THEORY OF PHASE-LOCKING IN SMALL JOSEPHSON-JUNCTION CELLS

Within the resistively shunted junction (RSJ) model, we performed a th eoretical analysis of phase locking in elementary strongly coupled Jos ephson-junction cells. For this purpose, we developed a systematic met hod allowing the investigation of phase locking in cells with small bu t nonvanishing loop inductance. The voltages across the junctions are found to be locked with very small phase difference for almost all val ues of external flux. However, the general behavior of phase locking i s found to be just contrary to that according to weak coupling. In the case of strong coupling there is nearly no influence of external magn etic flux on the phases, but the locking frequency becomes flux depend ent. The influence of parameter splitting is considered as well as the effect of small capacitive shunting of the junctions. Strongly couple d cells show synchronization even for large parameter splitting. Final ly, a study of the behavior under external microwave radiation shows t hat the frequency-locking range becomes strongly flux dependent, where as the locking frequency itself turns out to be flux independent.