When an ion confined in a linear ion trap interacts with a coherent laser field, the internal degrees of freedom, related to the electron transitions, couple to the vibrational degree of freedom of the ion. As a result of this interaction, quantum dynamics of the vibrational degree of freedom becomes complicated, and in some ranges of parameters even chaotic. We analyze the vibrational ion dynamics using a formal analogy with the solid-state problem of electron localization. In particular, we show how the resonant approximation used in analysis of the ion dynamics, leads to a transition from a two-dimensional (2D) to a one-dimensional problem (1D) of electron localization. The localization length in the solid-state problem is estimated in cases of weak and strong interaction between the cites of the 2D cell by using the methods of resonance perturbation theory, common in analysis of 1D time-dependent dynamical systems.
ISSN:2331-8422
DOI:10.48550/arxiv.0012098