Ring phases of spin-orbit coupled Bose-Einstein condensate in the radial optical lattices

  • Ji-Guo WangEmail author
  • Wei Wang
  • Xiao-Dong Bai
  • Shi-Jie Yang
Regular Article


We study the ground-state phases of two-dimensional spin-orbit coupled Bose-Einstein condensate loaded in the spin-dependent radial optical lattices. For strong depth of the spin-dependent radial optical lattice, three new types of the ring phases are found with isotropic spin-orbit coupling, i.e., the ring-stripe phase with the periodic density modulation along the radial direction, the ring-supersolid phase with the periodic density modulation both the radial and azimuthal directions and the windmill-supersolid phase with four vanes along the azimuthal direction. By increasing spin-orbit coupling, the system undergoes a sequence phase transitions from the ring-stripe phase to the ring-sueprsolid phase, and to the windmill-supersolid phase for the weak depth of radial optical lattice, however, the ring-stripe phase transforms to the windmill-supersolid phase directly for the strong depth of radial optical lattice. We also discuss the ground-state phases with anisotropic spin-orbit coupling, two-component Bose-Einstein condensates are easier condensed along the direction with larger spin-orbit coupling.


  1. 1.
    M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)ADSCrossRefGoogle Scholar
  2. 2.
    K.B. Davis, M.O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995)ADSCrossRefGoogle Scholar
  3. 3.
    M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(De), U. Sen, Adv. Phys. 56, 243 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    I.B. Spielman, Phys. Rev. A 79, 063613 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    G. Juzeliunas, J. Ruseckas, J. Dalibard, Phys. Rev. A 81, 053403 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    J.D. Sau, R. Sensarma, S. Powell, I.B. Spielman, S. Das Sarma, Phys. Rev. B 83, 140510(R) (2011)ADSCrossRefGoogle Scholar
  8. 8.
    D.L. Campbell, G. Juzeliunas, I.B. Spielman, Phys. Rev. A 84, 025602 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    Y.J. Lin, K. Jiménez-García, I.B. Spielman, Nature (London) 471, 83 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    C. Wang, C. Gao, C.M. Jian, H. Zhai, Phys. Rev. Lett. 105, 160403 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    T.L. Ho, S. Zhang, Phys. Rev. Lett. 107, 150403 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    C. Wu, I. Mondragon-Shem, Chin. Phys. Lett. 28, 097102 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    S. Sinha, R. Nath, L. Santos, Phys. Rev. Lett. 107, 270401 (2011)CrossRefGoogle Scholar
  14. 14.
    Z.F. Xu, R. Lu, L. You, Phys. Rev. A 83, 053602 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    H. Hu, B. Ramachandhran, H. Pu, X.J. Liu, Phys. Rev. Lett. 108, 010402 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    R.M. Wilson, B.M. Anderson, C.W. Clark, Phys. Rev. Lett. 111, 185303 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    G.I. Martone, Y. Li, S. Stringari, Phys. Rev. A 90, 041604(R) (2014)ADSCrossRefGoogle Scholar
  18. 18.
    X. Chen, M. Rabinovic, B.M. Anderson, L. Santos, Phys. Rev. A 90, 043632 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    J. Li, J. Lee, W. Huang, S. Burchesky, B. Shteynas, F.C. Top, A.G. Jamison, W. Ketterle, Nature 543, 94 (2017)ADSCrossRefGoogle Scholar
  20. 20.
    X.F. Zhang, M. Kato, W. Han, S.G. Zhang, H. Saito, Phys. Rev. A 95, 033620 (2017)ADSCrossRefGoogle Scholar
  21. 21.
    H. Wang, L.H. Wen, H. Yang, C.X. Shi, J.H. Li, J. Phys. B 50, 155301 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    A.C. White, Y.P. Zhang, T. Busch, Phys. Rev. A 95, 041604(R) (2017)ADSCrossRefGoogle Scholar
  23. 23.
    J.G. Wang, L.L. Xu, S.J. Yang, Phys. Rev. A 96, 033629 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    O. Mandel, M. Greiner, A. Widera, T. Rom, T.W. Hänsch, I. Bloch, Phys. Rev. Lett. 91, 010407 (2003)ADSCrossRefGoogle Scholar
  25. 25.
    B.M. Anderson, I.B. Spielman, G. Juzeliunas, Phys. Rev. Lett. 111, 125301 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    W. Han, G. Juzeliunas, W. Zhang, W.M. Liu, Phys. Rev. A 91, 013607 (2015)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    B.B. Baizakov, Boris A. Malomed, Mario Salerno, Phys. Rev. E 74, 066615 (2006)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Y.J. He, Boris A. Malomed, H.Z. Wang, Phys. Rev. A 76, 053601 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    C.M. Huang, S.S. Zhong, C.Y. Li, L.W. Dong, Phys. Rev. A 85, 063812 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    C.Q. Huang, L. Lyu, H. Huang, Z.P. Chen, S.H. Fu, H.S. Tan, B.A. Malomed, Y.Y. Li, Phys. Rev. A 96, 053617 (2017)ADSCrossRefGoogle Scholar
  31. 31.
    G.I. Martone, Y. Li, L.P. Pitaevskii, S. Stringari, Phys. Rev. A 86, 063621 (2012)ADSCrossRefGoogle Scholar
  32. 32.
    J.G. Wang, S.J. Yang, Phys. Rev. A 93, 043625 (2016)ADSCrossRefGoogle Scholar
  33. 33.
    S.W. Su, I.K. Liu, S.C. Gou, R.Y. Liao, O. Fialko, J. Brand, Phys. Rev. A 95, 053629 (2017)ADSCrossRefGoogle Scholar
  34. 34.
    F.E. Meijer, A.F. Morpurgo, T.M. Klapwijk, Phys. Rev. B 66, 033107 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    W. Bao, Multiscale Model. Simul. 2, 210 (2004)MathSciNetCrossRefGoogle Scholar
  36. 36.
    W. Jiang, Q.F. Chen, Y.S. Zhang, G.C. Guo, Phys. Rev. A 74, 043811 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    X.M. Cai, S. Chen, Y.P. Wang, Phys. Rev. A 84, 033605 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Ji-Guo Wang
    • 1
    • 2
    Email author
  • Wei Wang
    • 1
    • 2
  • Xiao-Dong Bai
    • 3
  • Shi-Jie Yang
    • 4
  1. 1.Department of Mathematics and PhysicsShijiazhuang TieDao UniversityShijiazhuangChina
  2. 2.Institute of Applied PhysicsShijiazhuang TieDao UniversityShijiazhuangChina
  3. 3.CAS Key Laboratory of Theoretical Physics, Institute of Theoretical PhysicsChinese Academy of SciencesBeijingChina
  4. 4.Department of PhysicsBeijing Normal UniversityBeijingChina

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