Nonlinear Landau-Zener tunneling in Majorana’s stellar representation

  • Qiuyi Guo
  • Haodi Liu
  • Tianji Zhou
  • Xu-Zong Chen
  • Biao Wu
Regular Article

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.

Graphical abstract

Keywords

Atomic Physics 

References

  1. 1.
    E. Majorana, Nuovo Cimento 57, 43 (1932)CrossRefGoogle Scholar
  2. 2.
    F. Bloch, I.I. Rabi, Rev. Mod. Phys. 17, 237 (1945)ADSCrossRefGoogle Scholar
  3. 3.
    R. Penrose, The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford University Press, Oxford, 1990)Google Scholar
  4. 4.
    H.D. Liu, L.B. Fu, Phys. Rev. Lett. 113, 240403 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    S. Tamate, K. Ogawa, M. Kitano, Phys. Rev. A 84, 052114 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    K. Ogawa, S. Tamate, H. Kobayashi, T. Nakanishi, M. Kitano, Phys. Rev. A 91, 062118 (2015)ADSCrossRefGoogle Scholar
  7. 7.
    P. Bruno, Phys. Rev. Lett. 108, 240402 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    Q. Niu, Physics 5, 65 (2012)CrossRefGoogle Scholar
  9. 9.
    T. Bastin, S. Krins, P. Mathonet, M. Godefroid, L. Lamata, E. Solano, Phys. Rev. Lett. 103, 070503 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    P. Ribeiro, R. Mosseri, Phys. Rev. Lett. 106, 180502 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    W. Ganczarek, M. Kuś, K. Życzkowski, Phys. Rev. A 85, 32314 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    D. Stamper-Kurn, M. Ueda, Rev. Mod. Phys. 85, 1191 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    B. Lian, T.L. Ho, H. Zhai, Phys. Rev. A 85, 051606 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    X.L. Cui, B. Lian, T.L. Ho, B.L. Lev, H. Zhai, Phys. Rev. A 88, 011601(R) (2013)ADSCrossRefGoogle Scholar
  15. 15.
    R. Barnett, D. Podolsky, G. Refael, Phys. Rev. B 80, 024420 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    A. Lamacraft, Phys. Rev. B 81, 184526 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    A.R. Usha Devi, Sudha, A.K. Rajagopal, Quantum Inf. Process. 11, 685 (2012)MathSciNetCrossRefGoogle Scholar
  18. 18.
    P. Ribeiro, J. Vidal, R. Mosseri, Phys. Rev. Lett. 99, 050402 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    P. Ribeiro, J. Vidal, R. Mosseri, Phys. Rev. E 78, 021106 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    B. Wu, Q. Niu, Phys. Rev. A. 61, 023402 (2000)ADSCrossRefGoogle Scholar
  21. 21.
    A.J. Leggett, Rev. Mod. Phys. 73, 307 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    J. Liu, B. Wu, Q. Niu, Phys. Rev. Lett. 90, 170404 (2003)ADSCrossRefGoogle Scholar
  23. 23.
    B. Wu, Q. Niu, New J. Phys. 5, 104 (2003)ADSCrossRefGoogle Scholar
  24. 24.
    Y.A. Chen, S.D. Huber, S. Trotzky, I. Bloch, E. Altman, Nat. Phys. 7, 61 (2011)CrossRefGoogle Scholar
  25. 25.
    M. Jona-Lasinio, O. Morsch, M. Cristiani, N. Malossi, J.H. Müller, E. Courtade, M. Anderlini, E. Arimondo, Phys. Rev. Lett. 91, 230406 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    A. Leggett, Rev. Mod. Phys. 73, 307 (2001)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Qiuyi Guo
    • 1
  • Haodi Liu
    • 2
  • Tianji Zhou
    • 3
  • Xu-Zong Chen
    • 1
  • Biao Wu
    • 4
    • 5
    • 6
    • 7
  1. 1.Institution of Quantum Electronics, School of Electronics Engineering & Computer Science, Peking UniversityBeijingChina
  2. 2.Center of Quantum Sciences and School of Physics, Northeast Normal UniversityChangchunChina
  3. 3.Department of Materials Science and EngineeringRensselaer Polytechnic InstituteTroyUSA
  4. 4.International Center for Quantum Materials, Peking UniversityBeijingChina
  5. 5.Collaborative Innovation Center of Quantum MatterBeijingChina
  6. 6.Wilczek Quantum Center, College of Science, Zhejiang University of TechnologyHangzhouChina
  7. 7.Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal UniversityChangshaChina

Personalised recommendations