Non-linear dynamical effects and crisis in an RF-driven graphene Josephson junction

Josephson junctions have been under extensive scientific investigation for the past 50 years with broad applications ranging from magnetometry to quantum computation. The dynamics of the superconducting phase difference across the junction is described by a resistively and capacitively shunted junction (RCSJ) model, which is equivalent to the dynamics of a driven damped simple pendulum. In the overdamped regime, phase-locked solutions exist which correspond to the well-known Shapiro steps. In this work, we present low-temperature voltage measurements on a graphene Josephson junction in the underdamped regime as a function of DC-current bias and RF power. At zero current bias and a certain range of RF power, we observe the presence of two metastable voltage states with intermittent switching between them. The switching timescale is extraordinarily long (~ s) and a power-law scaling for the timescale with RF power is observed. We reconcile our observations with theory by studying the evolution of an underdamped RCSJ model and show the existence of multiple unstable solutions and strange attractors. Our observations can be tentatively explained using the phenomenon of an interior crisis. We outline future measurements to understand non-linear dynamics of underdamped junctions.