Fiske modes in one-dimensional parallel Josephson-junction arrays

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Abstract
We have performed measurements on one-dimensional (1D) arrays of underdamped Josephson junctions connected in parallel by superconducting wires which in a magnetic field show resonances in the current-voltage characteristics. From analytical calculations, we find that the position of the steps is determined by the dispersion relation ω(k) of a 1D discrete, linear transmission line, where the Josephson junction has been replaced by the capacitor and the resistance of the junction. When nearest-neighbor inductances are accounted for, the model agrees well with the measured positions of the steps. Numerical calculations of the full dynamics with inclusion of inductances between all cells support our model. As an example of a system with a more complicated dispersion relation, we have measured 1D arrays with two different junctions per primitive cell. The measured dispersion relation shows an acoustic and an optical branch in agreement with numerical simulations of the full dynamics.