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arXiv:cond-mat/0401433 · International Journal of Modern Physics B

TOPOLOGY INDUCED MACROSCOPIC QUANTUM COHERENCE IN JOSEPHSON JUNCTION NETWORKS

Giovanni Giusiano, Francesco Paolo Mancini, Pasquale Sodano, Andrea Trombettoni

Published Feb 20, 2004• 6 citations
arXivHTMLPDF

Abstract

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 thermodynamical 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.

DOI
10.1142/s0217979204024318

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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 thermodynamical 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.
New coherent states may be induced by pertinently engineering the topology of a network. As an example, we consider the properties of non-interacting bosons on a star network, which may be realized with a dilute atomic gas in a star-shaped deep optical lattice. The ground state is localized around the star centre and it is macroscopically occupied below the Bose–Einstein condensation temperature T c . We show that T c depends only on the number of the star arms and on the Josephson energy of the bosonic Josephson junctions and that the non-condensate fraction is simply given by the reduced temperature T / T c .
We show that spatial Bose-Einstein condensation of non-interacting bosons occurs in dimension d < 2 over discrete structures with inhomogeneous topology and with no need of external confining potentials. Josephson junction arrays provide a physical realization of this mechanism. The topological origin of the phenomenon may open the way to the engineering of quantum devices based on Bose-Einstein condensation. The comb array, which embodies all the relevant features of this effect, is studied in detail.
We investigate the Bose–Einstein condensation on nonhomogeneous amenable networks for the model describing arrays of Josephson junctions. The resulting topological model, whose Hamiltonian is the pure hopping one given by the opposite of the adjacency operator, also has a mathematical interest in itself. We show that for the nonhomogeneous networks like the comb graphs, particles condensate in momentum and configuration space as well. In this case different properties of the network, of geometric and probabilistic nature, such as the volume growth, the shape of the ground state, and the transience, all play a role in the condensation phenomena. The situation is quite different for homogeneous networks where just one of these parameters, e.g., the volume growth, is enough to determine the appearance of the condensation.
The spontaneous emergence of enhanced responses and local orders are properties often associated with complex matter where nonlinearities and spatial inhomogeneities dominate. We discuss these phenomena in quantum devices realized with superconducting Josephson junction networks and cold atoms in optical lattices. We evidence how the pertinent engineering of the network's shape induces the enhancement of the zero-voltage Josephson critical currents in superconducting arrays as well as the emergence of spatially localized condensates for cold atoms in inhomogeneous optical lattices.
We investigate the properties of Josephson junction networks with inhomogeneous architecture. The networks are shaped as quare comb planar lattices on which Josephson junctions link superconducting islands arranged in the plane to generate the pertinent topology. Compared to the behavior of reference linear arrays, the temperature dependencies of the Josephson currents of the branches of the network exhibit relevant differences. The observed phenomena evidence new and surprising behavior of superconducting Josephson arrays as well as remarkable similarities with bosonic junction arrays.
We study a set of L spatial bosonic modes localized on a graph $\ensuremath{\Gamma}.$ The particles are allowed to tunnel from vertex to vertex by hopping along the edges of $\ensuremath{\Gamma}.$ We analyze how, in the exact many-body eigenstates of the system, i.e., Bose-Einstein condensates over single-particle eigenfunctions, the bipartite quantum entanglement of a graph vertex with respect to the rest of the graph depends on the topology of $\ensuremath{\Gamma}.$