Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Direct observation of Anderson localization of matter waves in a controlled disorder


In 1958, Anderson predicted the localization1 of electronic wavefunctions in disordered crystals and the resulting absence of diffusion. It is now recognized that Anderson localization is ubiquitous in wave physics2 because it originates from the interference between multiple scattering paths. Experimentally, localization has been reported for light waves3,4,5,6,7, microwaves8,9, sound waves10 and electron gases11. However, there has been no direct observation of exponential spatial localization of matter waves of any type. Here we observe exponential localization of a Bose–Einstein condensate released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle12. We operate in a regime of pure Anderson localization, that is, with weak disorder—such that localization results from many quantum reflections of low amplitude—and an atomic density low enough to render interactions negligible. We directly image the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary, exponentially localized wavefunction—a direct signature of Anderson localization. We extract the localization length by fitting the exponential wings of the profiles, and compare it to theoretical calculations. The power spectrum of the one-dimensional speckle potentials has a high spatial frequency cutoff, causing exponential localization to occur only when the de Broglie wavelengths of the atoms in the expanding condensate are greater than an effective mobility edge corresponding to that cutoff. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref. 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Observation of exponential localization.
Figure 2: Stationarity of the localized profile.
Figure 3: Localization length versus amplitude of the disordered potential.
Figure 4: Algebraic and exponential regimes in a one-dimensional speckle potential.


  1. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958)

    ADS  CAS  Article  Google Scholar 

  2. Van Tiggelen, B. in Wave Diffusion in Complex Media 1998 (ed. Fouque, J. P.) 1–60 (Kluwer, Dordrecht, 1999)

    Book  Google Scholar 

  3. Wiersma, D. S., Bartolini, P., Lagendijk, A. & Righini, R. Localization of light in a disordered medium. Nature 390, 671–673 (1997)

    ADS  CAS  Article  Google Scholar 

  4. Scheffold, F., Lenke, R., Tweer, R. & Maret, G. Localization or classical diffusion of light? Nature 398, 206–270 (1999)

    ADS  CAS  Article  Google Scholar 

  5. Störzer, M., Gross, P., Aegerter, C. M. & Maret, G. Observation of the critical regime near Anderson localization of light. Phys. Rev. Lett. 96, 063904 (2006)

    ADS  Article  Google Scholar 

  6. Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007)

    ADS  CAS  Article  Google Scholar 

  7. Lahini, Y. et al. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008)

    ADS  Article  Google Scholar 

  8. Dalichaouch, R., Armstrong, J. P., Schultz, S., Platzman, P. M. & McCall, S. L. Microwave localization by two-dimensional random scattering. Nature 354, 53–55 (1991)

    ADS  Article  Google Scholar 

  9. Chabanov, A. A., Stoytchev, M. & Genack, A. Z. Statistical signatures of photon localization. Nature 404, 850–853 (2000)

    ADS  CAS  Article  Google Scholar 

  10. Weaver, R. L. Anderson localization of ultrasound. Wave Motion 12, 129–142 (1990)

    Article  Google Scholar 

  11. Akkermans, E. & Montambaux, G. Mesoscopic Physics of Electrons and Photons (Cambridge Univ. Press, Cambridge, UK, 2006)

    MATH  Google Scholar 

  12. Goodman, J. W. Speckle Phenomena in Optics (Roberts, Greenwood Village, Colorado, 2007)

    Google Scholar 

  13. Sanchez-Palencia, L. et al. Anderson localization of expanding Bose-Einstein condensates in random potentials. Phys. Rev. Lett. 98, 210401 (2007)

    ADS  CAS  Article  Google Scholar 

  14. Giamarchi, T. & Schulz, H. J. Anderson localization and interactions in one-dimensional metals. Phys. Rev. B 37, 325–340 (1988)

    ADS  CAS  Article  Google Scholar 

  15. Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989)

    ADS  CAS  Article  Google Scholar 

  16. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold atoms. Rev. Mod. Phys.. (in the press); preprint at 〈〉 (2007)

  17. Lewenstein, M. et al. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007)

    ADS  Article  Google Scholar 

  18. Damski, B., Zakrzewski, J., Santos, L., Zoller, P. & Lewenstein, M. Atomic Bose and Anderson glasses in optical lattices. Phys. Rev. Lett. 91, 080403 (2003)

    ADS  CAS  Article  Google Scholar 

  19. Clément, D. et al. Suppression of transport of an interacting elongated Bose–Einstein condensate in a random potential. Phys. Rev. Lett. 95, 170409 (2005)

    ADS  Article  Google Scholar 

  20. Fort, C. et al. Effect of optical disorder and single defects on the expansion of a Bose–Einstein condensate in a one-dimensional waveguide. Phys. Rev. Lett. 95, 170410 (2005)

    ADS  CAS  Article  Google Scholar 

  21. Schulte, T. et al. Routes towards Anderson-like localization of Bose–Einstein condensates in disordered optical lattices. Phys. Rev. Lett. 95, 170411 (2005)

    ADS  CAS  Article  Google Scholar 

  22. Clément, D. et al. Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle. N. J. Phys. 8 165 doi: 10.1088/1367-2630/8/8/165 (2006)

    CAS  Article  Google Scholar 

  23. Moore, J. L., Robinson, J. C., Bharucha, C., Williams, P. E. & Raizen, M. G. Observation of dynamical localization in atomic momentum transfer: A new testing ground for quantum chaos. Phys. Rev. Lett. 73, 2974–2977 (1994)

    ADS  CAS  Article  Google Scholar 

  24. Chabé, J. et al. Experimental observation of the Anderson transition with atomic matter waves. Preprint available at 〈〉 (2007)

  25. Guerin, W. et al. Guided quasicontinuous atom laser. Phys. Rev. Lett. 97, 200402 (2006)

    ADS  CAS  Article  Google Scholar 

  26. Bilas, N. & Pavloff, N. Anderson localization of elementary excitations in a one-dimensional Bose–Einstein condensate. Eur. Phys. J. D 40, 387–397 (2006)

    ADS  CAS  Article  Google Scholar 

  27. Lugan, P., Clément, D., Bouyer, P., Aspect, A. & Sanchez-Palencia, L. Anderson localization of Bogolyubov quasiparticles in interacting Bose–Einstein condensates. Phys. Rev. Lett. 99, 180402 (2007)

    ADS  CAS  Article  Google Scholar 

  28. Fallani, L., Lye, J. E., Guarrera, V., Fort, C. & Inguscio, M. Ultracold atoms in a disordered crystal of light: towards a Bose glass. Phys. Rev. Lett. 98, 130404 (2007)

    ADS  CAS  Article  Google Scholar 

  29. Lugan, P. et al. Ultracold Bose gases in 1D-disorder: from Lifshits glass to Bose–Einstein condensate. Phys. Rev. Lett. 98, 170403 (2007)

    ADS  Article  Google Scholar 

  30. Sanpera, A., Kantian, A., Sanchez-Palencia, L., Zakrzewski, J. & Lewenstein, M. Atomic Fermi–Bose mixtures in inhomogeneous and random optical lattices: from Fermi glass to quantum spin glass and quantum percolation. Phys. Rev. Lett. 93, 040401 (2004)

    ADS  CAS  Article  Google Scholar 

  31. Kuhn, R. C., Miniatura, C., Delande, D., Sigwarth, O. & Müller, C. A. Localization of matter waves in two-dimensional disordered optical potentials. Phys. Rev. Lett. 95, 250403 (2005)

    ADS  CAS  Article  Google Scholar 

  32. Skipetrov, S. E., Minguzzi, A., van Tiggelen, B. A. & Shapiro, B. Anderson localization of a Bose-Einstein condensate in a 3D random potential. Phys. Rev. Lett. 100, 165301 (2008)

    ADS  CAS  Article  Google Scholar 

Download references


The authors are indebted to P. Chavel, T. Giamarchi, M. Lewenstein and G. Shlyapnikov for many discussions, to P. Georges and G. Roger for assistance with the laser, and to F. Moron, A. Villing and G. Colas for technical assistance on the experimental apparatus. This research was supported by the Centre National de la Recherche Scientifique (CNRS), the Délégation Générale de l’Armement (DGA), the Ministère de l’Education Nationale, de la Recherche et de la Technologie (MENRT), the Agence Nationale de la Recherche (ANR), the Institut Francilien de Recherche sur les Atomes Froids (IFRAF) and IXSEA; by the STREP programme FINAQS of the European Union; and by the programme QUDEDIS of the European Science Foundation (ESF).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Philippe Bouyer.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Billy, J., Josse, V., Zuo, Z. et al. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 891–894 (2008).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing