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arXiv:2203.09660 · Superconductor Science and Technology

Simulating the behaviour of travelling wave superconducting parametric amplifiers using a commercial circuit simulator

Thomas Sweetnam, D. Banys, V. Gilles, M. McCulloch, L. Piccirillo

Published Jul 28, 2022• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1361-6668/ac850b

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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.
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 We present the design and simulation methodology of a superconducting ridge-gap waveguide (RGWG) as a potential basis for mm-wave kinetic inductance travelling wave parametric amplifiers (KI-TWPAs). A superconducting RGWG was designed using Ansys HFSS to support a quasi-TEM mode of transmission over a bandwidth of 20–120 GHz with its internal dimensions optimised for integration with W-band rectangular waveguide. A design of an impedance loaded travelling wave structure incorporating periodic perturbations of the ridge was described. A method to simulate the nonlinear kinetic inductance via user-defined components in Keysight’s ADS was outlined, which yielded the power dependent S-parameters and parametric signal gain. A RGWG with a 30 nm NbTiN coating and 5 $$\upmu$$ μ m conductor spacing, corresponding to a kinetic inductance fraction α∼60%\alpha \sim 60\%α∼60% α ∼ 60 % was used for the description of a KI-TWPA with 900 perturbations equivalent to a physical length 25 cm that achieved more than 10 dB of signal gain over a 75–110 GHz bandwidth via 4-wave mixing (4WM).
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.
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.
Superconducting parametric amplifiers have great promise for quantum-limited readout of superconducting qubits and detectors. Until recently, most superconducting parametric amplifiers had been based on resonant structures, limiting their bandwidth and dynamic range. Broadband traveling-wave parametric amplifiers based both on the nonlinear kinetic inductance of superconducting thin films and on Josephson junctions are in development. By modifying the dispersion property of the amplifier circuit, referred to as dispersion engineering, the gain can be greatly enhanced and the size can be reduced. We present two theoretical frameworks for analyzing and understanding such parametric amplifiers: 1) generalized coupled-mode equations and 2) a finite difference time domain (FDTD) model combined with a small signal analysis. We show how these analytical and numerical tools may be used to understand device performance.
Kinetic inductance parametric amplifiers (KIPAs) have been widely studied for small-signal detection in superconducting quantum circuits. In this work, we demonstrate the modeling of a niobium nitride nanowire based KIPA using electromagnetic (EM) and circuit co-simulation, and compare the outcomes with experimental results. EM analysis is first performed on the device layout, taking into account the linear part of the kinetic inductance. The results are then integrated into a harmonic balance circuit simulator, in which the currentdependent inductance is modeled by representing the nanowire as a nonlinear inductor. Both linear and nonlinear responses of the device, including temperature-dependent resonance spectra and parametric gain, are extracted and show good agreement with experiments. We further show that when the KIPA operates as a degenerate amplifier, its phase-sensitive behavior can be accurately reproduced by the simulation. Our technique can serve as a valuable enabler for the simulation and design of quantum parametric amplifiers and superconducting kinetic inductance devices.