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 oscillators in a strongly coupled 27x27 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 of rf flux amplitude, in agreement with simulation.
@article{arxiv.1811.11261,
title = {Imaging collective behavior in an rf-SQUID metamaterial tuned by DC and RF magnetic fields},
author = {Alexander P. Zhuravel and Seokjin Bae and Alexander V. Lukashenko and Alexander S. Averkin and Alexey V. Ustinov and Steven M. Anlage},
journal= {arXiv preprint arXiv:1811.11261},
year = {2019}
}