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Nonlinear Landau-Zener tunneling in Majorana’s stellar representation

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Abstract

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.

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Authors and Affiliations

  1. Institution of Quantum Electronics, School of Electronics Engineering & Computer Science, Peking University, Beijing, 100871, China

    Qiuyi Guo & Xu-Zong Chen

  2. Center of Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China

    Haodi Liu

  3. Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York, 12180, USA

    Tianji Zhou

  4. International Center for Quantum Materials, Peking University, Beijing, 100871, China

    Biao Wu

  5. Collaborative Innovation Center of Quantum Matter, Beijing, China

    Biao Wu

  6. Wilczek Quantum Center, College of Science, Zhejiang University of Technology, Hangzhou, 310014, China

    Biao Wu

  7. Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, China

    Biao Wu

Authors
  1. Qiuyi Guo
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  2. Haodi Liu
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  3. Tianji Zhou
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  4. Xu-Zong Chen
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  5. Biao Wu
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Guo, Q., Liu, H., Zhou, T. et al. Nonlinear Landau-Zener tunneling in Majorana’s stellar representation. Eur. Phys. J. D 70, 128 (2016). https://doi.org/10.1140/epjd/e2016-70059-y

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  • DOI: https://doi.org/10.1140/epjd/e2016-70059-y

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