Realization and modeling of rf superconducting quantum interference device metamaterials

We have prepared meta-atoms based on radio frequency superconducting quantum interference devices (RF SQUIDs) and examined their tunability with dc magnetic field, rf current, and temperature. RF SQUIDs are superconducting split ring resonators in which the usual capacitance is supplemented with a Josephson junction, which introduces strong nonlinearity in the rf properties. We find excellent agreement between the data and a model which regards the Josephson junction as the resistively and capacitively-shunted junction. A magnetic field tunability of 80 THz/Gauss at 12 GHz is observed, a total tunability of 56$%$ is achieved, and a unique electromagnetically-induced transparency feature at intermediate excitation powers is demonstrated for the first time. An RF SQUID metamaterial is shown to have qualitatively the same behavior as a single RF SQUID with regards to DC flux and temperature tuning.