One of the most intriguing phenomena in physics is the localization of waves in disordered media 1 . This phenomenon was originally predicted by Anderson, fifty years ago, in the context of transport of electrons in crystals 2 . Anderson localization is actually a much more general phenomenon 3 , and it has been observed in a large variety of systems, including light waves 4,5 . However, it has never been observed directly for matter waves. Ultracold atoms open a new scenario for the study of disorder-induced localization, due to high degree of control of most of the system parameters, including interaction 6 . Here we employ for the first time a noninteracting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a onedimensional quasi-periodic lattice, a system which features a crossover between extended and exponentially localized states as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated by investigating transport properties, 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. Since the interaction in the condensate can be controlled at will, this system might be employed to solve open questions on the interplay of disorder and interaction 7 and to explore exotic quantum phases 8,9 .

We report on the direct observation of an oscillating atomic current in a one-dimensional array of Josephson junctions realized with an atomic Bose-Einstein condensate. The array is created by a laser standing wave, with the condensates trapped in the valleys of the periodic potential and weakly coupled by the interwell barriers. The coherence of multiple tunneling between adjacent wells is continuously probed by atomic interference. The square of the small-amplitude oscillation frequency is proportional to the microscopic tunneling rate of each condensate through the barriers and provides a direct measurement of the Josephson critical current as a function of the intermediate barrier heights. Our superfluid array may allow investigation of phenomena so far inaccessible to superconducting Josephson junctions and lays a bridge between the condensate dynamics and the physics of discrete nonlinear media.

We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting 87Rb 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.

An optical speckle potential is used to investigate the static and dynamic properties of a Bose-Einstein condensate in the presence of disorder. With small levels of disorder, stripes are observed in the expanded density profile and strong damping of dipole and quadrupole oscillations is seen. Uncorrelated frequency shifts of the two modes are measured and are explained using a sum-rules approach and by the numerical solution of the Gross-Pitaevskii equation.

We employ radio-frequency spectroscopy to investigate a polarized spin-mixture of ultracold 6 Li atoms close to a broad Feshbach scattering resonance. Focusing on the regime of strong repulsive interactions, we observe well-defined coherent quasiparticles even for unitarity-limited interactions. We characterize the many-body system by extracting the key properties of repulsive Fermi polarons: the energy E+, the effective mass m * , the residue Z and the decay rate Γ. Above a critical interaction, E+ is found to exceed the Fermi energy of the bath while m * diverges and even turns negative, thereby indicating that the repulsive Fermi liquid state becomes energetically and thermodynamically unstable.Landau's idea of mapping the behavior of impurity particles interacting with a complex environment into quasiparticle properties [1] plays a fundamental role in physics and materials science, from helium liquids [2] and colossal magnetoresistive materials [3,4] to polymers and proteins [5,6]. In the field of ultracold gases, the impurity problem and the associated concept of polaron quasiparticle have attracted over the last decade a growing interest [7][8][9][10]. Initiated with the investigation of polarized Fermi gases in the BEC-BCS crossover [11][12][13][14][15][16], the study of polaron physics has been extended to mass-imbalanced [17,18], low-dimensional fermionic systems [19], and also to bosonic environments [20][21][22]. The polaron properties are fundamentally relevant for understanding the more complex scenario of partially-polarized and balanced Fermi mixtures: the impurity limit exhibits some of the critical points of the full phase diagram, whose topology we can thus learn about by investigating polarized systems [8,16].While researchers initially focused on attractive interactions [14,15], more recently they have explored novel quasiparticles associated with repulsive interactions: these repulsive polarons [23][24][25][26][27] are centrally important for realizing repulsive many-body states [23,24,28,29] and therein exploring itinerant ferromagnetism [30][31][32]. In particular, if the polaron energy exceeds the Fermi energy of the surrounding medium, a fullyferromagnetic phase is favored against the paramagnetic Fermi liquid [23][24][25]27]. However, short-ranged strong repulsion always require an underlying weakly-bound molecular state, into which the system may rapidly decay [31,33], making the repulsive polaron an excited manybody state, whose theoretical and experimental investigation are challenging. In three dimensions, repulsive Fermi polarons have been first unveiled in a 6 Li -40 K mixture at a comparatively narrow Feshbach resonance [17], but they lack observation in the universal, broad * scazza@lens.unifi.it resonance case, for which the decay rate is expected to be the largest [10].In this Letter we report on reverse radio-frequency (RF) spectroscopy [17,34,35] experiments to unveil the existence and characterize the properties of repulsive polarons in a polarized Fermi mixture of lithium ...