Imaging collective behavior in an rf-SQUID metamaterial tuned by DC and RF magnetic fields

We examine the collective behavior of two-dimensional nonlinear superconducting metamaterials using a non-contact spatially resolved imaging technique. The metamaterial is made up of sub-wavelength nonlinear microwave oscillators in a strongly coupled 27 × 27 planar array of radio-frequency Superconducting QUantum Interference Devices (rf-SQUIDs). By using low-temperature laser scanning microscopy, we image microwave currents in the driven SQUIDs while in non-radiating dark modes and identify the clustering and uniformity of like-oscillating meta-atoms. We follow the rearrangement of coherent patterns due to meta-atom resonant frequency tuning as a function of external dc and rf magnetic flux bias. We find that the rf current distribution across the SQUID array at zero dc flux and small rf flux reveals a low degree of coherence. By contrast, the spatial coherence improves dramatically upon increasing the rf flux amplitude, in agreement with simulation.