Meta-Atom Interactions and Coherent Response in RF SQUID Metamaterials

We have designed, fabricated, and measured RF SQUID (radio frequency superconducting quantum interference devices) metamaterials and demonstrated their extreme tunability with temperature, DC magnetic field, and rf current [1]. The SQUID metamaterial can be modelled as an array of weakly coupled oscillators with tunable resonant frequencies. An array of identical SQUIDs under identical conditions will have a coherent collective response regardless of the strength of the interactions between them. In the presence of disorder (nonuniform magnetic flux for instance) the individual SQUIDs in the array may or may not tune coherently. Since we are interested in metamaterial applications, the coherent response is desirable. In this talk we examine the conditions required for the SQUIDs to tune coherently, and compare to experimental data on tuning and nonlinearity in a variety of RF SQUID metamaterials.\\[4pt] [1] M. Trepanier*, Daimeng Zhang*, Oleg Mukhanov, Steven M. Anlage, Phys. Rev. X (in press), arXiv:1308.1410v2