Stability analysis of a magnetic waveguide with self-generated offset field

The unexpected emerging stability of a time-modulated magnetic guide, realized without external offset fields, is demonstrated. We found a steady periodic solution around which the nonlinear dynamics is linearized. To investigate the orbital stability of the guiding, a formal criterion based on the...

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Bibliographic Details
Published inarXiv.org
Main Author Garrido Alzar, Carlos L
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.12.2019
Subjects
Domains
Dynamic stability
Dynamical systems
Eigenvalues
Equations of state
Nonlinear dynamics
Orbital stability
Parameters
Physics - Atomic Physics
Physics - Quantum Physics
Stability analysis
System dynamics
Transformations (mathematics)
Upper bounds
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Summary:The unexpected emerging stability of a time-modulated magnetic guide, realized without external offset fields, is demonstrated. We found a steady periodic solution around which the nonlinear dynamics is linearized. To investigate the orbital stability of the guiding, a formal criterion based on the analysis of the eigenvalues of the monodromy matrix of the system dynamics is used. To circumvent the difficulty in finding an analytical expression for these eigenvalues, a Lyapunov transformation of the system variables is proposed. From this transformation, an equation of state for the system parameters is derived, and it allows one to estimate an upper bound for the computed stability domains. In particular, we found a general expression for the threshold modulation frequency below which the guiding is unstable. Using experimentally accessible parameters, the stable guiding of 87Rb atoms is investigated.
ISSN:2331-8422
DOI:10.48550/arxiv.1912.06841