Modeling Flux Tunability in Josephson Traveling Wave Parameteric Amplifiers With an Open-Source Frequency-Domain Simulator

Josephson traveling wave parameteric amplifiers (JTWPAs) are integral parts of many experiments carried out in quantum technologies. Being composed of hundreds of Josephson junction-based unit cells, such devices exhibit complex nonlinear behavior that typically cannot be fully explained with simple analytical models, thus necessitating the use of numerical simulators. A very useful characteristic of JTWPAs is the possibility of being biased by an external magnetic flux, allowing in-situ control of the nonlinearity. It is, therefore, very desirable for numerical simulators to support this feature. Open-source numerical tools that allow to model JTWPA flux biasing, such as WRSPICE or PSCAN2, are based on time-domain approaches, which typically require long simulation times to get accurate results. In this work, we model the gain performance in a prototypical flux-tunable JTWPA by using JosephsonCircuits.jl, a recently developed frequency-domain open-source numerical simulator, which has the benefit of simulation times about 10 000 faster than time-domain methods. By comparing the numerical and experimental results, we validate this approach for modeling the flux dependent behavior of JTWPAs.