The superfluid insulator transition of ultra-cold bosons in disordered 1d traps

TL;DR

This paper models the superfluid-insulator transition of disordered 1D ultra-cold bosons using an effective quantum Josephson array, revealing a transition governed by a strong randomness fixed point and providing detailed phase diagrams.

Contribution

It introduces a first-principles derived effective model for disordered 1D bosons and analyzes the transition using renormalization group flows and finite size scaling.

Findings

Transition governed by a strong randomness fixed point

Phase diagram with corrections to mean-field theory

Renormalization group flows for specific disorder realizations

Abstract

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, indicate that weakly interacting bosons in a disorder potential undergo a superfluid insulator transition controlled by a strong randomness fixed point [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.