NDLI: Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere

Content Provider	PubMed Central
Author	Oh, Sangchul Hu, Xuedong Nori, Franco Kais, Sabre
Copyright Year	2016
Abstract	Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic path traced by the instantaneous eigenstate. However, the non-adiabatic Aharonov- Anandan geometric phase, measured by the area enclosed by the exact path, approaches smoothly the adiabatic Berry phase, proportional to the area enclosed by the adiabatic path. The singular limit of the time-energy uncertainty and the regular limit of the geometric phase are associated with the arc length and arc area of the cycloid on a Bloch sphere, respectively. Prolate and curtate cycloids are also traced by different initial states outside and inside of the rolling circle, respectively. The axis trajectory of the rolling circle, parallel to the adiabatic path, is shown to be an example of transitionless driving. The non-adiabatic resonance is visualized by the number of cycloid arcs.
Related Links	http://dx.doi.org/10.1038/srep20824
Starting Page	20824
File Format	PDF
ISSN	20452322
e-ISSN	20452322
Journal	Scientific Reports
Volume Number	6
Language	English
Publisher	Nature Publishing Group
Publisher Date	2016-02-26
Access Restriction	Open
Rights Holder	Nature Publishing Group
Subject Keyword	Science and technology Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

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