Arrays of several Josephson junctions connected to oscillatory circuit

摘要

Serial arrays of two and three Josephson junctions coupled to a high quality oscillator circuit are considered using analytical approach and numerical simulation. Two different oscillation modes, the in phase and anti-phase ones, are possible in the systems above resonance frequency. It is shown that the first mode can be formally described through the same analytic theory as was developed earlier for one-junction system. This approach allows also analysing resonance peculiarities and phase-locking effects caused by external irradiation. However, stability of the mode is upset at low frequency and therefore the system shows abrupt switching either to other mode or to resonance oscillation state or to rest in superconducting state. In the anti-phase mode, the junction oscillations run with high amplitude, although resulting amplitude of the fundamental harmonic of the voltage across the arrays is negligibly small. The upper frequency of the mode stability domain decreases rapidly with McCumber parameter of the junctions and therefore this mode is relevant basically for arrays of overdamped Josephson junctions.