Measurements of a Quantum Dot with an Impedance-Matching On-Chip LC Resonator at GHz Frequencies

We report the realization of a bonded-bridge on-chip superconducting coil and its use in impedance-matching a highly ohmic quantum dot (QD) to a rm{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. λ/4 impedance transformers and stub tuners) at potentially better signal-to-noise ratios. In particular for measurements of radiation emitted by the device, such as shot noise, the 50times larger bandwidth reduces the time to acquire the spectral density. The resonance frequency, close to 3.25 GHz, is three times higher than that of the one previously reported wire-bonded coil. As a proof of principle, we fabricated an LC circuit that achieves impedance-matching to a rm{sim 15 kΩ} load and validate it with a load defined by a carbon nanotube QD of which we measure the shot noise in the Coulomb blockade regime.