1. LENS and Dipartimento di Fisica, Università di Firenze, 50019 Sesto Fiorentino, Italy
2. INFM-CNR, 50019 Sesto Fiorentino, Italy
3. Museo Storico della Fisica e Centro Studi e Ricerche 'E. Fermi', 00184 Roma, Italy
4. Dipartimento di Matematica Applicata, Università di Firenze, 50139 Firenze, Italy
5. BEC-INFM Center, Università di Trento, 38050 Povo, Italy

Correspondence to: Massimo Inguscio^1,2 Correspondence and requests for materials should be addressed to M.I. (Email: inguscio@lens.unifi.it).

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 waves^{4, 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 phases^{8, 9}.

1. LENS and Dipartimento di Fisica, Università di Firenze, 50019 Sesto Fiorentino, Italy
2. INFM-CNR, 50019 Sesto Fiorentino, Italy
3. Museo Storico della Fisica e Centro Studi e Ricerche 'E. Fermi', 00184 Roma, Italy
4. Dipartimento di Matematica Applicata, Università di Firenze, 50139 Firenze, Italy
5. BEC-INFM Center, Università di Trento, 38050 Povo, Italy

Correspondence to: Massimo Inguscio^1,2 Correspondence and requests for materials should be addressed to M.I. (Email: inguscio@lens.unifi.it).

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