Length-scale dependence of the superconductor-to-insulator quantum phase transition in one dimension

One-dimensional (1D) arrays of small-capacitance Josephson junctions demonstrate a sharp transition, from Josephson-like behavior to the Coulomb blockade of Cooper-pair tunneling, as the effective Josephson coupling between nearest neighbors is tuned with an externally applied magnetic field. Comparing the zero-bias resistance of three arrays with 255, 127, and 63 junctions, we observe a critical behavior where the resistance, extrapolated to T = 0, is independent of length at a critical magnetic field. Comparison is made with a theory of this T = 0 quantum phase transition, which maps to the 2D classical XY model.