The Threshold of Phase Locking in the System of Two Multi-Junction Superconducting Loops

Coherent behavior (phase locking) in the system of two superconducting loops containing arrays of Josephson junctions and influencing each other by means of mutual inductance was numerically investigated. It is shown that under certain conditions the mutual interaction between loops can result in total phase-locking of the system. The threshold of the locking state depends on the strength of the interaction (mutual inductance). It is found that the basic behavior of the system in the phase-locked state can be explained by means of simple model of single multi-junction loop with an effective inductance which depends on mutual inductance. It is shown that synchronization in this system is possible and the mutual interaction increases the stability of phase locking in arrays.