Analogue simulation of two-body quantum dynamics with classical setup

One-dimensional Bose-Hubbard models provide a variety of intriguing predictions including the formation of repulsively bound two-boson pairs, their collapse and revival and the realization of the two-boson topological states. While probing such systems in quantum regime is quite a challenging task, there is another appealing option to explore the properties of repulsively bound bosons based on mapping of the one-dimensional interacting system onto the two-dimensional classical model described by the standard coupled-mode equations. Adopting the latter approach, we develop the procedure to probe the energy of bound boson pairs as well as to perform the tomography of the bound pair quantum state in realistic dissipative systems.