Skip to main content
SpringerLink
Log in

Infrared stability of ground states of spin-orbit coupled Bose–Einstein condensates

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We proved that the spin-1 Bose–Einstein condensate with one-dimensional spin-orbit coupling at the tricritical point is stable against excitations of Goldstone modes. The dispersion relations of these modes are anisotropic and cubic in some directions in the momentum space, which are much softer than the ordinary ones with linear form. A particular scaling form of the quantum depletions fraction on spin-orbit coupling strength is found, which is due to the special form of the dispersion relations of the Goldstone modes.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S.N. Bose, Z. Phys. 26, 178 (1924)

    Article  ADS  Google Scholar 

  2. A. Einstein, Sitzungsber. Kgl. Preuss, Akad. Wiss. 1924, 261 (1924)

    Google Scholar 

  3. A. Einstein, Sitzungsber. Kgl. Preuss, Akad. Wiss. 1925, 3 (1925)

    Google Scholar 

  4. F. London, Nature (London) 141, 643 (1938)

    Article  ADS  Google Scholar 

  5. P. Sokol, in Bose Einstein Condensation, edited by A. Griffin, D.W. Snoke, S. Stringari (Cambridge University Press, Cambridge, 1995), p. 51

  6. M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)

    Article  ADS  Google Scholar 

  7. 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)

    Article  ADS  Google Scholar 

  8. C.C. Bradley, C.A. Sackett, J.J. Tollett, R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995)

    Article  ADS  Google Scholar 

  9. Y.J. Lin, K. Jiménez-García, I.B. Spielman, Nature (London) 471, 83 (2011)

    Article  ADS  Google Scholar 

  10. J.-Y. Zhang, S.-C. Ji, Z. Chen, L. Zhang, Z.-D. Du, B. Yan, G.-S. Pan, B. Zhao, Y.-J. Deng, H. Zhai, S. Chen, J.-W. Pan, Phys. Rev. Lett. 109, 115301 (2012)

    Article  ADS  Google Scholar 

  11. P. Wang, Z.-Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, J. Zhang, Phys. Rev. Lett. 109, 095301 (2012)

    Article  ADS  Google Scholar 

  12. L.W. Cheuk, A.T. Sommer, Z. Hadzibabic, T. Yefsah, W.S. Bakr, M.W. Zwierlein, Phys. Rev. Lett. 109, 095302 (2012)

    Article  ADS  Google Scholar 

  13. J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature (London) 468, 545 (2010)

    Article  ADS  Google Scholar 

  14. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, K. West, Science, 316 1007 (2007)

    Article  ADS  Google Scholar 

  15. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J.M.J. Keeling, F.M. Marchetti, M.H. Szymańska, R. André, J.L. Staehli, V. Savona, P.B. Littlewood, B. Deveaud, Le Si Dang, Nature (London) 443, 409 (2010)

    Article  ADS  Google Scholar 

  16. A. Oosawa, M. Ishii, H. Tanaka, J. Phys.: Condens. Matter 11, 265 (1999)

    ADS  Google Scholar 

  17. T. Nikuni, M. Oshikawa, A. Oosawa, H. Tanaka, Phys. Rev. Lett. 84, 5868 (2000)

    Article  ADS  Google Scholar 

  18. V. Zapf, M. Jaime, C.D. Batista, Rev. Mod. Phys. 86, 563 (2014)

    Article  ADS  Google Scholar 

  19. L.D. Landau, E.M. Lifshitz, St tisticheski Fizikin Russian, Fizmatgiz, Moscow, 1951

  20. O. Penrose, Philos. Mag. 42, 1373 (1951)

    Article  Google Scholar 

  21. O. Penrose, L. Onsager, Phys. Rev. 104, 576 (1956)

    Article  ADS  Google Scholar 

  22. J. Goldstone, Nuovo Cimento 19, 154 (1961)

    Article  MathSciNet  Google Scholar 

  23. J. Goldstone, A. Salam, S. Weinberg, Phys. Rev. 127, 965 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  24. E.M. Lifshitz, L.P. Pitaevskii, in Landau and Lifshitz Course of Theoretical Physics: Statistical Physics (Butterworth-, Oxford, 1980), Pt. 2

  25. R.P. Feynman, in Progress in Low Temperature Physics, edited by C.J. Gorter (North Holland, Amsterdam, 1955), Vol. 1, Chapter II, pp. 17–53

  26. G.E. Astrakharchik, L.P. Pitaevskii, Phys. Rev. A 70, 013608 (2004)

    Article  ADS  Google Scholar 

  27. L.P. Pitaevskii, JETP Lett. 45, 185 (1987)

    ADS  Google Scholar 

  28. L. Pitaevskii, S. Stringari, J. Low Temp. Phys. 85, 377 (1991)

    Article  ADS  Google Scholar 

  29. J.Y. Zhang, S.C. Ji, Z. Chen, L. Zhang, Z.D. Du, B. Yan, G.S. Pan, B. Zhao, Y.J. Deng, H. Zhai, S. Chen, J.W. Pan, Phys. Rev. Lett. 109, 115301 (2012)

    Article  ADS  Google Scholar 

  30. P. Wang, Z.Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, J. Zhang, Phys. Rev. Lett. 109, 095301 (2012)

    Article  ADS  Google Scholar 

  31. L.W. Cheuk, A.T. Sommer, Z. Hadzibabic, T. Yefsah, W.S. Bakr, M.W. Zwierlein, Phys. Rev. Lett. 109, 095302 (2012)

    Article  ADS  Google Scholar 

  32. L. Huang, Z. Meng, P. Wang et al., Nat. Phys. 12, 540 (2016)

    Article  Google Scholar 

  33. Z. Wu, L. Zhang, W. Sun, X.R. Xu, B.Z. Wang, S.C. Ji, Y. Deng, S. Chen, X.J. Liu, J.W. Pan, Science 354, 6308 (2016)

    Google Scholar 

  34. H. Zhai, Int. J. Mod. Phys. B 26, 1230001 (2012)

    Article  ADS  Google Scholar 

  35. X. Zhou, Y. Li, Z. Cai, C. Wu, J. Phys. B: At. Mol. Opt. Phys. 46, 134001 (2013)

    Article  ADS  Google Scholar 

  36. N. Goldman, I.B. Spielman, Rep. Prog. Phys. 77, 126401 (2014)

    Article  ADS  Google Scholar 

  37. H. Zhai, Rep. Prog. Phys. 78, 026001 (2015)

    Article  ADS  Google Scholar 

  38. E.I. Rashba, Fiz. Tverd. Tela 2, 1224 (1960)

    Google Scholar 

  39. E.I. Rashba, Sov. Phys. Solid State 2, 1109 (1960)

    Google Scholar 

  40. R. Barnett, G.R. Boyd, V. Galitski, Phys. Rev. Lett. 109, 235308 (2012)

    Article  ADS  Google Scholar 

  41. P.S. He, R. Liao, W.M. Liu, Phys. Rev. A 86, 043632 (2012)

    Article  ADS  Google Scholar 

  42. P.S. He, W.L. You, W.M. Liu, Phys. Rev. A 87, 063603 (2013)

    Article  ADS  Google Scholar 

  43. T. Ozawa, G. Baym, Phys. Rev. Lett. 109, 025301 (2012)

    Article  ADS  Google Scholar 

  44. Z.Q. Yu, Phys. Rev. A 93, 033648 (2016)

    Article  ADS  Google Scholar 

  45. P.S. He, J. Zhao, A.C. Geng, D.H. Xu, R. Hu, Phys. Lett. A 377, 2207 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  46. N. Nagaosa, Quantum Field Theory in Condensed Matter Physics (Springer, Berlin, 1999)

  47. D.L. Campbell, R.M. Price, A. Putra, A. Valdés-Criel, D. Trypogeorgos, I.B. Spielman, Nat. Commun. 7, 10897 (2016)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Beijing Technology and Business University, Beijing, 100048, P.R. China

    Pei-Song He

  2. School of Physical Science and Technology, Soochow University, Suzhou, Jiangsu 215006, P.R. China

    Wen-Long You

Authors
  1. Pei-Song He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen-Long You
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Pei-Song He or Wen-Long You.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, PS., You, WL. Infrared stability of ground states of spin-orbit coupled Bose–Einstein condensates. Eur. Phys. J. D 72, 205 (2018). https://doi.org/10.1140/epjd/e2018-90325-2

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2018-90325-2

Keywords

Search

Navigation