Nonlinear characteristics of Ti, Nb, and NbN superconducting resonators for parametric amplifiers

TL;DR

This study investigates the nonlinear properties of Ti, Nb, and NbN superconducting resonators, demonstrating their potential as high-gain parametric amplifiers operable at cryogenic temperatures, with insights into their nonlinear responses and harmonic behaviors.

Contribution

It provides a comprehensive comparison of Ti, Nb, and NbN resonators under similar fabrication conditions, revealing their nonlinear characteristics and successful operation as parametric amplifiers at ~4 K.

Findings

Nb and NbN resonators achieved >20 dB gain.

Amplification occurs in fundamental and harmonic resonances.

High-temperature operation at ~4 K demonstrated.

Abstract

Superconducting resonators and parametric amplifiers are important components in scientific systems such as kinetic inductance detector arrays, frequency-domain multiplexers for other superconducting bolometers, spin-ensemble based memories, and circuit quantum electrodynamics demonstrators. In this paper, we report microwave measurements of superconducting Ti, Nb, and NbN resonators and their use as parametric amplifiers. These half-wave resonators were fabricated under near identical sputtering and lithographic conditions to ensure a like-for-like comparison of material properties. We report a wide range of properties and behaviours in terms of transition temperatures, resistivities, rate-limiting nonlinear response times, nonlinear dissipation, signs of the nonlinear inductances and their dependences on temperature and resonance harmonic. We have successfully operated Nb and NbN resonators as high gain parametric amplifiers, achieving greater than $20\,\mathrm{dB}$ of power amplification. We have shown that for a half-wave resonator, amplification can be realised not only in the fundamental resonance but also in the higher harmonic resonances. Further, for materials with high transition temperatures, e.g. Nb and NbN, amplification can be achieved at $\sim4\,\mathrm{K}$, i.e. a temperature maintained by a pulse tube cooler. Finally, in materials systems that have very fast response times, e.g. NbN, we have found that a cross-harmonic type of amplification can be achieved by placing pump tone in a different resonant mode as the signal and the idler. This wide range of observations will have important implications on the design and application of superconducting parametric amplifiers.