Analysis of the Stability of Resonances in a Periodically Driven Josephson Junction

Abstract

In the 17^th century Huyghens observed that two coupled pendula may synchronize their motion. Since that time much progress has been achieved to describe phase locking of oscillators^{1, 2}. One of the most perfect manifestation of phase locking happens whenever two superconductors are weakly coupled through a so-called Josephson junction. Constant voltage to frequency (Shapiro) steps observed at multiple of the flux quantum h/2e (∼2 × 10⁻¹⁵ V. s) in the voltage-intensity characteristic have been used³ to realize a voltage standard with a relative uncertainly of 10⁻⁷.