Theoretical and numerical study on multistacked Josephson junctions with a parametric modulation of their critical currents

Abstract

Flux-flow cavity-resonance properties in twofold Josephson junctions with different critical currents are investigated. While the critical current J21 of one of junctions is fixed, the critical current J10 of the other junction is parametrically increased up to extremely large values. Numerical simulations for inductively coupled twofold Josephson junctions are performed under several magnetic fields, and we observe resonance voltage steps at various ratios M≡J10∕J21. Obtained theoretical eigenequations include the parameter J10 that is different from the equations by the existent conventional theory for the homogeneous system. Almost all data points on a resonance voltage vs M domain obtained by the numerical simulations exist on the theoretical curves of eigenfrequency in voltage unit vs M. At M→∞ the twofold Josephson junctions can be regarded as a single junction. The lower critical-current (J21) junction works as a single junction with a new effective barrier thickness, and cavity resonance occurs in this single junction. At M→1 the theoretical eigenfrequencies in the voltage unit asymptotically approach the resonance voltages of the antiphase and in-phase modes of the conventional system. For the range with intermediate M values, there are no asymptotic approximate solutions, but the agreement of the results of the present theory with the numerical simulation results is excellent. The theory of the twofold Josephson junctions is able to extend to that of multifold junction with general index number N. At N=9, numerical simulations are performed and the agreement of its results with the theoretical results is good. At M→∞, the N-fold Josephson junction can also be regarded as a single junction with a new effective barrier thickness, dN″.

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