Semiclassical dynamics of a superconducting circuit: chaotic dynamics and fractal attractors

In this article, we study the semiclassical dynamics of a superconducting circuit constituted by two Josephson junctions in series, in the presence of a voltage bias. We show that the equations of motion describing the superconducting phase correspond to those controlling the dynamics of a planar rotor with an oscillating pivot and, consequently, to those of a Kapitza pendulum in the absence of gravity. In addition, we show that the system exhibits a rich dynamical behavior with chaotic properties and provide insight into its attractor’s fractal nature.