High-gain and large-bandwidth Josephson parametric amplifier influenced by Fabry-P\'erot interference

TL;DR

This paper presents a theoretical model and design methodology for a Josephson parametric amplifier that achieves high gain and broad bandwidth, while analyzing environmental effects like Fabry-Pérot interference on its performance.

Contribution

The authors develop an accurate model incorporating environmental interference, enabling improved design, characterization, and robustness of quantum-limited microwave amplifiers.

Findings

Achieves near-quantum-limited amplification with 20 dB gain and 50 MHz bandwidth.

Reproduces gain spectrum features caused by microwave reflections using Fabry-Pérot interference model.

Provides a framework for diagnosing and engineering environmental effects to optimize amplifier performance.

Abstract

Quantum-limited parametric amplifiers are essential components for many quantum technologies operating in the microwave domain. Achieving both high gain and broad bandwidth, however, remains challenging due to trade-offs between gain and bandwidth, pump efficiency, and dynamic range. Moreover, high-gain broadband amplifiers become increasingly sensitive to their external electromagnetic environment, which can distort their gain spectra and hinder reliable operation. Here, we present an accurate theoretical model and a systematic design methodology for a flux-driven, lumped-element Josephson parametric amplifier based on a SQUID array. Our device achieves near-quantum-limited, phase-preserving amplification with a net gain of 20 (maximally 44) dB and a 3-dB bandwidth of $\sim$50 ($\lesssim$0.2) MHz. We further show that the gain spectra exhibit pronounced sensitivity to weak reflections in the input-output waveguide caused by impedance mismatches in the microwave environment. By incorporating Fabry-P\'erot-type interference into a quantum input-output model, we analytically reproduce these complex spectral features and identify how they depend on the physical parameters of the environment. More generally, our results provide a practical framework for separating the intrinsic dynamics of parametric amplifiers from environmental effects. This approach enables reliable characterization and optimization of amplifier performance while providing a systematic strategy for diagnosing microwave reflections and engineering environmental interference to shape amplifier gain spectra, thereby offering a pathway toward robust, reproducible, and truly quantum-limited microwave amplification.