Interplay of coupling, residual, and quasiparticle losses for the frequency- and temperature-dependent quality factor of superconducting resonators

TL;DR

This study investigates how the quality factor of superconducting resonators depends on temperature and frequency, considering various loss mechanisms, and presents experimental data on lead-based resonators demonstrating these effects.

Contribution

The paper provides a comprehensive model and experimental validation of the frequency- and temperature-dependent losses in superconducting resonators, highlighting the interplay of different dissipation mechanisms.

Findings

Quality factor varies strongly with frequency and temperature.

Maximum quality factor occurs when residual and coupling losses match.

Measured Q exceeds 200,000 under optimal conditions.

Abstract

The overall, loaded quality factor $Q_\mathrm{L}$ quantifies the loss of energy stored in a resonator. Here we discuss on general grounds how $Q_\mathrm{L}$ of a planar microwave resonator made of a conventional superconductor should depend on temperature and frequency. We consider contributions to $Q_\mathrm{L}$ due to dissipation by thermal quasiparticles ($Q_\mathrm{QP}$), due to residual dissipation ($Q_\mathrm{Res}$), and due to coupling ($Q_\mathrm{C}$). We present experimental data obtained with superconducting stripline resonators fabricated from lead (Pb), with different center conductor widths and different coupling gaps. We probe the resonators at various harmonics between 0.7 GHz and 6 GHz and at temperatures between 1.5 K and 7 K. We find a strongly frequency- and temperature-dependent $Q_\mathrm{L}$, which we can describe by a lumped-element model. For certain resonators at lowest temperatures we observe a maximum in the frequency-dependent $Q_\mathrm{L}$ when $Q_\mathrm{Res}$ and $Q_\mathrm{C}$ match, and here the measured $Q_\mathrm{L}$ can exceed $2\times 10^5$.