Theory of phase-locking in generalized hybrid Josephson junction arrays

TL;DR

This paper extends an analytical model for hybrid Josephson junction arrays to include capacitive and inductive shunts, deriving conditions for in-phase synchronization and flux-dependent oscillation behaviors.

Contribution

It introduces a generalized analytical framework for hybrid Josephson arrays with complex shunt components, predicting synchronization and flux-induced switching.

Findings

Derived limits on design parameters for in-phase synchronization.

Formulas for flux-dependent oscillation frequencies.

Identified conditions for flux-induced switching between oscillation regimes.

Abstract

A recently proposed scheme for the analytical treatment of the dynamics of two-dimensional hybrid Josephson junction arrays is extended to a class of generalized hybrid arrays with ''horizontal'' shunts involving a capacitive as well as an inductive component. This class of arrays is of special interest, because the internal cell coupling has been shown numerically to favor in-phase synchronization for certain parameter values. As a result, we derive limits on the circuit design parameters for realizing this state. In addition, we obtain formulas for the flux-dependent frequency including flux-induced switching processes between the in-phase and anti-phase oscillation regime. The treatment covers unloaded arrays as well as arrays shunted via an external load.