Topology Induced Macroscopic Quantum Coherence in Josephson Junction Networks

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 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.

Topology-induced critical current enhancement in Josephson networks

“…Our experiments show remarkable similarities with behaviors expected to be observed for the systems of ultracold atoms, arranged in inhomogeneous comb-shaped optical lattices, analyzed in refs. 18,19.…”

“…Macroscopic Quantum Coherence occurs in a variety of physical systems such as Bose-Einstein condensates of atomic gases (1)(2)(3), superfluid Helium (4,5), superconductors (6,7), solid-state mesoscopic systems (8)(9)(10)(11)(12) and cold atoms in optical lattices (13)(14)(15). In this area, Josephson Junction Networks (JJN) are by now the prototype of a versatile solid-state system, which -by acting on a few control parameters -may be used for the engineering of a variety of macroscopically quantum states (16)(17)(18)(19). Very often the JJN that have attracted attention for modelling of superconductive systems have been planar arrays obtained by closing superconducting loops by point Josephson junctions (16).…”

Spatially Inhomogeneous Superconducting and Bosonic Networks With Emergent Complex Behaviors

“…(65) ψ E (y) are the delocalized eigenfunctions of the eigenvalue equation (29). For determining N B (y; τ ), one needs to compute N E 0 and N σ − , which are evaluated [32] in Appendix B. Using these results, an explicit analytical form for the number of bosons at site y, N B (y), may, then, be derived.…”

“…An hidden spectrum of the adjacency matrix emerges, for instance, when one analyzes bundled graphs [29] (i.e., those obtained by grafting a fiber graph to every point of a base graph) while, for graphs with constant coordination number (such as the Sierpinski gasket and the ladder graph), the adjacency matrix does not support any hidden spectrum [31]. In the following, we shall analyze the simple paradigmatic case of comb networks showing how the hidden spectrum of the adjacency matrix leads to unusual quantum behaviors such as the emergence of the spatial BEC on the comb's backbone for a Bose gas living on a combshaped optical lattice [30,32] and of the enhanced responses observed for classical combshaped JJNs made of Niobium grains [21,22][see Fig.1]. To better clarify our arguments, we find instructive to compare our results with those obtainable if the same devices were defined on a chain, since the latter is, after all, the simplest graph of euclidean dimension 1.…”

BEC in a star-comb graph

“…Although it is well known that free bosons hopping on translationally invariant networks cannot undergo Bose-Einstein condensation at finite temperature if the space dimension d is less or equal to two, very recent studies [1,2,3,4] hint to the exciting possibility that the network topology may act as a catalyst for inducing a finite temperature spatial Bose-Einstein condensation even if d < 2. This is indeed possible if one resorts to a suitable discrete inhomogeneous ambient space on which bosons are defined.…”