Advertisement

Journal of Low Temperature Physics

, Volume 194, Issue 1–2, pp 46–75 | Cite as

New Deep Superfluid Phases of Spin-1 Bosons in Optical Lattice

  • Aliaa G. Mohamed
  • M. F. Eissa
  • Mohamed MobarakEmail author
Article
First Online:
  • 31 Downloads

Abstract

We analyse theoretically a spin-1 Bose gas loaded into a three-dimensional optical lattice in order to emerge different superfluid phases with external magnetic field. To achieve this, we generalize the mean-field perturbation theory up to the sixth hopping order for the underlying spin-1 Bose–Hubbard model. Our results indicate that the condensate density can be valid deep in the superfluid phase in comparison with that of the fourth hopping order. At zero temperature, new deep superfluid phases for an anti-ferromagnetic interaction are determined in the presence of the external magnetic field. Moreover, we find the second-order quantum phase transition between Mott insulator and superfluid phase for both ferromagnetic and anti-ferromagnetic interactions. Within the anti-ferromagnetic interaction, the transitions between respective superfluid phases can be of the first order.

Keywords

Spinor Bose gas Bose–Hubbard model Superfluid–Mott- insulator transition Optical lattice 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

Support and Project Finance Office of Beni-Suef University is greatly appreciated for the financial support of this work.

References

  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.
    C.C. Bradley, C.A. Sackett, J.J. Tollett, R.G. Hulet, Phys. Rev. Lett. 75, 1687 (1995)ADSCrossRefGoogle Scholar
  4. 4.
    C.C. Bradley, C.A. Sackett, R.G. Hulet, Phys. Rev. Lett. 78, 985 (1997)ADSCrossRefGoogle Scholar
  5. 5.
    R. Feynman, Int. J. Theor. Phys. 21, 467 (1982)CrossRefGoogle Scholar
  6. 6.
    M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    M. Greiner, O. Mandel, T.W. Hänsch, I. Bloch, Nature 419, 51 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    J.K. Freericks, H. Monien, Phys. Rev. B 53, 2691 (1996)ADSCrossRefGoogle Scholar
  9. 9.
    D. van Oosten, P. Straten, H.T.C. Stoof, Phys. Rev. A 63, 053601 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    F.E.A. dos Santos, A. Pelster, Phys. Rev. A 79, 013614 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    B. Bradlyn, F.E.A. dos Santos, A. Pelster, Phys. Rev. A 79, 013615 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    N. Teichmann, D. Hinrichs, M. Holthaus, A. Eckardt, Phys. Rev. B 79, 100503 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    D. Hinrichs, A. Pelster, M. Holthaus, Appl. Phys. B 113, 57–67 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    B. Capogrosso-Sansone, N.V. Prokof’ev, B.V. Svistunov, Phys. Rev. B 75, 134302 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    B. Capogrosso-Sansone, S.G. Söyler, N. Prokof’ev, B. Svistunov, Phys. Rev. A 77, 015602 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    M.P.A. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher, Phys. Rev. B 40, 546 (1989)ADSCrossRefGoogle Scholar
  17. 17.
    D. Jaksch, C. Bruder, J.I. Cirac, C.W. Gardiner, P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)ADSCrossRefGoogle Scholar
  18. 18.
    S. Sachdev, Quantum Phase Transitions, 2nd edn. (Cambridge University Press, Cambridge, 2011)CrossRefzbMATHGoogle Scholar
  19. 19.
    G. Modugno, F. Ferlaino, R. Heidemann, G. Roati, M. Inguscio, Phys. Rev. A 68, 011601(R) (2003)ADSCrossRefGoogle Scholar
  20. 20.
    A. Albus, F. Illuminati, J. Eisert, Phys. Rev. A 68, 023606 (2003)ADSCrossRefGoogle Scholar
  21. 21.
    H.P. Büchler, G. Blatter, Phys. Rev. Lett. 91, 130404 (2003)CrossRefGoogle Scholar
  22. 22.
    M. Lewenstein, L. Santos, M. Baranov, H. Fehrmann, Phys. Rev. Lett. 92, 050401 (2004)ADSCrossRefGoogle Scholar
  23. 23.
    T. Wang, X.-F. Zhang, S. Eggert, A. Pelster, Phys. Rev. A 87, 063615 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    X.-F. Zhang, T. Wang, S. Eggert, A. Pelster, Phys. Rev. B 92, 014512 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    I. Bloch, Nature 453, 1016 (2008)ADSCrossRefGoogle Scholar
  26. 26.
    K.V. Krutitsky, A. Pelster, R. Graham, New J. Phys. 8, 187 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, Massimo Inguscio, Nature 453, 895 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    U. Bissbort, R. Thomale, W. Hofstetter, Phys. Rev. A 81, 063643 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    M. Lewenstein, A. Sanpera, V. Ahufinger, Ultracold Atoms in Optical Lattices, Simulating Quantum Many-Body Systems (Oxford University Press, Oxford, 2012)CrossRefzbMATHGoogle Scholar
  30. 30.
    K.D. McAlpine, S. Paganelli, S. Ciuchi, A. Sanpera, G. De Chiara, Phys. Rev. B 95, 235128 (2017)ADSCrossRefGoogle Scholar
  31. 31.
    T.-L. Ho, Phys. Rev. Lett. 81, 742 (1998)ADSCrossRefGoogle Scholar
  32. 32.
    T. Ohmi, K. Machida, J. Phys. Soc. Jpn. 67, 1822 (1998)ADSCrossRefGoogle Scholar
  33. 33.
    J. Stenger, S. Inouye, D.M. Stamper-Kurn, H.-J. Miesner, A.P. Chikkatur, W. Ketterle, Nature 396, 345 (1999)ADSCrossRefGoogle Scholar
  34. 34.
    D.M. Stamper-Kurn, M.R. Andrews, A.P. Chikkatur, S. Inouye, H.J. Miesner, J. Stenger, W. Ketterle, Phys. Rev. Lett. 80, 2027 (1998)ADSCrossRefGoogle Scholar
  35. 35.
    M.-S. Chang, C.D. Hamley, M.D. Barrett, J.A. Sauer, K.M. Fortier, W. Zhang, L. You, M.S. Chapman, Phys. Rev. Lett. 92, 140403 (2004)ADSCrossRefGoogle Scholar
  36. 36.
    H. Schmaljohann, M. Erhard, J. Kronjäger, M. Kottke, S. van Staa, L. Cacciapuoti, J.J. Arlt, K. Bongs, K. Sengstock, Phys. Rev. Lett. 92, 040402 (2004)ADSCrossRefGoogle Scholar
  37. 37.
    T. Kuwamoto, T. Araki, T. Eno, T. Hirano, Phys. Rev. A 69, 063604 (2004)ADSCrossRefGoogle Scholar
  38. 38.
    M. Uchiyama, J. Ieda, M. Wadati, J. Low Temp. Phys. 148, 399–404 (2007)ADSCrossRefGoogle Scholar
  39. 39.
    J.M. McGuirk, H.J. Lewandowski, D.M. Harber, T. Nikuni, J.E. Williams, E.A. Cornell, Phys. Rev. Lett. 89, 090402 (2002)ADSCrossRefGoogle Scholar
  40. 40.
    Q. Gu, K. Bongs, K. Sengstock, Phys. Rev. A 70, 063609 (2004)ADSCrossRefGoogle Scholar
  41. 41.
    C.K. Law, H. Pu, N.P. Bigelow, Phys. Rev. Lett. 81, 5257 (1998)ADSCrossRefGoogle Scholar
  42. 42.
    H. Pu, C.K. Law, S. Raghavan, J.H. Eberly, N.P. Bigelow, Phys. Rev. A 60, 1463 (1999)ADSCrossRefGoogle Scholar
  43. 43.
    A. Widera, F. Gerbier, S. Fölling, T. Gericke, O. Mandel, I. Bloch, Phys. Rev. Lett. 95, 190405 (2005)ADSCrossRefGoogle Scholar
  44. 44.
    A. Widera, F. Gerbier, S. Fölling, T. Gericke, O. Mandel, I. Bloch, New J. Phys. 8, 152 (2006)ADSCrossRefGoogle Scholar
  45. 45.
    C. Becker, P. Soltan-Panahi, J. Kronjäger, S. Dörscher, K. Bongs, K. Sengstock, New J. Phys. 12, 065025 (2010)ADSCrossRefGoogle Scholar
  46. 46.
    E. Demler, F. Zhou, Phys. Rev. Lett. 88, 163001 (2002)ADSCrossRefGoogle Scholar
  47. 47.
    S. Tsuchiya, S. Kurihara, T. Kimura, Phys. Rev. A 70, 043628 (2004)ADSCrossRefGoogle Scholar
  48. 48.
    N. Uesugi, M. Wadati, J. Phys. Soc. Jpn. 72, 1041 (2003)ADSCrossRefGoogle Scholar
  49. 49.
    M. Rizzi, D. Rossini, G. De Chiara, S. Montangero, R. Fazio, Phys. Rev. Lett. 95, 240404 (2005)ADSCrossRefGoogle Scholar
  50. 50.
    A. Imambekov, M. Lukin, E. Demler, Phys. Rev. A 68, 063602 (2003)ADSCrossRefGoogle Scholar
  51. 51.
    A.A. Svidzinsky, S.T. Chui, Phys. Rev. A 68, 043612 (2003)ADSCrossRefGoogle Scholar
  52. 52.
    M. Mobarak, A. Pelster, Laser Phys. Lett. 10, 115501 (2013)ADSCrossRefGoogle Scholar
  53. 53.
    M. Mobarak, A. Pelster, arXiv:1310.0600
  54. 54.
    A. Hoffmann, Bosonen im optischen Gitter. Diploma thesis, Freie Universität Berlin, Germany (2007)Google Scholar
  55. 55.
    G.G. Batrouni, V.G. Rousseau, R.T. Scalettar, Phys. Rev. Lett. 102, 140402 (2009)ADSCrossRefGoogle Scholar
  56. 56.
    M. Ohliger, Thermodynamic properties of spinor bosons in optical lattices. Diploma thesis, Freie Universität Berlin (2008)Google Scholar
  57. 57.
    T. Kimura, S. Tsuchiya, M. Yamashita, S. Kurihara, J. Phys. Soc. Jpn. 75, 074601 (2006)ADSCrossRefGoogle Scholar
  58. 58.
    S. Paganelli, M. Łącki, V. Ahufinger, J. Zakrzewski, A. Sanpera, J. Low Temp. Phys. 165, 227 (2011)ADSCrossRefGoogle Scholar
  59. 59.
    T. Kimura, S. Tsuchiya, M. Yamashita, S. Kurihara, Phys. Rev. Lett. 94, 110403 (2005)ADSCrossRefGoogle Scholar
  60. 60.
    J. Liu, J. Wu, Y. Li, arXiv:1711.05470v1

Copyright information

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

Authors and Affiliations

  • Aliaa G. Mohamed
    • 1
  • M. F. Eissa
    • 1
  • Mohamed Mobarak
    • 1
    Email author
  1. 1.Department of Physics, Faculty of ScienceBeni-Suef UniversityBeni SuefEgypt

Personalised recommendations