Capturing Complex Behaviour in Josephson Travelling Wave Parametric Amplifiers

TL;DR

This paper analyzes wave-mixing in Josephson Travelling Wave Parametric Amplifiers, highlighting limitations of existing models and proposing extended equations validated by circuit simulations to improve design accuracy.

Contribution

It extends the coupled mode equations to better capture complex mixing behavior in JTWPA, validated through circuit simulations and systematic comparison.

Findings

Extended CMEs improve agreement with WRspice simulations.

Careful modeling is essential for accurate JTWPA design.

WRspice is recommended as a primary design tool.

Abstract

We present an analysis of wave-mixing in recently developed Josephson Travelling Wave Parametric Amplifiers (JTWPAs). Circuit simulations performed using WRspice show the full behaviour of the JTWPA allowing propagation of all tones. The Coupled Mode Equations (CMEs) containing only pump, signal, and idler propagation are shown to be insufficient to completely capture complex mixing behaviour in the JTWPA. Extension of the CMEs through additional state vectors in the analytic solutions allows closer agreement with WRspice. We consider an ordered framework for the systematic inclusion of extended eigenmodes and make a qualitative comparison with WRspice at each step. The agreement between the two methods validates both approaches and provides insight into the operation of the JTWPA. We show that care should be taken when using the CMEs and propose that WRspice should be used as a design tool for non-linear superconducting circuits such as the JTWPA.