Two-tone spectroscopy of a SQUID metamaterial in the nonlinear regime

Abstract

Compact microwave resonantors made of superconducting rings containing Josephson junctions (SQUIDs) are attractive candidates for building frequency-tunable metamaterials with low losses and pronounced nonlinear properties. We explore the nonlinearity of a SQUID metamaterial by performing a two-tone resonant spectroscopy. The small-amplitude response of the metamaterial under strong driving by a microwave pump tone is investigated experimentally and theoretically. The transmission coefficient S_{21} of a weak probe signal is measured in the presence of the pump tone. When increasing the power of the pump, we observe pronounced oscillations of the SQUID's resonance frequency f_{res}. The shape of these oscillations varies significantly with the frequency of the pump tone f_{dr}. The response to the probe signal displays instabilities and sidebands. A state with strong second-harmonic generation is observed. We provide a theoretical analysis of these observations, which is in good agreement with the experimental results.