In Josephson traveling-wave parametric amplifiers, higher-order harmonics of the pump tone and its sidebands are commonly present and typically regarded as parasitic. Consequently, most design efforts have focused on suppressing these harmonics. In spite of that, motivated by transient simulations, we extend the coupled-mode theory and demonstrate that the third harmonic can enhance amplifier performance, improving both gain and bandwidth. We show that the recently developed plasma oscillation-based amplifier is particularly well-suited for exploiting this effect. Its dispersion relation enables us to observe the phenomenon in transient numerical simulations using JoSIM and WRspice. These simulations reveal the improvement of the amplifier’s performance, specifically doubling the bandwidth and increasing the gain.
In Josephson traveling-wave parametric amplifiers, higher-order harmonics of the pump tone and its sidebands are commonly present and typically regarded as parasitic. Consequently, most design efforts have focused on suppressing these harmonics. In spite of that, motivated by transient simulations, we extend the coupled-mode theory and demonstrate that the third harmonic can enhance amplifier performance, improving both gain and bandwidth. We show that the recently developed plasma oscillation-based amplifier is particularly well-suited for exploiting this effect. Its dispersion relation enables us to observe the phenomenon in transient numerical simulations using JoSIM and WRspice. These simulations reveal the improvement of the amplifier’s performance, specifically doubling the bandwidth and increasing the gain.
High gain and large bandwidth of traveling-wave parametric amplifier exploiting the nonlinearity of Josephson Junctions can be achieved by fulfilling the so-called phase-matching condition. This condition is usually addressed by placing resonant structures along the waveguide or by periodic modulations of its parameters, creating gaps in the waveguide’s dispersion. Here, we propose to employ the Josephson junctions, which constitute the centerline of the amplifier, as resonant elements for phase matching. By numerical simulations in JoSIM (and WRspice) software, we show that Josephson plasma oscillations can be utilized to create wave vector mismatch sufficient for phase matching as well as to prevent the conversion of the pump energy to higher harmonics. The proposed traveling wave parametric amplifier design has a gain of 15 dB and a 3 GHz bandwidth, which is comparable to the state-of-the-art TWPAs.
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.
The recent developments in quantum technologies, as well as advanced detection experiments, have raised the need to detect extremely weak signals in the microwave frequency spectrum. To this aim, the Josephson travelling wave parametric amplifier, a device capable of reaching the quantum noise limit while providing a wide bandwidth, has been proposed as a suitable cryogenic front-end amplifier. This work deals with the numerical study of a Josephson travelling wave parametric amplifier, without approximations regarding the nonlinearity of the key elements. In particular, we focus on the investigation of the system of coupled nonlinear differential equations representing all the cells of the Josephson travelling wave parametric amplifier, with proper input and output signals at the boundaries. The investigation of the output signals generated by the parametric amplification process explores the phase-space and the Fourier spectral analysis of the output voltage, as a function of the parameters describing the pump and signal tones that excite the device. Beside the expected behavior, i.e., the signal amplification, we show that, depending on the system operation, unwanted effects (such as pump tone harmonics, incommensurate frequency generation, and noise rise), which are not accounted for in simple linearized approaches, can be generated in the whole nonlinear system.
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.
The recently proposed Josephson traveling-wave parametric amplifier (JTWPA) based on a ladder transmission line consisting of radio-frequency superconducting quantum interference devices and exploiting three-wave mixing has great potential in achieving both a gain of 20 dB and a flat bandwidth of at least 4 GHz. To realize this concept in practical amplifiers, we model the advanced JTWPA circuit with periodic modulation of the circuit parameters (engineered dispersion loadings), which allow the basic mixing process, i.e., ωs=ωp−ωi, where ωs, ωp, and ωi are the signal, the pump, and the idler frequencies, respectively, and efficiently suppress propagation of unwanted higher tones, including ω2p=2ωp, ωp+s=ωp+ωs, ωp+i=ωp+ωi, etc. The engineered dispersion loadings allow achieving a sufficiently wide 3 dB-bandwidth from 3 to 9 GHz combined with a reasonably small ripple (±2 dB) in the gain-vs-frequency dependence.
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.