Anderson localization of waves in disordered media was originally predicted1 fifty years ago, in the context of transport of electrons in crystals2. The phenomenon is much more general3 and has been observed in a variety of systems, including light waves4,5. However, Anderson localization has not been observed directly for matter waves. Owing to the high degree of control over most of the system parameters (in particular the interaction strength), ultracold atoms offer opportunities for the study of disorder-induced localization6. Here we use a non-interacting Bose–Einstein condensate to study Anderson localization. The experiment is performed with a one-dimensional quasi-periodic lattice—a system that features a crossover between extended and exponentially localized states, as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated through investigations of the transport properties and spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. This controllable system may be used to investigate the interplay of disorder and interaction (ref. 7 and references therein), and to explore exotic quantum phases8,9.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
npj Quantum Information Open Access 25 March 2022
Nature Open Access 19 January 2022
Nature Photonics Open Access 17 June 2021
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958)
Lee, P. A. & Ramakrishnan, T. V. Disordered electronic systems. Rev. Mod. Phys. 57, 287–337 (1985)
Kramer, B. & MacKinnon, A. Localization: theory and experiment. Rep. Prog. Phys. 56, 1469–1564 (1993)
Van Albada, M. P. & Lagendijk, A. Observation of weak localization of light in a random medium. Phys. Rev. Lett. 55, 2692–2695 (1985)
Wiersma, D. S., Bartolini, P., Lagendijk, A. & Righini, R. Localization of light in a disordered medium. Nature 390, 671–673 (1997)
Damski, B., Zakrzewski, J., Santos, L., Zoller, P. & Lewenstein, M. Atomic Bose and Anderson glasses in optical lattices. Phys. Rev. Lett. 91, 080403 (2003)
Dubi, Y., Meir, Y. & Avishai, Y. Nature of the superconductor-insulator transition in disordered superconductor. Nature 449, 876–880 (2007)
Lewenstein, M. et al. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 56, 243–379 (2007)
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)
Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007)
Lahini, Y. et al. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008)
Lye, J. E. et al. Bose-Einstein condensate in a random potential. Phys. Rev. Lett. 95, 070401 (2005)
Clément, D. et al. Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential. Phys. Rev. Lett. 95, 170409 (2005)
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)
Schulte, T. et al. Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices. Phys. Rev. Lett. 95, 170411 (2005)
Lye, J. E. et al. Effect of interactions on the localization of a Bose-Einstein condensate in a quasi-periodic lattice. Phys. Rev. A 75, 061603 (2007)
Roati, G. et al. 39K Bose-Einstein condensate with tunable interactions. Phys. Rev. Lett. 99, 010403 (2007)
Harper, P. G. Single band motion of conduction electrons in a uniform magnetic field. Proc. Phys. Soc. A 68, 874–878 (1955)
Aubry, S. & André, G. Analyticity breaking and Anderson localization in incommensurate lattices. Ann. Israel Phys. Soc. 3, 133–140 (1980)
Grempel, D. R., Fishman, S. & Prange, R. E. Localization in an incommensurate potential: an exactly solvable model. Phys. Rev. Lett. 49, 833–836 (1982)
Aulbach, C., Wobst, A., Ingold, G.-L., Hänggi, P. & Varga, I. Phase-space visualization of a metal–insulator transition. New J. Phys. 6 doi: 10.1088/1367-2630/6/1/070 (2004)
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)
Fattori, M. et al. Atom interferometry with a weakly interacting Bose-Einstein condensate. Phys. Rev. Lett. 100, 080405 (2008)
Zhong, J. et al. Shape of the quantum front. Phys. Rev. Lett. 86, 2485–2489 (2001)
Pedri, P. et al. Expansion of a coherent array of Bose-Einstein condensates. Phys. Rev. Lett. 87, 220401 (2001)
Burger, S. et al. Quasi-2D Bose-Einstein condensation in an optical lattice. Europhys. Lett. 57, 1–6 (2002)
Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B. & Dalibard, J. Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006)
Lugan, P. et al. Ultracold Bose gases in 1D disorder: from Lifshits glass to Bose-Einstein condensate. Phys. Rev. Lett. 98, 170403 (2007)
Roux, G. et al. The quasi-periodic Bose-Hubbard model and localization in 1-dimensional cold atomic gases. Preprint at 〈http://arxiv.org/abs/0802.3774〉 (2008)
D’Errico, C. et al. Feshbach resonances in ultracold 39K. New J. Phys. 9 doi: 10.1088/1367-2630/9/7/223 (2007)
Ovchinnikov et al. Diffraction of a released Bose-Einstein condensate by a pulsed standing light wave. Phys. Rev. Lett. 83, 284–287 (1999)
Gerbier, F. et al. Interference pattern and visibility of a Mott insulator. Phys. Rev. A 72, 053606 (2005)
We thank J. Dalibard for discussions, S. Machluf for contributions, and all the colleagues of the Quantum Gases group at LENS. This work has been supported by MIUR, EU (IP SCALA), ESF (DQS–EuroQUAM), INFN and Ente CRF.
About this article
Cite this article
Roati, G., D’Errico, C., Fallani, L. et al. Anderson localization of a non-interacting Bose–Einstein condensate. Nature 453, 895–898 (2008). https://doi.org/10.1038/nature07071
This article is cited by
npj Quantum Information (2022)
International Journal of Theoretical Physics (2022)
Science China Physics, Mechanics & Astronomy (2022)
Nature Photonics (2021)