Synchronization of One Dimensional Array of Point Josephson Junctions Coupled to a Common Load

Abstract

We study the synchronization in a one dimensional array of point Josephson junctions coupled to a common capacitor, which establishes a long-range interaction between junctions and synchronizes them. The stability diagram of synchronization in a noise-free system is obtained. The current when junctions transform from resistive state into superconducting state, is then calculated and its dependence on the shunt parameters and the dissipation of junctions is revealed. In the presence of thermal noise, the synchronized oscillations are destroyed at a critical temperature and the system undergoes a continuous phase transition of desynchronization. A possible stability diagram of the synchronized oscillations with respect to thermal noise, current, dissipations and shunt capacitance is then constructed. Finally we investigate the dynamic relaxation from random oscillations into synchronized state. The relaxation time increases with the system size and temperature, but is reduced by the shunt capacitor.

11.2 pages, 14 figures

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• Hot spots and waves in Bi2Sr2CaCu2O8 intrinsic Josephson junction stacks -a study by Low Temperature Scanning Laser Microscopy
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• Generalized coupling in the Kuramoto model
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• Hot-spot formation in stacks of intrinsic Josephson junctions in Bi2Sr2CaCu2O8
• Thermal and electromagnetic properties of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ intrinsic Josephson junction stacks studied via one-dimensional coupled sine-Gordon equations
• In-plane dissipation as a possible synchronization mechanism for terahertz radiation from intrinsic Josephson junctions of layered superconductors
• 3D simulations of the electrothermal and THz emission properties of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ intrinsic Josephson junction stacks
• Noise Effects on birhythmic Josephson Junction coupled to a Resonator
• Manifestation of Resonance-Related Chaos in Coupled Josephson Junctions
• Noise and disorder effects in a series of birhythmic Josephson junctions coupled to a resonator
• Mutual synchronization of two stacks of intrinsic Josephson junctions in cuprate superconductors
• Variation of Longitudinal Plasma Wavelength under Irradiation and Double Resonance in Coupled Josephson Junctions
• Dependence of the maximal superconducting current on resonance frequency in shunted Josephson junction
• Optical control of the current-voltage relation in stacked superconductors