Mapping the spatial distribution of entanglement in optical lattices

In this work we study the entangled states that can be created in bipartite two-dimensional optical lattices loaded with ultracold atoms. We show that, by using only two sets of measurements, it is possible to compute a set of entanglement witness operators distributed over arbitrarily large regions of the lattice, and use these witnesses to produce two-dimensional plots of the entanglement content of these states. We also discuss the influence of noise on the states and on the witnesses, as well as the relation to ongoing experiments.