Tunnelling of spin-orbit coupled Bose-Einstein condensates in driven double-well potential

  • Zhen-Xia Niu
  • Ai-Xia Zhang
  • Ju-Kui XueEmail author
Regular Article


The tunnelling dynamics of spin-orbit (SO) coupled Bose-Einstein condensates in a periodically driven double-well potential are investigated both theoretically and numerically. We find that, when the SO coupling is absent, the atomic interactions suppress the tunnelling (as in usual Bose-Einstein condensed system), and the Zeeman field does not influence the usual tunnelling. When the SO coupling is present, the coupling of the atomic interactions and the Zeeman-field intensity can either enhance or suppress the tunnelling. The system undergoes rich transformations from the coherent tunnelling (CT) to the coherent destruction of tunnelling (CDT) when the SO coupling or the atomic interactions or the Zeeman-field intensity changes. In high-frequency region, the triangular structure and the circle structure are revealed in quasi-energy bands of the system, the width of the triangular structure or the circle structure and the localization width are relevant. And the SO coupling modifies traditional degenerate modes of quasi-energy bands. The results provide a possible way to control the usual tunnelling and the spin-flipping tunnelling in double-well potential.

Graphical abstract


Cold Matter and Quantum Gas 


  1. 1.
    F. Grossmann, T. Dittrich, P. Jung, P. Hänggi, Phys. Rev. Lett. 67, 516 (1991)ADSCrossRefGoogle Scholar
  2. 2.
    M. Grifoni, P. Hänggi, Phys. Rep. 304, 229 (1998)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    S. Kohler, J. Lehmann, P. Hänggi, Phys. Rep. 406, 379 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    K. Yosuke, S. Keiji, Phys. Rev. A 77, 010101(R) (2008)CrossRefGoogle Scholar
  5. 5.
    L.P. Li, X.B. Luo, X.Y. Lü, X.X. Yang, Y. Wu, Phys. Rev. A 91, 063804 (2015)ADSCrossRefGoogle Scholar
  6. 6.
    G. Della Valle, M. Ornigotti, E. Cianci, V. Foglietti, P. Laporta, S. Longhi, Phys. Rev. Lett. 98, 263601 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    E. Kierig, U. Schnorrberger, A. Schietinger, J. Tomkovic, M.K. Oberthaler, Phys. Rev. Lett. 100, 190405 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    A. Eckardt, M. Holthaus, H. Lignier, A. Zenesini, D. Ciampini, O. Morsch, E. Arimondo, Phys. Rev. A 79, 013611 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    X.B. Luo, L.P. Li, L. You, B. Wu, New J. Phys. 16, 013007 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, M.K. Oberthaler, Phys. Rev. Lett. 95, 010402 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    R. Franzosi, M. Cristiani, C. Sias, E. Arimondo, Phys. Rev. A 74, 013403 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    S. Raghavan, A. Smerzi, S. Fantoni, S.R. Shenoy, Phys. Rev. A 59, 620 (1999)ADSCrossRefGoogle Scholar
  13. 13.
    Q.H. Song, C. Zeng, S.M. Xiao, Phys. Rev. A 87, 013831 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    S. Longhi, Phys. Rev. A 86, 044102 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    C.E. Creffield, F. Sols, Phys. Rev. Lett. 100, 250402 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    S. Longhi, J. Phys.: Condens. Matter 24, 435601 (2012)ADSGoogle Scholar
  17. 17.
    M. Holthaus, Phys. Rev. A 64, 011601(R) (2001)ADSCrossRefGoogle Scholar
  18. 18.
    X.B. Luo, Q.T. Xie, B. Wu, Phys. Rev. A 76, 051802(R) (2007)ADSCrossRefGoogle Scholar
  19. 19.
    J. Gong, L. Morales-Molina, P. Hänggi, Phys. Rev. Lett. 103, 133002 (2009)ADSCrossRefGoogle Scholar
  20. 20.
    Y.J. Lin, K. Jiménez-García, I.B. Spielman, Nature 471, 83 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    N.R. Cooper, Phys. Rev. Lett. 106, 175301 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    W.Y. Wang, H. Cao, S.L. Zhu, J. Liu, L.B. Fu, Laser Phys. 25, 025501 (2015)ADSCrossRefGoogle Scholar
  23. 23.
    W.Y. Wang, H. Cao, J. Liu, L.B. Fu, Phys. Lett. A 379, 1762 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.L. Qi, S.C. Zhang, Science 318, 766 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    B.A. Bernevig, T.L. Hughes, S.C. Zhang, Science 314, 1757 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    Y.A. Chen, S. Nascimbène, M. Aidelsburger, M. Atala, S. Trotzky, I. Bloch, Phys. Rev. Lett. 107, 210405 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    S. Trotzky, P. Cheinet, S. Fölling, M. Feld, U. Schnorrberger, A.M. Rey, A. Polkovnikov, E.A. Demler, M.D. Lukin, I. Bloch, Science 319, 298 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    C. Castelnovo, J.S. Caux, S.H. Simon, Phys. Rev. A 93, 013613 (2016)ADSCrossRefGoogle Scholar
  29. 29.
    J. D’Ambroise, M. Salerno, P.G. Kevrekidis, F.K. Abdullaev, Phys. Rev. A 92, 053621 (2015)ADSCrossRefGoogle Scholar
  30. 30.
    W. Cairncross, A. Pelster, Eur. Phys. J. D 68, 106 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    H. Jiang, H. Susanto, T.M. Benson, K.A. Cliffe, Phys. Rev. A 89, 013828 (2014)ADSCrossRefGoogle Scholar
  32. 32.
    A. Lazarides, A. Das, R. Moessner, Phys. Rev. Lett. 115, 030402 (2015)ADSCrossRefGoogle Scholar
  33. 33.
    P.M. Poggi, F.J. Arranz, R.M. Benito, F. Borondo, D.A. Wisniacki, Phys. Rev. A 90, 062108 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    J. Larson, J. Martikainen, A. Collin, E. Sjöqvist, Phys. Rev. A 82, 043620 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)ADSCrossRefGoogle Scholar
  36. 36.
    D. Peter, K. Pawlowski, T. Pfau, K. Rzażewski, J. Phys. B 45, 225302 (2012)ADSCrossRefGoogle Scholar
  37. 37.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  38. 38.
    A. Eckardt, C. Weiss, M. Holthaus, Phys. Rev. Lett. 95, 260404 (2005)ADSCrossRefGoogle Scholar
  39. 39.
    R. Qi, X.L. Yu, Z.B. Li, W.M. Liu, Phys. Rev. Lett. 102, 185301 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    X.B. Luo, Q.T. Xie, B. Wu, Phys. Rev. A 77, 053601 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    Z.F. Yu, J.K. Xue, Phys. Rev. A 90, 033618 (2014)ADSCrossRefGoogle Scholar
  42. 42.
    Y.P. Zhang, C.W. Zhang, Phys. Rev. A 87, 023611 (2013)ADSCrossRefGoogle Scholar
  43. 43.
    Y. Seol, D.L. Stein, K. Visscher, Phys. Rev. Lett. 103, 050601 (2009)ADSCrossRefGoogle Scholar
  44. 44.
    D.W. Zhang, L.B. Fu, Z.D. Wang, S.L. Zhu, Phys. Rev. A 85, 043609 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010)ADSCrossRefGoogle Scholar
  46. 46.
    M. Melé-Messeguer, B. Juliá-Díaz, M. Guilleumas, A. Polls, A. Sanpera, New J. Phys. 13, 033012 (2011)ADSCrossRefGoogle Scholar
  47. 47.
    L. Pezzé, A. Smerzi, Phys. Rev. Lett. 102, 100401 (2009)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    J. Esteve, C. Gross, A. Weller, S. Giovanazzi, M.K. Oberthaler, Nature 455, 1216 (2008)ADSCrossRefGoogle Scholar
  49. 49.
    M.C. Tichy, M.K. Pedersen, K. Mølmer, J.F. Sherson, Phys. Rev. A 87, 063422 (2013)ADSCrossRefGoogle Scholar
  50. 50.
    I. Březinová, L.A. Collins, K. Ludwig, B.I. Schneider, J. Burgdörfer, Phys. Rev. A 83, 043611 (2011)ADSCrossRefGoogle Scholar
  51. 51.
    C. Weiss, N. Teichmann, Phys. Rev. Lett. 100, 140408 (2008)ADSCrossRefGoogle Scholar
  52. 52.
    A. Szameit, Y.V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V.A. Vysloukh, F. Lederer, L. Torner, Phys. Rev. Lett. 102, 153901 (2009)ADSCrossRefGoogle Scholar
  53. 53.
    M. Holthaus, Phys. Rev. A 64, 011601(R) (2001)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Key Laboratory of Atomic & Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronics Engineering, Northwest Normal UniversityLanzhouP.R. China

Personalised recommendations