The European Physical Journal B

, Volume 68, Issue 3, pp 435–443 | Cite as

Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential

  • X. Deng
  • R. Citro
  • E. Orignac
  • A. MinguzziEmail author


Using exact diagonalisation and Density Matrix Renormalisation group (DMRG) approach we analyse the transition to a localised state of a weakly interacting quasi-1D Bose gas subjected to a quasiperiodic potential. The analysis is performed by calculating the superfluid fraction, density profile, momentum distribution and visibility for different periodicities of the second lattice and in the presence (or not) of a weak repulsive interaction. It is shown that the transition is sharper towards the maximally incommensurate ratio between the two lattice periodicities, and shifted to higher values of the second lattice strength by weak repulsive interactions. We also relate our results to recent experiments.


03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations 71.23.An Theories and models; localized states 68.65.Cd Superlattices 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. O. Morsch, M. Oberthaler, Rev. Mod. Phys. 78, 179 (2006)Google Scholar
  2. R.P. Feynman, Int. J. Theor. Phys. 21, 467 (1982)Google Scholar
  3. P.W. Anderson, Phys. Rev. 109, 1492 (1958)Google Scholar
  4. M.P. Van Albada, A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985)Google Scholar
  5. D.S. Wiersma, P. Bartolini, A. Lagendijk, R. Righini, Nature 390, 671 (1997)Google Scholar
  6. M. Störzer, P. Gross, C.M. Aegerter, G. Maret, Phys. Rev. Lett. 96, 063904 (2006)Google Scholar
  7. H. Hu, A. Strybulevich, J.H. Page, S.E. Skipetrov, B.A. van Tiggelen, Nature Phys. 4, 945 (2008)Google Scholar
  8. P.A. Lee, T.V. Ramakhrishnan, Rev. Mod. Phys. 57, 287 (1985)Google Scholar
  9. F. Albergamo, J. Bossy, J.V. Pearce, H. Schober, H.R. Glyde, Phys. Rev. B 76, 064503 (2007)Google Scholar
  10. A. van Oudenaarden, S.J.K. Várdy, J.E. Mooij, Phys. Rev. Lett. 77, 4257 (1996)Google Scholar
  11. B. Damski, J. Zakrzewski, L. Santos, P. Zoller, M. Lewenstein, Phys. Rev. Lett. 91, 080403 (2003)Google Scholar
  12. J.E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, M. Inguscio, Phys. Rev. Lett. 95, 070401 (2005)Google Scholar
  13. L. Fallani, J.E. Lye, V. Guarrera, C. Fort, M. Inguscio, Phys. Rev. Lett. 98, 130404 (2007)Google Scholar
  14. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, A. Aspect, Nature 453, 891 (2008)Google Scholar
  15. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature 453, 895 (2008)Google Scholar
  16. R.B. Diener, G.A. Georgakis, J. Zhong, M. Raizen, Q. Niu, Phys. Rev. A 64, 033416 (2001)Google Scholar
  17. D.R. Grempel, S. Fishman, R.E. Prange, Phys. Rev. Lett. 49, 833 (1982)Google Scholar
  18. J.B. Sokoloff, Phys. Rep. 126, 189 (1985)Google Scholar
  19. P.G. Harper, Proc. Phys. Soc. London A 68, 874 (1955)Google Scholar
  20. S. Aubry, in Solitons and Condensed Matter Physics, edited by A. R. Bishop, T. Schneider (Springer, New York, 1978); S. Aubry, G. André, Ann. Isr. Phys. Soc. 3, 133 (1980); S. Aubry, J. Phys. (Paris) 44, 147 (1983)Google Scholar
  21. D.R. Hofstadter, Phys. Rev. B 14, 2239 (1976)Google Scholar
  22. S.Y. Jitomirskaya, Ann. Math. 150, 1159 (1999)Google Scholar
  23. N.F. Mott, W.D. Twose, Adv. Phys. 10, 107 (1961)Google Scholar
  24. T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, M. Lewenstein, Phys. Rev. Lett. 95, 170411 (2005); T. Schulte, S. Drenkelforth, J. Kruse, R. Tiemeyer, K. Sacha, J. Zakrzewski, M. Lewenstein, W. Ertmer, J.J. Arlt, New J. Phys. 8, 230 (2006)Google Scholar
  25. T. Roscilde, Phys. Rev. A 77, 063605 (2008)Google Scholar
  26. T Roscilde, e-print arXiv:0804.2769 Google Scholar
  27. M.P. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher, Phys. Rev. B 40, 546 (1989)Google Scholar
  28. T. Giamarchi, H.J. Schulz, Phys. Rev. B 37, 325 (1988)Google Scholar
  29. C. Doty, D.S. Fisher, Phys. Rev. B 45, 2167 (1992)Google Scholar
  30. K. Runge, G.T. Zimanyi, Phys. Rev. B 49, 15212 (1994)Google Scholar
  31. G.G. Batrouni, R.T. Scalettar, Phys. Rev. B 46, 9051 (1992)Google Scholar
  32. B.V. Svistunov, Phys. Rev. B 54, 16131 (1996), N.V. Prokof’ev, B.V. Svistunov, Phys. Rev. Lett. 80, 4355 (1998)Google Scholar
  33. J.K. Freericks, H. Monien, Phys. Rev. B 53, 2691 (1996)Google Scholar
  34. P. Schmitteckert, T. Schulze, C. Schuster, P. Schwab, U. Eckern, Phys. Rev. Lett. 80, 560 (1998)Google Scholar
  35. G. Roux, T. Barthel, I.P. McCulloch, C. Kollath, U. Schollwoeck, T. Giamarchi, Phys. Rev. A 78, 023628 (2008)Google Scholar
  36. X. Deng, R. Citro, A. Minguzzi, E. Orignac, Phys. Rev. A 78, 013625 (2008)Google Scholar
  37. D. Jaksch et al., Phys. Rev. Lett. 81, 3108 (1998)Google Scholar
  38. H.P. Buechler, G. Blatter, W. Zwerger, Phys. Rev. Lett. 90, 130401 (2003)Google Scholar
  39. I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 50, 885 (2008)Google Scholar
  40. J.E. Lye, L. Fallani, C. Fort, V. Guarrera, M. Modugno, D.S. Wiersma, M. Inguscio, Phys. Rev. A 75, 061603(R) (2007)Google Scholar
  41. D.J. Thouless, Phys. Rep. 13, 93 (1974)Google Scholar
  42. S.R. White, Phys. Rev. Lett. 69, 2863 (1992); S.R. White, Phys. Rev. B 48, 10345 (1993)Google Scholar
  43. U. Schollwoeck, Rev. Mod. Phys. 77, 259 (2005); R.M. Noack, S. Manmara AIP Conf. Proc. 789, 93 (2005); K. Hallberg, Adv. Phys. 55, 477 (2006)Google Scholar
  44. M.N. Barber in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic Press, New York, 1983), Vol. 8Google Scholar
  45. The presence of a shallow trapping potential would not alter the conclusions of our analysisGoogle Scholar
  46. F.D.M. Haldane, Phys. Rev. Lett. 81, 1840 (1981)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Université Joseph Fourier, Laboratoire de Physique et Modélisation des Mileux Condensés, CNRS B.P. 166GrenobleFrance
  2. 2.Department of Physics “E.R. Caianiello” and C.N.I.S.M.Università di SalernoSalernoItaly
  3. 3.Université de Lyon, Laboratoire de Physique de l’École Normale Supérieure de Lyon, CNRS UMR5672Lyon Cedex 07France

Personalised recommendations