Nonlinear Landau-Zener tunneling in Majorana's stellar representation

By representing the evolution of a quantum state with the trajectories of the stars on a Bloch sphere, the Majorana's stellar representation provides an intuitive way to understand quantum motion in a high dimensional projective Hilbert space. In this work we show that the Majorana's repre...

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Bibliographic Details
Published in:The European Physical Journal D
Main Authors: Guo, Qiuyi, Liu, Haodi, Zhou, Tianji, Chen, Xu-Zong, Wu, Biao
Other Authors: Guo, QY (reprint author), Peking Univ, Sch Elect Engn & Comp Sci, Inst Quantum Elect, Beijing 100871, Peoples R China., Peking Univ, Sch Elect Engn & Comp Sci, Inst Quantum Elect, Beijing 100871, Peoples R China., NE Normal Univ, Ctr Quantum Sci, Changchun 130024, Peoples R China., NE Normal Univ, Sch Phys, Changchun 130024, Peoples R China., Rensselaer Polytech Inst, Dept Mat Sci & Engn, Troy, NY 12180 USA., Peking Univ, Int Ctr Quantum Mat, Beijing 100871, Peoples R China., Collaborat Innovat Ctr Quantum Matter, Beijing, Peoples R China., Zhejiang Univ Technol, Coll Sci, Wilczek Quantum Ctr, Hangzhou 310014, Zhejiang, Peoples R China., Hunan Normal Univ, Synerget Innovat Ctr Quantum Effects & Applicat, Changsha 410081, Hunan, Peoples R China.
Format: Journal/Newspaper
Language:English
Published: EUROPEAN PHYSICAL JOURNAL D 2016
Subjects:
GASES
South Pole
South pole
Online Access:https://hdl.handle.net/20.500.11897/492184
https://doi.org/10.1140/epjd/e2016-70059-y
Description
Summary:By representing the evolution of a quantum state with the trajectories of the stars on a Bloch sphere, the Majorana's stellar representation provides an intuitive way to understand quantum motion in a high dimensional projective Hilbert space. In this work we show that the Majorana's representation offers a very interesting and intuitive way to understand the nonlinear Landau-Zener tunneling. In particular, the breakdown of adiabaticity in this tunneling phenomenon can be understood as some of the stars never reaching the south pole. We also establish a connection between the Majorana stars in the second quantized model and the single star in the mean field model by using the reduced density matrix. National Fundamental Research Program of China [2011CB921501, 2012CB921300, 2013CB921900]; National Natural Science Foundation of China [61027016, 61078026, 10934010, 91336103, 11274024, 11334001, 11429402, 11405008]; Fundamental Research Funds for the Central Universities [2412015KJ009] SCI(E) ARTICLE qyguo@pku.edu.cn 6 70

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