Effect of Coupling on Hysteretic rf SQUID metamaterials*

Radio frequency Superconducting Quantum Interference Device (rf SQUID) has been established as a viable building block for microwave frequency metamaterials [1,2]. The single rf SQUID resonance frequency is tunable under applied dc flux, with a period of one flux quantum and the upper-frequency range scaling as √(1+β_rf). The previous experimental works restricted the parameter rf below unity to avoid hysteresis, and limited the coupling strength among SQUIDs to small and negative values, which resulted in single-SQUID like behaviors. In this work, we have built new arrays of rf SQUID meta-atoms in the hysteretic regime (β_rf>1) with strong negative and positive couplings. We experimentally observed period doublings in the dc flux tunability, and band gap formations, both of which emerged from collective behaviors of a strongly interacting and highly nonlinear system. These nontrivial behaviors demonstrated the potential for the rf SQUID metamaterial as a platform to study many-body physics.

[1] Phys. Rev. X, 3, 041029 (2013)  https://doi.org/10.1103/PhysRevX.3.041029

[2] Phys. Rev. X, 5, 041045 (2015) https://doi.org/10.1103/PhysRevX.5.041045