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IEEE Transactions on Applied Superconductivity

Investigating the $\chi ^{(3)}$ Nonlinearity of a Josephson Junction Array for Travelling-Wave Parametric Amplification in the W-Band

Javier Navarro Montilla, Ryan Stephenson, A. Barbier, Nikita S. Klimovich, Yves Bortolotti, E. F. C. Driessen, Peter K. Day, Boon-Kok Tan

Published Nov 24, 2025• 1 citation
Publisher

Abstract

At microwave frequencies, Josephson junction arrays have been widely employed to create metamaterials exhibiting a third-order ($\chi ^{(3)}$) nonlinearity, analogous to the Kerr effect in optics. These nonlinear metamaterials enable parametric amplification, as in Josephson Travelling-Wave Parametric Amplifiers (JTWPAs), which achieve quantum-limited noise performance over multi-gigahertz bandwidths. The exceptional properties of JTWPAs make them ideal for the sensitive readout of weak microwave signals, with applications in quantum computing, astrophysics, and fundamental physics experiments. Extending JTWPAs to higher frequencies, such as the W-band (70–110 GHz), holds promise for first-stage amplification in astronomical receivers, lowering system noise; as well as for reading out emerging superconducting qubit architectures at these frequencies. In this work, we investigate the$\chi ^{(3)}$nonlinear properties of Josephson arrays operating in the W-band as a step toward realising parametric gain at these frequencies. We designed and fabricated an array composed of 704 Nb/Al-AlO$_{\mathrm{x}}$/Nb tunnel junctions and experimentally demonstrated four-wave mixing via idler tone generation, providing clear evidence of third-order nonlinearity. These results mark an important step toward novel millimetre-wave and sub-millimetre-wave parametric-amplifier-based receiver technologies.

DOI
10.1109/tasc.2025.3636612

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Investigating the χ(3)\chi ^{(3)}χ(3) Nonlinearity of a Josephson Junction Array for Travelling-Wave Parametric Amplification in the W-Band
At microwave frequencies, Josephson junction arrays have been widely employed to create metamaterials exhibiting a third-order (χ(3)\chi ^{(3)}χ(3)) nonlinearity, analogous to the Kerr effect in optics. These nonlinear metamaterials enable parametric amplification, as in Josephson Travelling-Wave Parametric Amplifiers (JTWPAs), which achieve quantum-limited noise performance over multi-gigahertz bandwidths. The exceptional properties of JTWPAs make them ideal for the sensitive readout of weak microwave signals, with applications in quantum computing, astrophysics, and fundamental physics experiments. Extending JTWPAs to higher frequencies, such as the W-band (70–110 GHz), holds promise for first-stage amplification in astronomical receivers, lowering system noise; as well as for reading out emerging superconducting qubit architectures at these frequencies. In this work, we investigate theχ(3)\chi ^{(3)}χ(3)nonlinear properties of Josephson arrays operating in the W-band as a step toward realising parametric gain at these frequencies. We designed and fabricated an array composed of 704 Nb/Al-AlOx_{\mathrm{x}}x​/Nb tunnel junctions and experimentally demonstrated four-wave mixing via idler tone generation, providing clear evidence of third-order nonlinearity. These results mark an important step toward novel millimetre-wave and sub-millimetre-wave parametric-amplifier-based receiver technologies.
Recent progress in physics has increased the necessity for ultra-low noise amplifiers capable of operating at the quantum limit performance. These amplifiers are essential to enhance astronomical detection, dark-matter search, and qubit readout in quantum computing, among other applications. Superconducting Josephson junction Travelling Wave Parametric Amplifiers (JTWPAs) operated in the microwave range, have demonstrated high gain over several gigahertz (GHz) bandwidth, with quantum-limited noise performance and minimal heat dissipation. These excellent properties make JTWPAs an ideal solution for ultra-low noise amplification. This thesis delves into the design, fabrication and characterisation of JTWPAs operated in the microwave (1-16 GHz) and the W-band (70-115GHz) regimes. A generalised coupled-mode equations (CME) framework describing JTWPAs based on Josephson junctions and DC superconducting quantum interference devices (SQUIDs) is introduced. This framework can be combined with electromagnetic (EM) simulation softwares to model the JTWPAs, facilitating their design. It is therefore used to model two microwave JTWPA designs, using parallel plate capacitors (PPCs) and interdigitated capacitors (IDCs). The fabrication and characterisation of both designs are presented, and possible fabrication and design issues are carefully discussed. Despite these issues, we observed broadband gain in the JTWPA with PPCs, achieving > 20 dB gain at several frequency points, and a measured P1dB = −95.8dBm when operated at 17.3 dB. The RF properties of a 500-junction Josephson array are also presented in this manuscript. The device creates a Fabry-Perot cavity, leading to non-travelling wave parametric effects, such as narrow-band gain. We also observed indications of efficient phase-sensitive amplification. The thesis is concluded with the first — to the best of our knowledge — experimental attempt to extend the operational frequency of a JTWPA to the W-band. The novel design, fabrication techniques and characterisation of the W-band JTWPA are discussed in detail in this manuscript, leading to promising results suggesting that JTWPA could operate at high frequencies.
Abstract A Josephson traveling-wave parametric amplifier (JTWPA) is indispensable for the high-fidelity readout of superconducting qubits, owing to its broadband gain and near-quantum-limited noise performance. Conventional JTWPAs implemented with 0-Josephson junctions (0-JTWPAs) avoid magnetic-flux bias but rely on Kerr nonlinearity, which leads to pump-power-dependent phase mismatch, gain ripple, and a limited dynamic range. More recently, three-wave-mixing (3WM) JTWPAs employing flux-biased rf-SQUIDs have been proposed to suppress Kerr effects. However, these designs require a significant external flux bias per unit cell, which complicates cryogenic hardware, introduces sensitivity to flux noise, and limits scalability in large arrays. In this study, we propose and analyze a π -junction-based JTWPA ( π -JTWPA) in which the intrinsic π phase shift of the junction effectively displaces the operating point of the current–phase relation. This approach aims to realize 3WM-type nonlinearity with reduced flux bias while preserving broadband amplification, thereby simplifying flux-bias distribution, enhancing robustness against flux noise, and providing a pathway toward scalable, multiplexed quantum readout architectures. In addition, we examine the potential applicability of the π -JTWPA in four-wave-mixing (4WM) operation.
This work presents the design, fabrication strategy, and numerical modeling of niobium-based Josephson traveling-wave parametric amplifiers (JTWPAs) for quantum microwave readout. These devices are designed as nonlinear transmission lines composed of more than two thousand Josephson junction unit cells, with periodically embedded resonators enabling phase matching. The use of Nb trilayer technology (Nb/AlO[Formula: see text]/Nb) with respect to Al-based devices ensures higher junction uniformity, lower losses, and higher resilience to stray magnetic fields. We developed a multi-scale modeling framework combining harmonic balance methods and time-domain simulations of nonlinear coupled differential equations to describe wave propagation, parametric amplification, and spectral dynamics. Numerical results predict broadband gain up to 20[Formula: see text]dB over multi-GHz bandwidths. These results demonstrate the potential of Nb-based JTWPAs as scalable components for quantum applications.
Abstract Josephson traveling wave parametric amplifiers can have high gain and wide frequency range, high sensitivity, and low noise, which makes them promising for quantum computing, array receiver readout systems, spectroscopy, single-photon detectors, etc. In this paper, the authors investigate samples of traveling wave parametric amplifiers based on a three-layer Nb/AlO x /Nb superconductor–insulator–superconductor (SIS) structure with a SNAIL (Superconducting Nonlinear Asymmetric Inductive Elements) series array. Each SNAIL cell consists of the kinetic inductance of four SIS junctions and the nonlinear inductance of a smaller SIS junction. The cells are alternately connected in antiphase with respect to the magnetic flux, which ensures a change in the sign of the Kerr nonlinearity and a reduction in the phase mismatch for the pump frequency, signal frequency, and idler frequency. The transmission spectra of the samples were measured at temperatures of 4.2 and 2.8 K in the frequency range of 0.1–6 GHz.
We develop a novel concept of a Josephson traveling-wave parametric amplifier with three-wave mixing. The proposed amplifier consists of a microwave transmission line formed by a serial array of nonhysteretic one-junction SQUIDs. These SQUIDs are flux-biased such that the phase drops across the Josephson junctions are equal to 90°. This one-dimensional metamaterial possesses large quadratic nonlinearity and minimal cubic (Kerr-like) nonlinearity. This property allows phase matching and exponential power gain in a wide frequency range. The proof-of-principle measurements performed at temperature T = 4.2 K on Nb trilayer samples have demonstrated the validity of our concept of a practical Josephson parametric amplifier with great promise for quantum-limited performance.
Josephson traveling-wave parametric amplifiers (JTWPAs) are promising platforms for realizing broadband quantum-limited amplification of microwave signals. However, substantial gain in such systems is attainable only when strict constraints on phase matching of the signal, idler, and pump waves are satisfied---this is rendered particularly challenging in the presence of nonlinear effects, such as self- and cross-phase modulation, which scale with the intensity of propagating signals. In this work, we present a simple JTWPA based on ``left-handed'' (negative-index) nonlinear Josephson metamaterial, which has phase matching native to its design, precluding the need for any complicated circuit or dispersion engineering. The resultant efficiency of the four-wave-mixing process can implement gains in excess of 20 dB over few-gigahertz bandwidths with much shorter lines than previous implementations. Furthermore, the intrinsic phase matching considerably simplifies the JTWPA design and operation compared to the previous implementations based on ``right-handed'' (positive-index) Josephson metamaterials, making the proposed architecture particularly appealing for integration with large superconducting architectures. The left-handed Josephson transmission line introduced here constitutes an alternative modality in distributed Josephson circuits, and forms a crucial piece of the unified framework that can be used to inform the optimal design and operation of broadband microwave amplifiers.