Vulnerability to Parameter Spread in Josephson Traveling-Wave Parametric Amplifiers

TL;DR

This paper investigates how circuit parameter variations affect the performance of Josephson traveling-wave parametric amplifiers, focusing on flux-biased rf-SQUIDs with dispersion engineering techniques to improve robustness and optimize gain.

Contribution

It introduces a detailed analysis of parameter spread effects on JTWPAs using circuit simulations, comparing resonant phase-matching and periodic capacitance modulation methods.

Findings

PCM is less sensitive to parameter spread than RPM.

Flux-bias points with Kerr-free nonlinearity are near optimal for critical current spread.

Simulation approach accounts for reflections, unwanted mixing, and pump depletion.

Abstract

We analyze the effect of circuit parameter variation on the performance of Josephson traveling-wave parametric amplifiers (JTWPAs). Specifically, the JTWPA concept we investigate is using flux-biased nonhysteretic rf-SQUIDs in a transmission line configuration, which harnesses the three-wave mixing (3WM) regime. Dispersion engineering enables phasematching to achieve power gain of $\sim$20 dB, while suppressing the generation of unwanted mixing processes. Two dispersion engineering concepts using a 3WM-JTWPA circuit model, i.e., resonant phase-matching (RPM) and periodic capacitance modulation (PCM), are discussed, with results potentially also applicable to four-wave-mixing (4WM) JTWPAs. We propose suitable circuit parameter sets and evaluate amplifier performance with and without circuit parameter variance using transient circuit simulations. This approach inherently takes into account microwave reflections, unwanted mixing products, imperfect phasematching, pump depletion, etc. In the case of RPM the resonance frequency spread is critical, while PCM is much less sensitive to parameter spread. We discuss degrees of freedom to make the JTWPA circuits more tolerant to parameter spread. Finally, our analysis shows that the flux-bias point where rf-SQUIDs exhibit Kerr-free nonlinearity is close to the sweet spot regarding critical current spread.