# Josephson parametric converter saturation and higher order effects

## TL;DR

This paper investigates the gain saturation in Josephson parametric converters, revealing that Kerr nonlinearities, not pump depletion, dominate the behavior and proposing methods to optimize device performance considering these effects.

## Contribution

It demonstrates that Kerr nonlinearities are the main cause of saturation in Josephson parametric converters and introduces a new approach to optimize device performance amidst these nonlinearities.

## Key findings

- Kerr nonlinearities dominate gain saturation behavior.
- Saturation can occur at both lower and higher gains depending on bias.
- A new methodology for device optimization considering Kerr effects.

## Abstract

Microwave parametric amplifiers based on Josephson junctions have become a key component of many quantum information experiments. One key limitation which has not been well predicted by theory is the gain saturation behavior which determines its ability to process large amplitude signals. The typical explanation for this behavior in phase-preserving amplifiers based on three-wave mixing is pump depletion, in which the consumption of pump photons to produce amplification results in a reduction in gain. However, in this work we present experimental data and theoretical calculations showing that the fourth-order Kerr nonlinearities inherent in the Josephson junctions are the dominant factor in the Josephson Parametric Converter (JPC). The Kerr-based theory has the unusual property of causing saturation to both lower and higher gains, depending on bias conditions. This work presents a new methodology for optimizing device performance in the presence of Kerr nonlinearities while retaining device tunability, and points to the necessity of controlling higher-order Hamiltonian terms to make further improvements in parametric devices.