THEORY OF PHASE-LOCKING IN SMALL JOSEPHSON JUNCTION CELLS

TL;DR

This paper provides a theoretical analysis of phase-locking in small Josephson junction cells, revealing how strong coupling affects flux dependence and synchronization, with implications for understanding superconducting circuit behavior.

Contribution

It introduces a systematic method for analyzing phase-locking in small Josephson junction cells with non-zero loop inductance, highlighting differences from weak coupling behavior.

Findings

Voltages are locked with small phase difference across most external flux values.

Strong coupling reduces flux influence on phases but makes locking frequency flux-dependent.

Synchronization persists despite large parameter splitting and small capacitive shunting.

Abstract

Within the RSJ model, we performed a theoretical analysis of phase-locking in elementary strongly coupled Josephson junction cells. For this purpose, we developed a systematic method allowing the investigation of phase-locking in cells with small but non-vanishing loop inductance.The voltages across the junctions are found to be locked with very small phase difference for almost all values of external flux. However, the general behavior of phase-locking is found to be just contrary to that according to weak coupling. In case of strong coupling there is nearly no influence of external magnetic flux on the phases, but the locking-frequency becomes flux-dependent. The influence of parameter splitting is considered as well as the effect of small capacitive shunting of the junctions. Strongly coupled cells show synchronization even for large parameter splitting. Finally, a study of the behavior under external microwave radiation shows that the frequency locking-range becomes strongly flux-dependent, whereas the locking frequency itself turns out to be flux-independent.