Circuit quantum electrodynamic model of dissipative-dispersive Josephson traveling-wave parametric amplifiers

TL;DR

This paper develops a quantum mechanical model for Josephson traveling-wave parametric amplifiers that incorporates substrate losses and thermal fluctuations, enabling accurate predictions of gain spectra and noise characteristics.

Contribution

It introduces an analytic quantum model including substrate losses and thermal noise, advancing understanding of amplifier behavior under realistic conditions.

Findings

Predicts asymmetric gain spectrum due to substrate losses

Quantifies added input noise including quantum and thermal contributions

Matches experimental data accurately

Abstract

We present a quantum mechanical model for a four-wave mixing Josephson traveling-wave parametric amplifier including substrate losses and associated thermal fluctuations. Under the assumption of a strong undepleted classical pump tone, we derive an analytic solution for the bosonic annihilation operator of the weak signal photon field using temporal equations of motion in a reference timeframe, including chromatic dispersion. From this result, we can predict the asymmetric gain spectrum of a Josephson traveling-wave parametric amplifier due to non-zero substrate losses. We also predict the equivalent added input noise including quantum fluctuations as well as thermal noise contributions. Our results are in excellent agreement with recently published experimental data.