Dynamics of Josephson-junction ladders

Abstract

We have numerically studied dynamical behaviors of Josephson-junction ladders consisting of Np plaquettes, where the 2(Np+1) superconducting islands are coupled by resistively shunted Josephson junctions with negligible capacitance. When a ladder is subjected to a current of the form Idc+Iacsin(ωt) in the [10] direction the dc I-V curve, in the presence of a transverse external magnetic field, becomes a devil’s staircase for Np=1, and exhibits hysteresis and a transition to chaos for Np≥2. We have identified the ‘‘symmetric state,’’ where the phase variables of the junctions satisfy symmetry relations and motion of the system is constrained to the phase space of smaller dimension than the original one. The dynamic behavior of each junction in the ladder depends very sensitively on whether the number of the plaquettes in a ladder is odd or even. However, the averaged dc I-V curves of the whole ladders with Np≥3 turn out similar to one another, enabling one to understand the dynamical behavior of a large ladder from that of a three-plaquette ladder.

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