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.

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.

We produce a Bose-Einstein condensate of ${}^{39}\mathrm{K}$ atoms. Condensation of this species with a naturally small and negative scattering length is achieved by a combination of sympathetic cooling with ${}^{87}\mathrm{Rb}$ and direct evaporation, exploiting the magnetic tuning of both inter- and intraspecies interactions at Feshbach resonances. We explore the tunability of the self-interactions by studying the expansion and the stability of the condensate. We find that a ${}^{39}\mathrm{K}$ condensate is interesting for future experiments requiring a weakly-interacting Bose gas.