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 novel imaging technique. The metamaterial is made up of self-resonating microwave oscillators in a strongly coupled 27 x 27 planar array of radio-frequency Superconducting QUantum Interference Devices (rf SQUIDs). By using low-temperature laser scanning microscopy (LSM) we image the photoresponse caused by local heating across the SQUID array, and this corresponds to the strength of oscillation of each meta-atom. Complex collective modes of the metamaterial which are not revealed in global measurements become visible to the LSM. The clustering of active meta-atoms in each collective mode of the metamaterial are imaged. We observe 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 excited rf SQUID distribution across the metamaterial at zero dc flux and small rf flux reveals a low degree of coherence. By contrast, the spatial coherence heals upon increasing of rf flux amplitude. We discuss possible origins of such coherence variations.