Ultracold bosons in one dimensional traps are typically weakly interacting, whereas the disorder potential generated e.g. by speckle potential, is highly tunable. How is superfluidity destroyed in such a system with increasing disorder strength?
I will derive an effective model for this system, showing that the transition is described by a recently proposed strong randomness fixed point, and not by the established weak disorder analysis of Giamarchi and Schulz. Using the effective model we find the full phase diagram of the system. We predict that at the critical point the system is characterized by universal mesoscopic fluctuations in various properties, which decay
as the logarithm of system size. I will describe how such signatures of the transition can be detected by analysis of the statistics of fringe patterns in interference experiments.