Superposition of Inductive and Capacitive Coupling in Superconducting LC Resonators

We present an experimental investigation of lumped-element superconducting LC resonators designed to provide different types of coupling to a transmission line. We have designed four resonator geometries including dipole and quadrupole configured inductors connected in parallel with low-loss
${\rm SiN}_{\rm x}$
dielectric parallel-plate capacitors. The design of the resonator allows a change in the symmetry of the inductor or grounding of the capacitor to create LC resonators with: 1) inductive coupling, 2) capacitive coupling, 3) both types of coupling, or 4) greatly reduced coupling. We measured all four designs at a temperature of 30 mK at different values of power. We compare the extracted data from the four resonator types and find that both capacitive and inductive coupling can be included and that when nominally turned off, the coupling is greatly reduced from only minor changes in the circuit design. We also find a variation in the measured loss tangent of less than a few percent between the designs over a large range of internal quality factors, which are created by using
${\rm SiN}_{\rm x}$
as a nonlinear lossy element within the capacitor.