Skip to main content
SpringerLink
Log in

Diffusion and localization of cold atoms in 3D optical speckle

  • Cold Matter and Quantum Gases
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract.

In this work we re-formulate and solve the self-consistent theory for localization to a Bose-Einstein condensate expanding in a 3D optical speckle. The long-range nature of the fluctuations in the potential energy, treated in the self-consistent Born approximation, make the scattering strongly velocity dependent, and its consequences for mobility edge and fraction of localized atoms have been investigated numerically.

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. A. Lagendijk, B.A. van Tiggelen, D.S. Wiersma, Phys. Today 62, 24 (2009)

    Article  Google Scholar 

  2. A. Aspect, M. Inguscio, Phys. Today 62, 30 (2009)

    Article  Google Scholar 

  3. P.W. Anderson, Phys. Rev. 109, 1492 (1958)

    Article  ADS  Google Scholar 

  4. B. Kramer, A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993)

    Article  ADS  Google Scholar 

  5. D.S. Wiersma, P. Bartolini, A. Lagendijk, R. Righini, Nature 390, 671 (1997)

    Article  ADS  Google Scholar 

  6. H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov, B.A. van Tiggelen, Nature Phys. 4, 945 (2008)

    Article  ADS  Google Scholar 

  7. J. Chabé, G. Lemarie, B. Gremaud, D. Delande, P. Szriftgiser, J. Garreau, Phys. Rev. Lett. 101, 255702 (2008)

    Article  ADS  Google Scholar 

  8. E. Abrahams, P.W. Anderson, D.C. Licciardello, T.V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979)

    Article  ADS  Google Scholar 

  9. J.T. Edwards, D. Thouless, J. Phys. C 5, 807 (1972)

    Article  ADS  Google Scholar 

  10. D. Vollhardt, P. Wölfle, Selfconsistent theory of Anderson Localization, in Electronic Phase Transitions, edited by W. Hanke, Ya.V. Kopaev (North-Holland, Amsterdam, 1992)

  11. H. Kroha, T. Kopp, P. Wölfle, Phys. Rev. B 41, 888 (1990)

    Article  ADS  Google Scholar 

  12. G. Roati et al., Nature 453, 895 (2008)

    Article  ADS  Google Scholar 

  13. J. Billy et al., Nature 453, 891 (2008)

    Article  ADS  Google Scholar 

  14. L. Sanchez-Palencia et al., Phys. Rev. Lett. 98, 210401 (2007)

    Article  ADS  Google Scholar 

  15. P. Lugan, A. Aspect, L. Sanchez-Palencia, D. Delande, B. Grémaud, C. Müller, C. Miniatura, Phys. Rev. A 80, 023605 (2009)

    Article  ADS  Google Scholar 

  16. R.C. Kuhn, C. Miniatura, D. Delande, O. Sigwarth, C.M. Müller, Phys. Rev. Lett. 98, 21041 (2007)

    Google Scholar 

  17. R.C. Kuhn, C. Miniatura, D. Delande, O. Sigwarth, C.M. Müller, New J. Phys. 9, 161 (2007)

    Article  ADS  Google Scholar 

  18. A. Lagendijk, B.A. Van Tiggelen, Phys. Rep. 270, 143 (1996). The Bethe-Salpeter equation is given by Eq. (4.65), the associated exact kinetic transport equation is Eq. (4.66).

    Article  ADS  Google Scholar 

  19. N.E. Cusack, The Physics of Structurally Disordered Matter (IOPP, 1987)

  20. S.E. Skipetrov, A. Minguzzi, B.A. Van Tiggelen, B. Shapiro, Phys. Rev. Lett. 100, 165301 (2008)

    Article  ADS  Google Scholar 

  21. G.D. Mahan, Many-Particle Physics, 3rd edn. (Kluwer/Plenum, 2000), see Section 8.1.2; equations (8.63-8.70) of this section lead to Eqs. (5) and (6) in this work. In first edition (Plenum, New York, 1981), see Section 7.1.C. Note that we do not perform the integral over the energy as in this reference, since the expanding bosons are not in thermal equilibrium and not subject to any thermal distribution.

  22. Yu.N. Barabanenkov, V.D. Ozrin, Phys. Lett. A 154, 38 (1991)

    Article  ADS  Google Scholar 

  23. B.A. van Tiggelen, D.S. Wiersma, A. Lagendijk, Europhys. Lett. 30, 1 (1995)

    Article  ADS  Google Scholar 

  24. B.A. van Tiggelen, A. Lagendijk, A. Tip, G.F. Reiter, Europhys. Lett. 15, 535 (1991). In this work the slightly different value 0.98 was obtained from a less rigorous moment expansion.

    Article  ADS  Google Scholar 

  25. E.N. Economou, C.M. Soukoulis, A.D. Zdetsis, Phys. Rev. B 30, 1686 (1984)

    Article  ADS  Google Scholar 

  26. Y. Castin, R. Dum, Phys. Rev. Lett. 77, 5315 (1996)

    Article  ADS  Google Scholar 

  27. R. Zimmermann, Ch. Schindler, Phys. Rev. B 80, 144202 (2009)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique et de Modélisation des Milieux Condensés, CNRS /Université Joseph Fourier, Maison des Magistères, BP 166, 38042, Grenoble Cedex 9, France

    A. Yedjour & B. A. Van Tiggelen

  2. Laboratoire de Physique des Plasmas, des Matériaux Conducteurs, et leurs Applications, Départment de Physique, Université des Sciences et de la Technologie d’Oran, USTO, 31000, Oran, Algeria

    A. Yedjour

Authors
  1. A. Yedjour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. A. Van Tiggelen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. A. Van Tiggelen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yedjour, A., Van Tiggelen, B. Diffusion and localization of cold atoms in 3D optical speckle. Eur. Phys. J. D 59, 249–255 (2010). https://doi.org/10.1140/epjd/e2010-00141-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjd/e2010-00141-5

Keywords

Search

Navigation