Journal of Low Temperature Physics

, Volume 194, Issue 1–2, pp 76–87 | Cite as

Ferromagnetic-Core Spin Vortex of Quasi-2D Spin-1 Condensate in a Harmonic Trap

  • Gong-Ping ZhengEmail author
  • Ting Li
  • Ya-Jie Xue


We study the ferromagnetic (FM)-core spin vortex of spin-1 condensate in a 2D harmonic trap with homogeneous magnetic field. It is shown that such a topological excitation may exist when the system stays at the easy-axis phase with the negative quadratic-Zeeman-energy parameter larger than a critical value. The exact spatial distributions of number density and local spin are obtained with a variational method. A polar ring with local spin \( F=0\) appears in the FM-core spin vortex. The density–density interaction can significantly affect both the spatial distribution of local spin and the position of the polar ring. The local spin in most areas is larger for the stronger ferromagnetic interaction. More interestingly, a local minimum emerges near the polar ring in the curve of total number density when the spin–spin interaction is large enough. In such easy-axis phase, the quadratic-Zeeman-energy parameter cannot control the FM-core spin vortex. An easily controlled experiment scheme is provided to realize the FM-core spin vortex.


Ferromagnetic-core spin vortex Spin-1 condensate Harmonic trap 



This work was supported by the Natural Science Foundation of Henan Province of China (Grant No. 182300410176), and the High Performance Computing Center of Henan Normal University.


  1. 1.
    J. Stenger, S. Inouye, D.M. Stamper-Kurn, H.-J. Miesner, A.P. Chikkatur, W. Ketterle, Nature 396, 345 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    T.L. Ho, Phys. Rev. Lett. 81, 742 (1998)ADSCrossRefGoogle Scholar
  3. 3.
    T. Ohmi, K. Machida, J. Phys. Soc. Jpn. 67, 1822 (1998)ADSCrossRefGoogle Scholar
  4. 4.
    G.-P. Zheng, Y.-G. Tong, F.-L. Wang, Phys. Rev. A 81, 063633 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    G.-P. Zheng, L.-K. Xu, S.-F. Qin, W.-T. Jian, J.-Q. Liang, Ann. Phys. 334, 341 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    G.-P. Zheng, P. Li, T. Li, Y.-J. Xue, Ann. Phys. 389, 102 (2018)ADSCrossRefGoogle Scholar
  7. 7.
    D.M. Stamper-Kurn, M. Ueda, Rev. Mod. Phys. 85, 1191 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    M. Ueda, Annu. Rev. Condens. Matter Phys. 3, 263 (2011)CrossRefGoogle Scholar
  9. 9.
    Y. Kawaguchi, M. Ueda, Phys. Rep. 520, 253 (2012)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    L.E. Sadler, J.M. Higbie, S.R. Leslie, M. Vengalattore, D.M. Stamper-Kurn, Nature 443, 312 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    J.Y. Choi, W.J. Kwon, Y.I. Shin, Phys. Rev. Lett. 108, 035301 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    J. Choi, W.J. Kwon, M. Lee, H. Jeong, K. An, Y. Shin, New. J. Phys. 14, 053013 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    L.S. Leslie, A. Hansen, K.C. Wright, B.M. Deutsch, N.P. Bigelow, Phys. Rev. Lett. 103, 250401 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    M.W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, D.S. Hall, Nature 505, 657 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    M.W. Ray, E. Ruokokoski, K. Tiurev, M. Möttönen, D.S. Hall, Science 348, 544 (2015)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    A.E. Leanhardt, A. Görlitz, A.P. Chikkatur, D. Kielpinski, Y. Shin, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 89, 190403 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    A.E. Leanhardt, Y.I. Shin, D. Kielpinski, D.E. Pritchard, W. Ketterle, Phys. Rev. Lett. 90, 140403 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    S. Kobayashi, Y. Kawaguchi, M. Nitta, M. Ueda, Phys. Rev. A 86, 023612 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    H. Saito, Y. Kawaguchi, M. Ueda, Phys. Rev. Lett. 96, 065302 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    K. Kudo, Y. Kawaguchi, Phys. Rev. A 91, 053609 (2015)ADSCrossRefGoogle Scholar
  21. 21.
    L.A. Williamson, P.B. Blakie, Phys. Rev. Lett. 116, 025301 (2016)ADSCrossRefGoogle Scholar
  22. 22.
    L.A. Williamson, P.B. Blakie, Phys. Rev. A 94, 023608 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    L.A. Williamson, P.B. Blakie, Phys. Rev. A 94, 063615 (2016)ADSCrossRefGoogle Scholar
  24. 24.
    L.A. Williamson, P.B. Blakie, Phys. Rev. Lett. 119, 255301 (2017)ADSCrossRefGoogle Scholar
  25. 25.
    L. Pitaevskii, S. Stringari, Bose–Einstein Condensation (Clarendon Press, London, 2003)zbMATHGoogle Scholar
  26. 26.
    P. Muruganandam, S.K. Adhikari, Comput. Phys. Commun. 180, 1888 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    C.J. Pethick, H. Smith, Bose–Einstein Condensation in Dilute Gases (Cambridge University Press, London, 2002)Google Scholar
  28. 28.
    F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)ADSCrossRefGoogle Scholar
  29. 29.
    H.Z.S. Kohaku, M. Ueda, Phys. Rev. A 96, 023628 (2017)ADSCrossRefGoogle Scholar
  30. 30.
    A.L. Fetter, A.A. Svidzinsky, J. Phys.: Condens. Matter 13, R135 (2001)ADSGoogle Scholar
  31. 31.
    A.L. Fetter, Rev. Mod. Phys. 81, 647 (2009)ADSCrossRefGoogle Scholar
  32. 32.
    J.E. Williams, M.J. Holland, Nature 401, 568 (1999)ADSCrossRefGoogle Scholar
  33. 33.
    M.R. Matthews, B.P. Anderson, P.C. Haljan, D.S. Hall, C.E. Wieman, E.A. Cornell, Phys. Rev. Lett. 83, 2498 (1999)ADSCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Physics and Materials ScienceHenan Normal UniversityXinxiangChina

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