Correlation function of weakly interacting bosons in a disordered lattice

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.

16 pages, 8 figures

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• Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• The eight-fold way for optical quasicrystals
• Quantum phases of incommensurate optical lattices due to cavity backaction
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• One-Dimensional Disordered Bosonic Systems
• Superfluid-insulator transition in weakly interacting disordered Bose gases: a kernel polynomial approach
• Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the Sine-Gordon transition: a Worm Algorithm Monte Carlo study