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We show how two-dimensional waveguide arrays can be used to probe the effectof on-site interaction on Anderson localization of two interacting bosons inone dimension. It is shown that classical light and linear elements aresufficient to experimentally probe the interplay between interaction anddisorder in this setting. For experimental relevance, we evaluate theparticipation ratio and the intensity correlation function as measures oflocalization for two types of disorder (diagonal and off-diagonal), for twotypes of interaction (repulsive and attractive), and for a variety of initialinput states. Employing a commonly used set of initial states, we show that theeffect of interaction on Anderson localization is strongly dependent on thetype of disorder and initial conditions, but is independent of whether theinteraction is repulsive or attractive. We then analyze a certain type ofentangled input state where the type of interaction is relevant and discuss howit can be naturally implemented in waveguide arrays. We conclude by laying outthe details of the two-dimensional photonic lattice implementation includingthe required parameter regime.

Probing the effects of interaction in Anderson localization using linear photonic lattices