Measurement of the mobility edge for 3D Anderson localization

Abstract

Anderson localization is a universal phenomenon affecting non-interacting quantum particles in a disordered environment. In three spatial dimensions, theory predicts a quantum phase transition from localization to diffusion at a critical energy, the mobility edge, which depends on the disorder strength. Although it has been recognized already long ago as a prominent feature of disordered systems, a complete experimental characterization of the mobility edge is still missing. Here we report the measurement of the mobility edge for ultracold atoms in a disordered potential created by laser speckles. We are able to control both the disorder strength and the energy of the system, so as to probe the position of the localization threshold in the disorder–energy plane. Our results might allow a direct experiment–theory comparison, which is a prerequisite to study the even more challenging problem of disorder and interactions.

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Figure 1: 3D speckle disorder.
Figure 2: Expansion and localization dynamics.
Figure 3: Momentum and energy distribution.
Figure 4: Excitation spectrum.
Figure 5: Measured mobility edge versus the disorder strength.

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Acknowledgements

We acknowledge discussions with V. Josse and L. Pezzé. This work was supported by ERC (grants 247371 and 258325), and partially by EU - H2020 research and innovation programme (grant 641122), INFN (MICRA collaboration) and MIUR (grant RBFR08H058).

Author information

G.Semeghini and M.L. designed the experiment; G.Semeghini, M.L. and G.M. analysed the data and performed the numerical simulations; all the other authors participated to the experiment, data analysis, discussion of the results and writing of the manuscript.

Correspondence to G. Modugno.

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The authors declare no competing financial interests.

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Semeghini, G., Landini, M., Castilho, P. et al. Measurement of the mobility edge for 3D Anderson localization. Nature Phys 11, 554–559 (2015). https://doi.org/10.1038/nphys3339

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