Mode entanglement and entangling power in bosonic graphs

We analyze the quantum entanglement properties of bosonic particles hopping over graph structures. Mode entanglement of a graph vertex with respect to the rest of the graph is generated, starting from a product state, by turning on for a finite time a tunneling along the graph edges. The maximum achieved during the dynamical evolution by this bipartite entanglement characterizes the entangling power of a given hopping Hamiltonian. We studied this entangling power as a function of the self-interaction parameters, i.e., nonlinearities, for all the graphs up to four vertices and for two different natural choices of the initial state. The role of graph topology and self-interaction strengths in optimizing entanglement generation is extensively studied by means of exact numerical simulations and by perturbative calculations.