Global stability of phase lock near a chaotic crisis in the rf-biased Josephson junction

Abstract

The global stability of phase lock in the rf-biased Josephson junction is studied through digital simulations. Global stability is determined by calculating the lifetime of the phase-locked state in the presence of thermal noise. This lifetime, the mean time required for thermal noise to induce a 2π phase slip, increases exponentially with inverse temperature in the limit of low temperatures, and the low-temperature asymptote can be parametrized in terms of an activation energy ℰ and an attempt time τ0. The activation energy is a useful measure of global stability for both periodic and chaotic phase-locked states. The behavior of ℰ and τ0 is studied over a range of critical-current densities which take the system from a region of harmonic motion through a period-doubling cascade and into a region of phase-locked chaotic behavior which is ended by a chaotic crisis. At the crisis point, the activation energy goes to zero and the attempt time goes to infinity. The results are used to determine the optimum critical-current density for series-array voltage standards.