Measuring a Quantum Dot with an Impedance-Matching On-Chip Superconducting LC Resonator at Gigahertz Frequencies

We report on the realization of a bonded-bridge on-chip superconducting coil and its use in impedance matching a highly ohmic quantum dot (QD) to a 3-GHz measurement setup. The coil, modeled as a lumped-element LC resonator, is more compact and has a wider bandwidth than resonators based on coplanar transmission lines (e.g., lambda/4 impedance transformers and stub tuners), at potentially better signal-to-noise ratios. Specifically, for measurements of radiation emitted by the device, such as shot noise, the 50x-larger bandwidth reduces the time to acquire the spectral density. The resonance frequency, close to 3.25 GHz, is 3 times higher than that of the one previously reported, a wire-bonded coil. As a proof of principle, we fabricate an LC circuit that achieves impedance matching to an approximately 15-k Omega. load and validate it with a load defined by a carbon nanotube QD, whose shot noise we measure in the Coulomb-blockade regime.