Modeling of the quantum dynamics of frustrated networks of Josephson junctions

We report a theoretical study of the macroscopic quantum dynamics in frustrated networks of interacting Josephson junctions (f-NJJs). We consider two exemplary types of f-NJJs: quasi-1D sawtooth arrays and 2D Kagome lattice of small (quantum) Josephson junctions. The frustration is provided by periodically arranged 0- and π-Josephson junctions. In the frustration regime the clockwise (anticlockwise) persistent currents penetrate each basic cell, i.e., three superconducting islands connected by Josephson junctions. Collective quantum dynamics of persistent currents is described by the effective interacting spins Hamiltonian where we take into account the quantum superposition of persistent currents in a single cell induced by the macroscopic quantum tunneling of Josephson phases and a long- range interaction between persistent currents. Two types of interaction are discussed: charge interaction between superconducting islands in sawtooth arrays and topological constraints in Kagome lattice. We demonstrate that the long-interaction between spins in these f-NJJs allows one to realize the various collective quantum phases with a large quantum entanglement. We anticipate that f-NJJs can be a perspective platform for modeling complex strongly correlated electronic solid state, molecular, and biological systems, as well as frustrated magnetic systems.

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