Probing the sign of the Hubbard interaction by two-particle quantum walks

We address the discrimination between attractive and repulsive interaction in systems made of two identical bosons propagating on a one-dimensional lattice, and suggest a probing scheme exploiting the dynamical properties of the corresponding two-particle quantum walks. In particular, we show that the sign of the interaction leaves a clear signature in the dynamics of the two walkers, which is governed by the Hubbard model, and in their quantum correlations, thus permitting one to discriminate between the two cases. We also prove that these features are strictly connected to the band structure of the Hubbard Hamiltonian.