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.

Using a species-selective dipole potential, we create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration during expansion. We find an interaction-dependent amplitude reduction of the oscillation of the impurities' size with no measurable frequency shift, and study it as a function of the interaction strength. We discuss possible theoretical interpretations of the data. We compare, in particular, with a polaronic mass shift model derived following Feynman variational approach.

We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting ${}^{87}\mathrm{Rb}$ bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.

We produce a quantum degenerate mixture composed by two Bose-Einstein condensates of different atomic species, ${}^{\mathrm{41}}\mathrm{K}$ and ${}^{\mathrm{87}}\mathrm{R}\mathrm{b}$. We study the dynamics of the superfluid system in an elongated magnetic trap, where off-axis collisions between the two interacting condensates induce scissorlike oscillations.