Dual relaxation oscillations in a Josephson-junction array

We report relaxation oscillations in a one-dimensional array of Josephson junctions, wherein the array dynamically switches between low-current and high-current states. The oscillations are current-voltage dual to those ordinarily observed in single junctions. The current-voltage dual circuit quantitatively accounts for temporal dynamics of the array, including the dependence on biasing conditions. Injection locking of the oscillations results in well-developed current plateaux. A thermal model explains the self-consistent reduction of the superconducting gap due to overheating of the array in the high-current state. Our work suggests that overheating determines the switching from the high-current state to the low-current state.