Determination of spontaneous frequency shift and phase retardation of coupled non-linear Josephson oscillations in cuprate superconductors

We discuss coupling interactions to synchronize macroscopic Josephson oscillations induced in intrinsic Josephson junction (IJJ) mesa stacks made of Bi2212 single crystals. Synchronized emissions are found under common voltage and current bias operations of connected two mesas with close individual emission frequencies while uncoupled and bimodal emissions are often found in two mesas with different individual emission frequencies. The detailed observations on polarization of the emitted electromagnetic wave when two mesas are biased in parallel or series allow us to reveal the coupling matrix components which includes ratios of synchronized IJJs in the mesas and phase retardation between the macroscopic Josephson oscillations.