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.

Chiral edge states are a hallmark of quantum Hall physics. In electronic systems, they appear as a macroscopic consequence of the cyclotron orbits induced by a magnetic field, which are naturally truncated at the physical boundary of the sample. Here we report on the experimental realization of chiral edge states in a ribbon geometry with an ultracold gas of neutral fermions subjected to an artificial gauge field. By imaging individual sites along a synthetic dimension, we detect the existence of the edge states, investigate the onset of chirality as a function of the bulk-edge coupling, and observe the edge-cyclotron orbits induced during a quench dynamics. The realization of fermionic chiral edge states is a fundamental achievement, which opens the door towards experiments including edge state interferometry and the study of non-Abelian anyons in atomic systems.Ultracold atoms in optical lattices represent an ideal platform to investigate the physics of condensed-matter problems in a fully tunable, controllable environment [1,2]. One of the remarkable achievements in recent years has been the realization of synthetic background gauge fields, akin to magnetic fields in electronic systems. Indeed, by exploiting light-matter interaction, it is possible to imprint a Peierls phase onto the atomic wavefunction, which is analogous to the Aharanov-Bohm phase experienced by a charged particle in a magnetic field [3][4][5]. These gauge fields, first synthesized in Bose-Einstein condensates [6], have recently allowed for the realization of the HarperHofstadter Hamiltonian in ultracold bosonic 2D lattice gases [7,8], paving the way towards the investigation of different forms of bulk topological matter in bosonic atomic systems [5,9]. In the present work we are instead interested in the edge properties of fermionic systems under the effects of a synthetic gauge field. Fermionic edge states are a fundamental feature of 2D topological states of matter, such as quantum Hall and chiral spin liquids [10,11]. Moreover, they are robust against changing the geometry of the system by keeping its topology, and can be observed even on Hall ribbons [12]. In addition, they offer very attractive perspectives in quantum science, such as the realization of robust quantum information buses [13], and they are ideal starting points for the realization of non-Abelian anyons akin to Majorana fermions [14,15].Here, we report the observation of chiral edge states in a system of neutral fermions subjected to a synthetic magnetic field. We exploit the high level of control in our system to investigate the emergence of chirality as a function of the Hamiltonian couplings. These results have been enabled by an innovative experimental approach, where an internal (nuclear spin) degree of freedom of the atoms is used to encode a lattice structure lying in an "extra dimension" [12], providing direct access to edge physics. In addition, we validate the chiral nature of our FIG. 1. A synthetic gauge field in a synthetic dimension. a. We confine the mot...