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Superconductor Science and Technology

Extending the kinetic-inductance travelling wave parametric amplifiers coupled-mode framework to other symmetric nonlinear mediums with χ ( 3 ) nonlinearity

Javier Navarro Montilla, Boon-Kok Tan

Published Jun 4, 2025• 1 citation
Publisher

Abstract

Abstract Superconducting travelling-wave parametric amplifiers (TWPAs) play a vital role in a range of high-sensitivity applications. These devices can be realised using various superconducting materials, such as high kinetic inductance films or low-loss transmission lines embedded with discrete nonlinear elements like Josephson junctions (JJs) or superconducting quantum interference devices (SQUIDs), and can operate across different wave-mixing regimes. However, a unifying framework for quick assessment and thus efficiently evaluating the performance of these diverse TWPA architectures, particularly during the design phase, remains lacking. Most existing models are derived from first principles for specific TWPA designs and lack general applicability. While certain simulation program with integrated circuit emphasis (SPICE) tools can more accurately emulate TWPA behaviour post-design, they are typically computationally intensive, time-consuming, and offer limited physical insight; especially regarding key performance-determining factors such as phase matching. This, in turn, impedes the rapid identification of optimal TWPA configurations. In this work, we extend a previously introduced framework for kinetic-inductance (KI-) TWPAs and demonstrate its applicability to a broader class of χ ( 3 ) -type TWPA configurations, including bare JJ (JTWPA) and symmetric SQUID-based TWPAs, operating in all wave-mixing modes. This approach facilitates rapid design-space exploration prior to detailed optimisation using SPICE-based simulations. Our method accommodates a wide range of unit cell topologies and meta-material parameters without requiring ground-up derivations from first principles. We validate the framework by comparing it against representative models from the literature, including JJ-, KI-, and DC SQUID-based TWPA designs, and show that it reliably captures the first-order behaviour of their gain–bandwidth characteristics.

DOI
10.1088/1361-6668/ade0f2

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Abstract Superconducting travelling-wave parametric amplifiers (TWPAs) play a vital role in a range of high-sensitivity applications. These devices can be realised using various superconducting materials, such as high kinetic inductance films or low-loss transmission lines embedded with discrete nonlinear elements like Josephson junctions (JJs) or superconducting quantum interference devices (SQUIDs), and can operate across different wave-mixing regimes. However, a unifying framework for quick assessment and thus efficiently evaluating the performance of these diverse TWPA architectures, particularly during the design phase, remains lacking. Most existing models are derived from first principles for specific TWPA designs and lack general applicability. While certain simulation program with integrated circuit emphasis (SPICE) tools can more accurately emulate TWPA behaviour post-design, they are typically computationally intensive, time-consuming, and offer limited physical insight; especially regarding key performance-determining factors such as phase matching. This, in turn, impedes the rapid identification of optimal TWPA configurations. In this work, we extend a previously introduced framework for kinetic-inductance (KI-) TWPAs and demonstrate its applicability to a broader class of χ ( 3 ) -type TWPA configurations, including bare JJ (JTWPA) and symmetric SQUID-based TWPAs, operating in all wave-mixing modes. This approach facilitates rapid design-space exploration prior to detailed optimisation using SPICE-based simulations. Our method accommodates a wide range of unit cell topologies and meta-material parameters without requiring ground-up derivations from first principles. We validate the framework by comparing it against representative models from the literature, including JJ-, KI-, and DC SQUID-based TWPA designs, and show that it reliably captures the first-order behaviour of their gain–bandwidth characteristics.
Abstract Kinetic inductance travelling wave parametric amplifiers (KI-TWPAs) have been simulated using Keysight’s Advanced Design System. A lumped element representation of a superconducting transmission line has been developed using nonlinear inductor elements to represent the current dependency of the intrinsic kinetic inductance. This provides a fast, simple and easily modifiable method for analysing the parametric processes that occur in nonlinear kinetic inductance devices, such as parametric oscillators or amplifiers while also allowing the accompanying RF network to be optimised. This methodology is used to model the behaviour of a select number of KI-TWPA designs operating in the 3-wave mixing (3WM) and 4-wave mixing (4WM) regimes. S-parameters and dispersion properties are extracted from large signal S-parameter simulations, and the gain curve of each amplifier design is generated from harmonic balance simulations. The results are compared to the gain expression from the analytic solutions of the coupled mode equations while making reference to the gain curves of the equivalent KI-TWPAs from literature.
Background: Kinetic Inductance Travelling Wave Parametric Amplifiers (KITWPAs) are a variant of superconducting amplifier that can potentially achieve high gain with quantum-limited noise performance over broad bandwidth, which is important for many ultra-sensitive experiments. In this paper, we present a novel modelling technique that can better capture the electromagnetic behaviour of a KITWPA without the translation symmetry assumption, allowing us to flexibly explore the use of more complex transmission line structures and better predict their performance. Methods: In order to design a KITWPA with optimal performance, we investigate the use of different superconducting thin film materials, and compare their pros and cons in forming a high-gain low-loss medium feasible for amplification. We establish that if the film thickness can be controlled precisely, the material used has less impact on the performance of the device, as long as it is topologically defect-free and operating within its superconducting regime. With this insight, we propose the use of Titanium Nitride (TiN) film for our KITWPA as its critical temperature can be easily altered to suit our applications. We further investigate the topological effect of different commonly used superconducting transmission line structures with the TiN film, including the effect of various non-conducting materials required to form the amplifier. Results: Both of these comprehensive studies led us to two configurations of the KITWPA: 1) A low-loss 100 nm thick TiN coplanar waveguide amplifier, and 2) A compact 50 nm TiN inverted microstrip amplifier. We utilise the novel modelling technique described in the first part of the paper to explore and investigate the optimal design and operational setup required to achieve high gain with the broadest bandwidth for both KITWPAs, including the effect of loss. Conclusions: Finally, we conclude the paper with the actual layout and the predicted gain-bandwidth product of our KITWPAs.
Background: Kinetic Inductance Travelling Wave Parametric Amplifiers (KITWPAs) are a new variant of superconducting amplifier that can potentially achieve high gain with quantum-limited noise performance over broad bandwidth, which is important for many ultra-sensitive experiments. In this paper, we present a novel modelling technique that can better capture the electromagnetic behaviour of a KITWPA without the translation symmetry assumption, allowing us to flexibly explore the use of more complex transmission line structures and better predict their performance. Methods: In order to design a KITWPA with optimal performance, we investigate the use of different superconducting thin film materials, and compare their pros and cons in forming a high-gain low-loss medium feasible for amplification. We establish that if the film thickness can be controlled precisely, the material used has less impact on the performance of the device, as long as it is topologically defect-free and operating within its superconducting regime. With this insight, we propose the use of Titanium Nitride (TiN) film for our KITWPA as its critical temperature can be easily altered to suit our applications. We further investigate the topological effect of different commonly used superconducting transmission line structures with the TiN film, including the effect of various non-conducting materials required to form the amplifier. Results: Both of these comprehensive studies led us to two configurations of the KITWPA: 1) A low-loss 100nm thick TiN coplanar waveguide amplifier, and 2) A compact 50nm TiN inverted microstrip amplifier. We utilise the novel modelling technique described in the first part of the paper to explore and investigate the optimal design and operational setup required to achieve high gain with the broadest bandwidth for both KITWPAs, including the effect of loss. Conclusions: Finally, we conclude the paper with the actual layout and the predicted gain-bandwidth product of our KITWPAs.
We present a detailed simulation and design framework for realizing traveling wave parametric amplifiers (TWPAs) using the nonlinear kinetic inductance of disordered superconductors -- in our case niobium-titanium-nitride (NbTiN). These kinetic inductance TWPAs (KITs) operate via three-wave mixing (3WM) to achieve high broadband gain and near-quantum-limited (nQL) noise. Representative fabricated devices -- realized using an inverted microstrip (IMS), dispersion-engineered, artificial transmission line -- demonstrate power gains above 25 dB, bandwidths beyond 3 GHz, and achieve ultimate system noise levels of 1.1 quanta even when operated with no magnetic shielding. These performance metrics are competitive with state-of-the-art Josephson-junction-based TWPAs but involve simpler fabrication and able to providing three orders of magnitude higher dynamic range (IIP1=−68IIP_1 = -68IIP1​=−68 dBm, IIP3=−55IIP_3 = -55IIP3​=−55 dBm), and high magnetic field resilience -- making KITs an attractive technology for highly multiplexed readout of quantum information and superconducting detector systems.
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.
We present the design and experimental characterization of a kinetic-inductance traveling-wave parametric amplifier (KI-TWPA) for sub-GHz frequencies. KI-TWPAs amplify signals through nonlinear mixing processes supported by the nonlinear kinetic inductance of a superconducting transmission line. The device described here utilizes a compactly meandered TiN microstrip transmission line to achieve the length needed to amplify sub-GHz signals. It is operated in a frequency translating mode where the amplified signal tone is terminated at the output of the amplifier, and the idler tone at approximately 2.5~GHz is brought out of the cryostat. By varying the pump frequency, a gain of up to 22 dB was achieved in a tunable range from about 450 to 850~MHz. Use of TiN as the nonlinear element allows for a reduction of the required pump power by roughly an order of magnitude relative to NbTiN, which has been used for previous KI-TWPA implementations. This amplifier has the potential to enable high-sensitivity and high-speed measurements in a wide range of applications, such as quantum computing, astrophysics, and dark matter detection.