Skip to main content
Log in

Superfluid-Insulator Transition of a Bose–Einstein Condensation in a Periodic Potential and Its Interference Pattern

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript


Recent experiments have succeeded in observing the superfluid-Mott insulator quantum phase transition of an alkali atomic Bose–Einstein condensate in an optical lattice potential. Motivated by this work, we studied the two-dimensional Bose gas in a periodic potential by analyzing the Gross–Pitaevskii equation. We found evidence of a superfluid-insulator transition that occurs as the potential depth of the lattice is increased. For the periodic potential, the phase of the macroscopic wave function in the ground state is localized in each potential minimum. Also, according to the resugts using the Hartree–Fock–Bogoliubov equation, an energy gap appears in the lowest excitation state. We then added a parabolic trapping potential to the periodic potential and studied how the dynamics of the wave function and its interference pattern depend on the initial ground state. For the initial ground state localized by the deep periodic potential, the wave function oscillates in the central potential minimum after removing only the trapping potential. After turning off both the trapping and periodic potentials, the wave packets with periodicity escape from the condensate.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others


  1. F. S. Cataliotti,S. Burger,C. Fort,P. Maddaloni,F. Minardi,A. Trombettoni,A. Smerzi and M. Inguscio,Science 293, 843 (2001).

    Google Scholar 

  2. M. Greiner,I. Bloch,O. Mandel,T. W. Hansch and T. Esslinger, Phys. Rev. Lett. 87, 160405 (2001).

    Google Scholar 

  3. M. Greiner,O. Mandel,T. Esslinger,T. W. Hansch and I. Bloch,Nature 415, 39 (2002).

    Google Scholar 

  4. M. Greiner,O. Mandel,T. W. Hansch and I. Bloch,Nature 419 51 (2002).

    Google Scholar 

  5. M. P. A. Fisher,P. B. Weichman,G. Grinstein and D. S. Fisher, Phys. Rev. B 40, 546 (1989).

    Google Scholar 

  6. E. P. Gross, J. Math. Phys. 4 195 (1963).

    Google Scholar 

  7. L. P. Pitaevskii, Soviet Phys.-JETP 13 451 (1961).

    Google Scholar 

  8. T. R. Taha and M. J. Ablowitz, J. Comput. Phys. 55 203 (1984).

    Google Scholar 

  9. A. Griffin, Phys. Rev. B 53, 9341 (1996).

    Google Scholar 

  10. S. Stringari, Bose-Einstein Condensation (Cambridge University Press, (1995), edited by A. Griffe,D. W. Snoke, and S. Stringari,86.

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Kobayashi, M., Tsubota, M. Superfluid-Insulator Transition of a Bose–Einstein Condensation in a Periodic Potential and Its Interference Pattern. Journal of Low Temperature Physics 134, 665–670 (2004).

Download citation

  • Issue Date:

  • DOI: