A ladder of Josephson junctions provides a realization of the discrete sine-Gordon chain. The spring constant and incommensurability can be varied by the supercurrent and the magnetic field. As the magnetic field is increased there is a transition to a vortex state. Due to charging effects (quantum fluctuations) the ladder becomes normal in the vicinity of this transition.

• Received 23 October 1985

DOI:https://doi.org/10.1103/PhysRevB.33.3125