Control of global variables for identical and non-identical Josephson junctions arrays

In the paper a way to solve an LQ-problem for a Josephson junction array with a common LRC-load is proposed. The cases of identical and non-identical Josephson junctions are considered. The solution ensures phase stabilization of Josephson current in every junction. The results are obtained using computer simulation in Jupyter Notebook and MATLAB.

Description of zero field steps on the potential energy surface of a Frenkel-Kontorova model for annular Josephson junction arrays

We explain the emergence of zero field steps (ZFS) in a Frenkel-Kontorova (FK) model for a 1D annular chain being a model for an annular Josephson junction array. We demonstrate such steps for a case with a chain of 10 phase differences. We necessarily need the periodic boundary conditions. We propose a mechanism for the jump from M fluxons to $$M+1$$ M + 1 in the chain. Graphic abstract

High dynamic resistance elements based on a Josephson junction array

A chain of superconductor–insulator–superconductor junctions based on Al–AlO x –Al nanostructures and fabricated using conventional lift-off lithography techniques was measured at ultra-low temperatures. At zero magnetic field, the low current bias dynamic resistance can reach values of ≈1011 Ω. It was demonstrated that the system can provide a decent quality current biasing circuit, enabling the observation of Coulomb blockade and Bloch oscillations in ultra-narrow Ti nanowires associated with the quantum phase-slip effect.

High dynamic resistance elements based on Josephson junction array

Chain of superconductor-insulator-superconductor junctions based on Al-AlO x -Al... lift-off fabricated nanostructures was measured at ultra-low temperatures. At zero magnetic field the low current bias dynamic resistance can reach values ~1011 W. The system has been proved to provide a decent quality current biasing circuit enabling observation of Coulomb blockade and Bloch oscillations in ultra-narrow Ti nanowires associated with quantum phase slip effect.