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.

Self-bound quantum droplets are a newly discovered phase in the context of ultracold atoms. In this Letter, we report their experimental realization following the original proposal by Petrov [ Phys. Rev. Lett. 115, 155302 (2015)], using an attractive bosonic mixture. In this system, spherical droplets form due to the balance of competing attractive and repulsive forces, provided by the mean-field energy close to the collapse threshold and the first-order correction due to quantum fluctuations. Thanks to an optical levitating potential with negligible residual confinement, we observe self-bound droplets in free space, and we characterize the conditions for their formation as well as their size and composition. This work sets the stage for future studies on quantum droplets, from the measurement of their peculiar excitation spectrum to the exploration of their superfluid nature.

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.

We report on the formation of heteronuclear quantum droplets in an attractive bosonic mixture of ${}^{41}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$. We observe long-lived self-bound states, both in free space and in an optical waveguide. In the latter case, the dynamics under the effect of a species-dependent force confirms their bound nature. By tuning the interactions from the weakly to the strongly attractive regime, we study the transition from expanding to localized states, in both geometries. We compare the experimental results with beyond-mean-field theory and we find good agreement in the full range of explored interactions. Our findings provide access to the production of long-lived droplets with important implications for further research.

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.