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.
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.
Bringing signals from quantum to classical, from few-photon to many-photon levels for further processing, is a common challenge in rising quantum technologies. These include quantum computing, quantum communication, quantum sensing, radio astronomy, and dark matter searches, typically operating at microwave frequencies and millikelvin temperatures. Superconducting parametric amplifiers, as the first piece in the readout chain, have become a cornerstone of these technologies, since they offer unrivaled noise performance near the quantum-mechanical limit and high gain to surpass the noise of subsequent amplifiers. A notable implementation is the Josephson traveling-wave parametric amplifier (TWPA), which stands out due to its bandwidth of several Gigahertz and high saturation power, often larger than -100 dBm. These key properties come at the cost of complexity in design and fabrication: TWPA metamaterials often contain several thousands of Josephson junctions. Designing high-gain TWPAs involves three major challenges: ensuring impedance-matching, phase-matching of parametric amplification, and suppressing unwanted processes, all achievable through sub-wavelength dispersion engineering. This thesis covers the circuit design and analysis, implementation, and experimental characterization of a dispersion-engineered TWPA based on radio-frequency superconducting interference devices (rf-SQUIDs). It focuses on a detailed investigation of dispersion-engineering techniques and their effects on amplifier performance, particularly through the use of time-domain circuit simulations to analyze the multimode dynamics of the circuit. The experimentally realized device features 18 dB of gain, an instantaneous bandwidth spanning from 2.2 to 6.7 GHz, a system noise of 2.5 quanta, and a saturation power of (−86.5 ± 4.0) dBm. With these characteristics, it is suitable for frequency-multiplexed readout of detector arrays or qubits. Its high saturation power, about 10 dB higher than other reported Josephson-junction-based TWPAs, allows increasing the number of qubits per readout line, or decreasing the intermodulation between frequency-multiplexed qubits, both crucial for scaling up quantum computation.
Ultralow-noise microwave amplification and detection play a central role in different applications, going from fundamental physics experiments to the deployment of quantum technologies. In many applications the necessity of reading multiple detectors, or cavities or qubits, calls for large bandwidth amplifiers with the lowest possible noise. Current technologies are based on High Electron Mobility Transistors and Josephson Parametric Amplifiers. Both have limitations, the former in terms of the minimum noise, the latter in terms of bandwidth. Superconducting Traveling Wave Parametric Amplifiers (TWPAs) have the potential of offering quantum limited noise and large bandwidth. These amplifiers are based on the parametric amplification of microwaves traveling along a transmission line with embedded nonlinear elements. We are developing superconducting TWPAs based both on Josephson junction arrays (Traveling Wave Josephson Parametric Amplifiers) and on nonlinear kinetic inductance (Dispersion Engineered Traveling Wave Kinetic Inductance Amplifiers). Our goal is to achieve large bandwidth (in the 5 to 10 GHz range), large gain (more than 20 dB), large saturation power (more than −50 dBm), and near quantum limited noise (noise temperature less than 600 mK). Current achievements in the design and development of the high performance TWPAs are here reported and discussed, together with current limitations and possible future developments.
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.
Traveling-wave parametric amplifiers may be fabricated from superconducting films that exhibit highly nonlinear kinetic inductance. The coplanar waveguide of such a microwave device, extending to a meter or more in length but compacted to reside on a chip of the order of a square centimeter, is engineered with periodic variations in its width. These width variations, or loadings, alter the dispersion characteristics of a nonlinear current propagating along the waveguide, changing its group velocity and modulation behavior. A strong pump and a small signal injected into one end of the waveguide mix parametrically in the presence of the nonlinear kinetic inductance. Engineered dispersion induces the favorable conditions of overall phase matching, leading to generation of idler products as well as signal amplification of wide bandwidth, high dynamic range, and low noise, making the device of particular use in quantum computing and photon detection. The authors present a theoretical framework in which signal gain may be calculated solely from loading design. This involves construction of a metamaterial band theory of the engineered dispersion, which is used as a basis to describe the mixing of nonlinear traveling waves.
This research investigates the realization of parametric amplification in superconducting circuits and structures where nonlinearity is provided by Josephson junction (JJ) elements. We aim to develop a systematic analysis over JJ-based devices toward design of novel traveling-wave Josephson parametric amplifiers (TW-JPA). Chapters of this thesis fall into three categories: lumped JPA, superconducting periodic structures and discrete Josephson transmission lines (DJTL). \nThe unbiased Josephson junction (JJ) is a nonlinear element suitable for parametric amplification through a four-photon process. Two circuit topologies are introduced to capture the unique property of the JJ in order to efficiently mix signal, pump and idler signals for the purpose of signal amplification. Closed-form expressions are derived for gain characteristics, bandwidth determination, noise properties and impedance for this kind of parametric power amplifier. The concept of negative resistance in the gain formulation is observed. A design process is also introduced to find the regimes of operation for gain achievement. Two regimes of operation, oscillation and amplification, are highlighted and distinguished in the result section. Optimization of the circuits to enhance the bandwidth is also carried out. \nMoving toward TW-JPA, the second part is devoted to modelling the linear wave propagation in a periodic superconducting structure. We derive closed-form equations for dispersion and s-parameters of infinite and finite periodic structures, respectively. Band gap formation is highlighted and its potential applications in the design of passive filters and resonators are discussed. The superconducting structures are fabricated using YBCO and measured, illustrating a good correlation with the numerical results. \nA novel superconducting Transmission Line (TL), which is periodically loaded by Josephson junctions (JJ) and assisted by open stubs, is proposed as a platform to realize a traveling-wave parametric device. Using the TL model, this structure is modeled by a system of nonlinear partial differential equations (PDE) with a driving source and mixed-boundary conditions at the input and output terminals, respectively. This model successfully emulates parametric and nonlinear microwave propagation when long-wave approximation is applicable. The influence of dispersion to sustain three non-degenerate phased-locked waves through the TL is highlighted. \nA rigorous and robust Finite Difference Time Domain (FDTD) solver based on the explicit Lax-Wendroff and implicit Crank-Nicolson schemes has been developed to investigate the device responses under various excitations. Linearization of the wave equation, under small-amplitude assumption, dispersion and impedance analysis is performed to explore more aspects of the device for the purpose of efficient design of a traveling-wave parametric amplifier. \nKnowing all microwave characteristics and identifying different regimes of operation, which include impedance properties, cut-off propagation, dispersive behaviour and shock-wave formation, we exploit perturbation theory accompanied by the method of multiple scale to derive the three nonlinear coupled amplitude equations to describe the parametric interaction. A graphical technique is suggested to find three waves on the dispersion diagram satisfying the phase-matching conditions. Both cases of perfect phase-matching and slight mismatching are addressed in this work. The incorporation of two numerical techniques, spectral method in space and multistep Adams-Bashforth in time domain, is employed to monitor the unilateral gain, superior stability and bandwidth of this structure. Two types of functionality, mixing and amplification, with their requirements are described. These properties make this structure desirable for applications ranging from superconducting optoelectronics to dispersive readout of superconducting qubits where high sensitivity and ultra-low noise operation is required.
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=−68 dBm, IIP3=−55 dBm), and high magnetic field resilience -- making KITs an attractive technology for highly multiplexed readout of quantum information and superconducting detector systems.