Correlation function of weakly interacting bosons in a disordered lattice

TL;DR

This paper presents the first experimental analysis of the correlation function in a weakly interacting bosonic system within a disordered lattice, revealing insights into localization, superfluid fragmentation, and phase crossover.

Contribution

It introduces the first experimental measurement of the correlation function in a disordered bosonic lattice, elucidating the transition from Anderson glass to a coherent extended state.

Findings

Correlation length increases during delocalization crossover.

Shape of the correlation function changes with phase transition.

Formation of larger coherent fragments consistent with Bose glass.

Abstract

One of the most important issues in disordered systems is the interplay of the disorder and repulsive interactions. Several recent experimental advances on this topic have been made with ultracold atoms, in particular the observation of Anderson localization, and the realization of the disordered Bose-Hubbard model. There are however still questions as to how to differentiate the complex insulating phases resulting from this interplay, and how to measure the size of the superfluid fragments that these phases entail. It has been suggested that the correlation function of such a system can give new insights, but so far little experimental investigation has been performed. Here, we show the first experimental analysis of the correlation function for a weakly interacting, bosonic system in a quasiperiodic lattice. We observe an increase in the correlation length as well as a change in shape of the correlation function in the delocalization crossover from Anderson glass to coherent, extended state. In between, the experiment indicates the formation of progressively larger coherent fragments, consistent with a fragmented BEC, or Bose glass.