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Anderson localization of a non-interacting Bose–Einstein condensate

Abstract

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.

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Figure 1: The quasi-periodic optical lattice.
Figure 2: Probing the localization with transport.
Figure 3: Observing the nature of the localized states.
Figure 4: Momentum distribution.
Figure 5: Interference of localized states.

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Acknowledgements

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.

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Correspondence to Massimo Inguscio.

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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

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