Entrainment of Locally-Coupled Josephson Junction SQUID Arrays to an External Magnetic Field*

The entrainment of nonlinear oscillators to a driving sinusoidal wave is a subject of much investigation as the behaviors and the mathematics used to describe them are nontrivial. In this work, we study arrays of locally coupled rf SQUIDs in a spatially uniform, sinusoidally time-varying magnetic field. In the case of underdamped SQUIDs we observe a dephasing of the flux oscillations based on the inductive coupling of each SQUID with its nearest neighbor. This dephasing occurs only when the ratio of frequency of the driving field to the natural frequency of the SQUIDs was close to or less than one. Floquet analysis demonstrates no correlation between the dephasing and the stability of the entrainment. Both numerical and analytical computations show that the Floquet exponents are equal to half the damping strength while the system is underdamped, so in the highly underdamped regime all the Floquet exponents are very close to zero. However, the Floquet exponents experience no change at the specific coupling strengths that cause the SQUIDs to dephase. This talk will explain the computational results and the physical causes of those results.