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Philosophical Magazine B

Current-biased inductive cubic networks of Josephson junctions

Roberto De Luca, Tiziana Di Matteo, A. Tuohimaa, Jaakko A.J. Paasi

Published May 1, 2000• 3 citations
Publisher

Abstract

The electrodynamic response of a current-biased inductive network of small Josephson junctions located at the edges of a cube of side a is studied. The dynamical equations for the gauge-invariant phase differences across the junctions are derived in the presence of a constant magnetic field H applied along an arbitrary direction in space. When H is applied in a direction parallel to one of the sides, it is found that the time evolution of the voltages across the branches of the network reproduces the well known features present in superconducting auantum interference devices.

DOI
10.1080/01418630008221956

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The electrodynamic response of a current-biased inductive network of small Josephson junctions located at the edges of a cube of side a is studied. The dynamical equations for the gauge-invariant phase differences across the junctions are derived in the presence of a constant magnetic field H applied along an arbitrary direction in space. When H is applied in a direction parallel to one of the sides, it is found that the time evolution of the voltages across the branches of the network reproduces the well known features present in superconducting auantum interference devices.
We have performed a quantitative electrodynamic experiment on a Josephson oxide tunneling junction. Using a current source at 30 Mc/sec, we have verified the time dependence of the Josephson equation, j=j0j={j}_{0}j=j0​ $sin [{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]$, where $(\frac{\ensuremath{\partial}}{\ensuremath{\partial}t})[{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}{l}^{r}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]=\ensuremath{-}(\frac{2eV}{\ensuremath{\hbar}})$. Thus the limiting voltage is shown to obey the quantum relationship relationship, $2eV=\ensuremath{\hbar}\ensuremath{\omega}$. Measurements were made completely in the coherent state showing the diffraction nature of the junction as a function of applied magnetic field. The Josephson (parametric) inductance of the junction was directly observed and is in good agreement with the theory.
Two parallel stacks of coupled Josephson junctions are investigated to clarify the physics of transitions between the rotating and oscillating states and their effect on the IV-characteristics of the system. The detailed study of phase dynamics and bias dependence of the superconducting and diffusion currents allows one to explain all features of simulated IV-characteristics and demonstrate the correspondence in their behavior. The coupling between JJ in the stacks leads to the branching of IV-characteristics and a decrease in the hysteretic region. The crucial role of the diffusion current in the formation of the IV-characteristic of the parallel stacks of coupled Josephson junctions is demonstrated. We discuss the effect of symmetry in a number of junctions in the stacks and show a decrease of the branching in the symmetrical stacks. The observed effects might be useful for development of superconducting electronic devices based on intrinsic Josephson junctions.
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Two parallel stacks of coupled Josephson junctions (JJs) are investigated to clarify the physics of transitions between the rotating and oscillating states and their effect on the IV -characteristics of the system. The detailed study of phase dynamics and bias dependence of the superconducting and diffusion currents allows one to explain all features of simulated IV -characteristics and demonstrate the correspondence in their behavior. The coupling between JJ in the stacks leads to the branching of IV -characteristics and a decrease in the hysteretic region. The crucial role of the diffusion current in the formation of the IV -characteristic of the parallel stacks of coupled JJs is demonstrated. We discuss the effect of symmetry in a number of junctions in the stacks and show a decrease of the branching in the symmetrical stacks. The observed effects might be useful for development of superconducting electronic devices based on intrinsic JJs.