Geometric Superinductors for Mesoscopic Physics*

High impedance has recently risen as a tool for circuit engineering in cQED. For regular microwave circuits the agreed upon impedance is 50Ω, vacuum itself has an impedance of 377Ω. In the quantum realm however there is a threshold above which a superconducting circuit is considered high impedance, the resistance quantum R_Q=6kΩ. In fact impedance of the environment affects the quantum fluctuations of phase and charge and when the quantum resistance is surpassed charge fluctuations are suppressed to below 2e. Most interesting is the behavior of the Josephson junction (a key element for superconducting qubits) in this regime. The low charge fluctuations allow for the measurement of Coulomb blockade and Bloch oscillations of charge. This work demonstrates how the use of geometric superconducting inductors can become a new method to achieve high impedance. The inductor consists of a superconducting high density planar coil suspended on a 220nm silicon membrane which can achieve characteristic impedances of 14kΩ while having a self-resonance frequency above 8GHz. We present this new circuit element and it’s applications for the measurement of Josephson junctions in the high impedance regime.