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Superconducting QUantum Interference Device (SQUID) metamaterials aresuperconducting artificial media whose function relies both on their geometryand the extraordinary properties of superconductivity and the Josephson effect.Recent experiments on one- and two-dimensional radio-frequency (rf) SQUIDmetamaterials have revealed their wide-band tuneability, significantly reducedlosses, dynamic multistability, and tunable broadband transparency. Thesimplest version of an rf SQUID involves a superconducting ring interrupted bya Josephson junction; this device is a highly nonlinear resonator with a strongresponse to applied magnetic fields. SQUID metamaterials exhibit peculiarmagnetic properties such as negative diamagnetic permeability, predicted bothfor the quantum and the classical regime. The applied alternating fields induce(super)currents in the SQUID rings, which are therefore coupled throughdipole-dipole magnetic forces. This interaction is weak due to its magneticnature. However, it couples the SQUIDs non-locally since it falls-off as theinverse cube of their center-to-center distance.

Chimera states and synchronization in magnetically driven SQUID metamaterials