Effect of 2$^\text{nd}$ harmonic current--phase relation on a behavior of a Josephson Traveling Wave Parametric Amplifier

TL;DR

This paper numerically studies how second-harmonic current-phase relations affect the gain, stability, and operating modes of Josephson traveling wave parametric amplifiers, revealing optimal harmonic contributions for maximum gain.

Contribution

It introduces a detailed numerical analysis of second-harmonic effects on Josephson TWPAs, identifying optimal harmonic weights for enhanced amplification without dispersion engineering.

Findings

Gain up to ~13 dB achieved.

Harmonic contributions influence device stability.

Optimal harmonic weighting maximizes amplification.

Abstract

We numerically investigate the behavior of a Josephson traveling wave parametric amplifier assuming a current-phase relation with a second--harmonic contribution. We find that varying the weight of harmonic terms in the Josephson current affects the gain profile. The analysis of gain characteristics, phase-space portraits, Poincar\'e sections, and Fourier spectra demonstrates that the nonsinusoidal contribution influences the operating mode and stability of the device. In particular, we identify the optimal weighting of harmonic contributions that maximizes amplification, achieving gains up to $\sim 13\;\text{dB}$ in a device without dispersion engineering.