arXiv:2402.12037 · IEEE Transactions on Applied Superconductivity
Numerical Simulations of Josephson Traveling Wave Parametric Amplifiers (JTWPAs): Comparative Study of Open-Source Tools
Anna Levochkina, Halima Giovanna Ahmad, P. Mastrovito, I. Chatterjee, D. Massarotti, Domenico Montemurro, Francesco Tafuri, Giovanni Piero Pepe, Martina Esposito
Josephson Traveling Wave Parametric Amplifiers (JTWPAs) are largely exploited in quantum technologies for their broadband and low noise performance in the microwave regime. When one or more microwave tones are applied at the input, such devices show a complex wave-mixing response due to their intrinsic nonlinear nature. Numerical simulations of the JTWPAs nonlinear behaviour provide useful insights not only for the design of such devices, but also for the interpretation and validation of the experimental results. Here we present and discuss a comparative analysis of different open-source tools which can be used for JTWPAs numerical simulations. We focus on two tools for transient simulations, WRSPICE and PSCAN2, and on one tool for direct simulation of the frequency domain behaviour, JosephsonCircuit.jl. We describe the working principle of these three tools and test them considering as a benchmark a JTWPA based on SNAILs (Superconducting Nonlinear Asymmetric Inductive eLement) with realistic experimental parameters. Our results can serve as a guide for numerical simulations of JTWPAs with open-source tools, highlighting advantages and disadvantages depending on the simulation tasks.
Josephson Traveling Wave Parametric Amplifiers (JTWPAs) are largely exploited in quantum technologies for their broadband and low noise performance in the microwave regime. When one or more microwave tones are applied at the input, such devices show a complex wave-mixing response due to their intrinsic nonlinear nature. Numerical simulations of the JTWPAs nonlinear behaviour provide useful insights not only for the design of such devices, but also for the interpretation and validation of the experimental results. Here we present and discuss a comparative analysis of different open-source tools which can be used for JTWPAs numerical simulations. We focus on two tools for transient simulations, WRSPICE and PSCAN2, and on one tool for direct simulation of the frequency domain behaviour, JosephsonCircuit.jl. We describe the working principle of these three tools and test them considering as a benchmark a JTWPA based on SNAILs (Superconducting Nonlinear Asymmetric Inductive eLement) with realistic experimental parameters. Our results can serve as a guide for numerical simulations of JTWPAs with open-source tools, highlighting advantages and disadvantages depending on the simulation tasks.
Josephson traveling wave parameteric amplifiers (JTWPAs) are integral parts of many experiments carried out in quantum technologies. Being composed of hundreds of Josephson junction-based unit cells, such devices exhibit complex nonlinear behavior that typically cannot be fully explained with simple analytical models, thus necessitating the use of numerical simulators. A very useful characteristic of JTWPAs is the possibility of being biased by an external magnetic flux, allowing in-situ control of the nonlinearity. It is, therefore, very desirable for numerical simulators to support this feature. Open-source numerical tools that allow to model JTWPA flux biasing, such asWRSPICEorPSCAN2, are based on time-domain approaches, which typically require long simulation times to get accurate results. In this work, we model the gain performance in a prototypical flux-tunable JTWPA by usingJosephsonCircuits.jl, a recently developed frequency-domain open-source numerical simulator, which has the benefit of simulation times about 10 000 faster than time-domain methods. By comparing the numerical and experimental results, we validate this approach for modeling the flux dependent behavior of JTWPAs.
The development of large-scale superconducting quantum computers critically depends on the accurate readout of qubit states. To enable this, cryogenic parametric amplifiers have been proposed and developed, and have since found widespread use in small-signal detection applications. Among various amplifier architectures, Josephson traveling-wave parametric amplifiers (JTWPAs) are widely adopted due to their broad bandwidth, high saturation power, and compatibility with superconducting qubits. In this work, we present a design workflow of JTWPAs based on a co-simulation approach combining electromagnetic (EM) and circuit-level simulation. We apply this method to a uniform JTWPA, comparing our simulation results with experimental data. To mitigate the challenge of constructing lumped element circuit models usually used in conventional simulation method, we directly perform full EM analysis of the device to accurately determine its linear response. The extracted S parameters are then fed into a nonlinear harmonic balance simulator with Josephson junctions modeled as circuit elements. By doing so, the linear and gain properties of the JTWPA are extracted. Different factors that impact device performance including gain compression, phase matching, and fabrication imperfections are further investigated and modeled. A good agreement between simulation and measurements is identified, establishing the effectiveness of our approach in designing quantum parametric amplifiers.
Recent advancements in quantum technologies and advanced detection experiments have underscored the pressing need for the detection of exceedingly weak signals within the microwave frequency spectrum. Addressing this challenge, the Josephson Traveling Wave Parametric Amplifier (JTWPA) has been proposed as a cryogenic front-end amplifier capable of approaching the quantum noise limit while providing a relevant bandwidth. This research is centered on a comprehensive numerical investigation of the JTWPA, without resorting to simplifications regarding the nonlinearity of the essential components. Specifically, this study focuses on a thorough examination of the system, characterized by coupled nonlinear differential equations representing all components of the device. Proper input and output signals at the device's boundaries are considered. The analysis of the output signals undergoing the parametric amplification process involves a detailed exploration of phase-space dynamics and Fourier spectral analysis of the output voltage. This study is conducted while considering the parameters ruling the response of the device under pump and signal excitations. In addition to the expected signal amplification, the findings reveal that the nonlinear nature of the system can give rise to unforeseen phenomena, depending on the system's operational conditions, which include: the generation of pump tone harmonics, modulation of the signal gain, and incommensurate frequency generation—effects that are not easily accommodated by simplistic linearized approaches.
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 Traveling wave parametric amplifiers (TWPAs) are extensively employed in experiments involving weak microwave signals for their highly desirable quantum-limited and broadband characteristics. However, TWPAs’ broadband nature comes with the disadvantage of admitting the activation of spurious nonlinear processes, such as harmonics generation, that can potentially degrade amplification performance. Here we experimentally investigate a Josephson TWPA device with superconducting nonlinear asymmetric inductive element-based unit cells focusing on the amplification behaviour along with the generation of second and third harmonics of the pump. By comparing experimental results with transient numerical simulations, we demonstrate the influence of Josephson junctions’ fabrication imperfections on the occurrence of harmonics and on the gain behaviour.
Josephson traveling-wave parametric amplifiers (JTWPAs) are critical for superconducting quantum computers in enabling simultaneous high-fidelity measurements of many qubits. Despite their importance, translating designs to working hardware remains a significant obstacle, with numerical modeling increasingly being used to help close this gap. Unfortunately, existing time-domain (TD) circuit modeling methods struggle to close this gap due to their inability to model the physical layout of a device. In principle, finite-element time-domain (FETD) methods can model the JTWPA physical layout, but these simulations are complicated by the wide bandwidths and multiscale features involved. Here, we develop an unconditionally stable 1-D FETD model for JTWPAs that can model dispersive losses over wide bandwidths to begin overcoming these challenges. We validate our method against harmonic balance (HB) simulations of a Floquet-mode JTWPA before simulating a realistic multiplexed qubit readout scenario where HB is impractical.