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 a 2D kagome lattice of small (quantum) Josephson junctions. The frustration is provided by periodically arranged 0- and π-Josephson junctions. In the frustrated regime, the clockwise (anticlockwise) persistent currents penetrate each basic cell, i.e., three superconducting nodes connected by Josephson junctions. The collective quantum dynamics of persistent currents is described by an 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 long-range interactions between persistent currents. Two types of interactions are discussed: charge interaction between superconducting nodes in sawtooth arrays and topological constraints in the kagome lattice. We demonstrate that the long-range interaction between spins in these f-NJJs allows one to realize various collective quantum phases with a large quantum entanglement. We anticipate that f-NJJs can be a prospective platform for modeling complex strongly correlated electronic solid state, molecular, and biological systems, as well as frustrated magnetic systems.