Eur. Phys. J. D (2016) 70: 128
https://doi.org/10.1140/epjd/e2016-70059-y

Regular Article

Nonlinear Landau-Zener tunneling in Majorana’s stellar representation

¹ Institution of Quantum Electronics, School of Electronics Engineering & Computer Science, Peking University, Beijing 100871, P.R. China
² Center of Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, P.R. China
³ Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
⁴ International Center for Quantum Materials, Peking University, Beijing 100871, P.R. China
⁵ Collaborative Innovation Center of Quantum Matter, Beijing, P.R. China
⁶ Wilczek Quantum Center, College of Science, Zhejiang University of Technology, Hangzhou 310014, P.R. China
⁷ Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, P.R. China

^a e-mail: qyguo@pku.edu.cn

Received: 30 January 2016
Received in final form: 18 April 2016
Published online: 7 June 2016

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.