Three-dimensional localization of ultracold atoms in an optical disordered potential


In disordered media, quantum interference effects are expected to induce complete suppression of electron conduction. The phenomenon, known as Anderson localization, has a counterpart with classical waves that has been observed in acoustics, electromagnetism and optics, but a direct observation for particles remains elusive. Here, we report the observation of the three-dimensional localization of ultracold atoms in a disordered potential created by a speckle laser field. A phenomenological analysis of our data distinguishes a localized component of the resulting density profile from a diffusive component. The observed localization cannot be interpreted as the classical trapping of particles with energy below the classical percolation threshold in the disorder, nor can it be understood as quantum trapping in local potential minima. Instead, our data are compatible with the self-consistent theory of Anderson localization tailored to our system, involving a heuristic energy shift that offers scope for future interpretation.

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Figure 1: Experiment.
Figure 2: Evolution of the atomic cloud for two different amplitudes of the disorder.
Figure 3: Localized fraction versus disorder amplitude.
Figure 4: Diffusion coefficient versus disorder amplitude.
Figure 5: Evolution of the density profiles in a strong disorder (VR/h=680 Hz): experiment versus theory.


  1. 1

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

    ADS  Article  Google Scholar 

  2. 2

    Lagendijk, A., Van Tiggelen, B. A. & Wiersma, D. Fifty years of Anderson localization. Phys. Today 62, 24–29 (August 2009).

    Article  Google Scholar 

  3. 3

    Abrahams, E., Anderson, P. W., Licciardello, D. C. & Ramakrishnan, T. V. Scaling theory of localization: Absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673–676 (1979).

    ADS  Article  Google Scholar 

  4. 4

    Lee, P. A. & Ramakrishnan, T. V. Disordered electronic systems. Rev. Mod. Phys. 57, 287–337 (1985).

    ADS  Article  Google Scholar 

  5. 5

    Van Tiggelen, B. A. in Mathematical and Physical Sciences Vol. 531 (ed. Fouque, J.) 1–60 (Nato Advanced Science Institutes Series, Series C, Addison Wesley, 1999).

    Google Scholar 

  6. 6

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

    ADS  Article  Google Scholar 

  7. 7

    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 

  8. 8

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

    ADS  Article  Google Scholar 

  9. 9

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

    ADS  Article  Google Scholar 

  10. 10

    Dalichaouch, R., Armstrong, J. P., Schultz, S., Platzman, P. M. & McCall, S. L. Microwave localization by 2-dimensional random scattering. Nature 354, 53–55 (1991).

    ADS  Article  Google Scholar 

  11. 11

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

    ADS  Google Scholar 

  12. 12

    Hu, H., Strybulevych, A., Page, J. H., Skipetrov, S. E. & Van Tiggelen, B. A. Localization of ultrasound in a three-dimensional elastic network. Nature Phys. 4, 845–848 (2008).

    Article  Google Scholar 

  13. 13

    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  Article  Google Scholar 

  14. 14

    Roth, R. & Burnett, K. Phase diagram of bosonic atoms in two-color superlattices. Phys. Rev. A 68, 023604 (2003).

    ADS  Article  Google Scholar 

  15. 15

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

    ADS  Article  Google Scholar 

  16. 16

    Piraud, M., Lugan, P., Bouyer, P., Aspect, A. & Sanchez-Palencia, L. Localization of a matter wave packet in a disordered potential. Phys. Rev. A 83, 031603 (2011).

    ADS  Article  Google Scholar 

  17. 17

    Kuhn, R. C., Sigwarth, O., Miniatura, C., Delande, D. & Müller, C. A. Coherent matter wave transport in speckle potentials. New J. Phys. 9, 161 (2007).

    ADS  Article  Google Scholar 

  18. 18

    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  Article  Google Scholar 

  19. 19

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

    ADS  Article  Google Scholar 

  20. 20

    Roati, G. et al. Anderson localization of a non-interacting Bose–Einstein condensate. Nature 453, 895–898 (2008).

    ADS  Article  Google Scholar 

  21. 21

    Robert-de-Saint-Vincent, M. et al. Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential. Phys. Rev. Lett. 104, 220602 (2010).

    ADS  Article  Google Scholar 

  22. 22

    Pezzé, L. et al. Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder. New J. Phys. 13, 095015 (2011).

    ADS  Article  Google Scholar 

  23. 23

    Aspect, A. & Inguscio, M. Anderson localization of ultracold atoms. Phys. Today 62, 30–35 (August 2009).

    Article  Google Scholar 

  24. 24

    Sanchez-Palencia, L. & Lewenstein, M. Disordered quantum gases under control. Nature Phys. 6, 87–95 (2010).

    ADS  Article  Google Scholar 

  25. 25

    Moore, F. 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  Article  Google Scholar 

  26. 26

    Chabé, J. et al. Experimental observation of the Anderson metal–insulator transition with atomic matter waves. Phys. Rev. Lett. 101, 255702 (2008).

    ADS  Article  Google Scholar 

  27. 27

    Vollhardt, D. & Wölfle, P. in Electronic Phase Transitions (eds Hanke, W. & Kopalev, Y.) 1 (Elsevier, 1992).

    Google Scholar 

  28. 28

    Clément, D. et al. Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle. New J. Phys. 8, 165 (2006).

    ADS  Article  Google Scholar 

  29. 29

    Goodman, J. W. Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

    Google Scholar 

  30. 30

    Wölfle, P. & Bhatt, R. N. Electron localization in anisotropic systems. Phys. Rev. B 30, 3542–3544 (1984).

    ADS  Article  Google Scholar 

  31. 31

    Piraud, M., Pezzé, L. & Sanchez-Palencia, L. Matter wave transport and Anderson localization in anisotropic 3D disorder. Preprint at (2011).

  32. 32

    Ioffe, A. F. & Regel, A. R. Non crystalline, amorphous, and liquid electronic semiconductors. Prog. Semicond. 4, 237–291 (1960).

    Google Scholar 

  33. 33

    Yedjour, A. & Van Tiggelen, B. A. Diffusion and localization of cold atoms in 3D optical speckle. Eur. Phys. J. D 59, 249–255 (2010).

    ADS  Article  Google Scholar 

  34. 34

    Kondov, S. S., McGehee, W. R., Zirbel, J. J. & DeMarco, B. Three-dimensional Anderson localization of ultracold fermionic matter. Science 333, 66–68 (2011).

    ADS  Article  Google Scholar 

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We thank S. Seidel and V. Volchkov for experimental contributions, M. Besbes for assistance on numerical calculations, M. Lecrivain for helping design and realize the suspending coils, A. Villing and F. Moron for assistance with the electronics, and T. Giamarchi and B. van Tiggelen for fruitful discussions. This research was supported by the European Research Council (Starting grant ‘ALoGlaDis’, FP7/2007-2013 Grant Agreement No. 256294, and Advanced grant ‘Quantatop’), the Agence Nationale de la Recherche (ANR-08-blan-0016-01), the Ministère de l’Enseignement Supérieur et de la Recherche, the Délégation Générale de l’Armement, the Triangle de la Physique and the Institut Francilien de Recherche sur les Atomes Froids. We acknowledge the use of the computing facility cluster Grappe massivement parallèle de calcul scientifique of the LUmiere MATière research federation (Fédération de Recherche LUmiere MATière 2764).

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All authors have contributed equally.

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Correspondence to V. Josse.

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Jendrzejewski, F., Bernard, A., Müller, K. et al. Three-dimensional localization of ultracold atoms in an optical disordered potential. Nature Phys 8, 398–403 (2012).

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