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Abstract We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency superconducting quantum interference devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the $N\times N\times 2$overlapping metamaterial array, where we develop an understanding of the many ( $8N^2-8N+3$) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant responses of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10–30 GHz range on capacitively and inductively coupled rf SQUID metamaterials. 

ARIADNE (Axion Resonant InterAction Detection Experiment) is a table-top experiment that intends to search for QCD axions from exotic spin-dependent interactions mediated by axion between nuclei at sub-mm range. This experiment includes a non-magnetic mass to source the axion field, and a dense ensemble of hyper-polarized 3He nuclei to detect the axion field with nuclear-magnetic-resonance (NMR)-based method. The expected NMR signal from the interaction could be easily buried in the noise spectrum of the magnetometer, especially in a frequency range (~ 100 Hz) where the interaction signal is supposed to exist. In this work, we report optimization of SQUID gradiometer for ARIADNE including noise spectrum measurement.