Superfluid-insulator transition of ultracold bosons in disordered one-dimensional traps

We derive an effective quantum Josephson array model for a weakly interacting one-dimensional condensate that is fragmented into weakly coupled puddles by a disorder potential. The distribution of coupling constants, obtained from first principles, indicates that weakly interacting bosons in a disorder potential undergo a superfluid insulator transition controlled by a strong randomness fixed point [E. Altman et al., Phys. Rev. Lett. 93, 150402 (2004)]. We compute renormalization-group flows for concrete realizations of the disorder potential to facilitate finite size scaling of experimental results and allow comparison to the behavior dictated by the strong randomness fixed point. The phase diagram of the system is obtained with corrections to mean-field results.