Harmonic resonances in nonlinear Josephson junction circuits: experimental and analytical studies

This thesis presents a study of resonance dynamics in circuits of superconducting Josephson junctions. The Josephson junction is an intrinsically nonlinear device which, under certain conditions, can exhibit harmonic oscillations. This research begins with the dynamics of Josephson junctions connected in parallel with either periodic (ring geometry) or open-ended (row geometry) boundary conditions. Previous studies of the single ring system have established the existence of periodic, quasi-periodic, and even sub-harmonic resonances in this system, while only periodic resonances have been observed in the single row systems. The measurements and analysis presented here add suband super-harmonic resonances to the long row systems. They also show that the collective oscillations of junctions in very long systems are only slightly perturbed by the boundaries and thus resemble the solutions of ring systems. The dynamics of both open-ended and ring arrays become particularly rich when two such arrays are inductively coupled. For symmetrically coupled rows, the harmonic and sub-harmonic resonances split into two frequencies, corresponding to inphase and anti-phase oscillations. This is observed in both experiments and numerical simulations. An ansatz for the phase solutions at resonance is used to derive the two natural frequencies from the coupled nonlinear equations. Inductively coupled rings can be analyzed in the same way if they have identical numbers of trapped fluxons. When this is not true, the solutions to the coupled ring system are more complex. Through DC measurements and numerical simulations, a survey of some new and unexpected dynamical states is presented. A preliminary analysis is used to discuss those features of the data which are related to resonances in the dynamical system. Finally, a portion of this research is dedicated to obtaining useful AC power from Josephson junction circuits operating at resonance. The parallel row is first considered, along with the possibility of increasing the power by using the in-phase mode of inductively coupled rows. A new system with three junctions per cell (triangular cell) is also considered. Both single triangle-cell rows as well as large two-dimensional arrays are shown to have sharp resonance steps in DC measurements. AC power is coupled from these arrays to an on-chip detector junction, which responds by showing Shapiro steps in its DC current-voltage characteristic. The possibilities for future improvement in this design are discussed. Thesis Supervisor: T. P. Orlando, Professor of Electrical Engineering