Topology induced macroscopic quantum coherence in Josephson junction networks

We argue that Josephson junction networks may be engineered to allow for the emergence of new and robust quantum coherent states. We provide a rather intuitive argument showing how the change in topology may affect the quantum properties of a bosonic particle hopping on a network. As a paradigmatic example, we analyze in detail the quantum and thermodynamic properties of non-interacting bosons hopping on a comb graph. We show how to explicitly compute the inhomogeneities in the distribution of bosons along the comb's fingers, evidencing the effects of the topology induced spatial Bose-Einstein condensation characteristic of the system. We propose an experiment enabling to detect the spatial Bose-Einstein condensation for Josephson networks built on comb graphs.