| The results of a experimental and theoretical study of phase-locking in Joesphson junction arrays are presented. Externally induced phase-locking, with its characteristic Shapiro steps, was investigated in Josephson junction ladder arrays and single plaquettes (a four junction array). Experiments performed on superconductor-normal metal-superconductor ladders arrays with 1 x 600 and 9 x 1000 plaquettes show the presence of fractional giant Shapiro steps at non-commensurate values of frustration. Numerical simulations on ladder arrays and single plaquettes qualitatively agree with the experimental results. These results are contrasted with the vortex lattice model proposed by Benz which only permits fractional Shapiro steps at commensurate values of frustration. In fact, simulations show that a single plaquette can generate all orders of fractional steps at irrational values of frustration. In addition, the effects of noise and junction disorder on the ladder current-voltage (I-V) characteristics were studied with numerical simulations. Simulations also show that the zero-field fractional Shapiro steps are not due to disorder, as previously suggested.; Phase-locking between the oscillating junctions in a DC-biased plaquette was also studied. Plaquettes with shunted tunnel junctions were fabricated with a characteristic oscillation frequency of 20GHz. A asymmetric bias was applied to gauge the strength of phase-locking. Sample plaquettes including a "detector" junction were fabricated. This method was used to confirm the coherent voltage output from the plaquette. Using an external magnetic field, the voltage coherence of the plaquette was modulated. The coherent voltage was detected as "humps" in the I-V characteristic. Detailed simulations were performed to model the effects of disorder, noise, and screening inductance on the dynamic states of the plaquette. The simulations show good qualitative agreement with the experimental data.; Numerical Simulations were performed to study the dynamics of a modified ladder (ML) array. This array, which consists essentially of plaquettes with a parallel bias arrangement, was shown to share the stable phase-locking properties of the single plaquette. This array was found to tolerate more than 50% disorder in its junction parameters and layout in contrast to globally-coupled arrays which tolerate only 7%. The stability of ML arrays was studied using direct integration, Floquet analysis, and a novel passive network model. Each method shows that the ML array oscillation is stable to small perturbations with decay exponents which scale as the square of the array size, N. The network model predicts that the decay of the perturbations in the array occurs diffusively, thus explaining the N{dollar}sp2{dollar} dependence of the decay time constants. |
