In this paper, we present the design of a resonance phase-matched Josephson travelling-wave parametric amplifier that have a 12 GHz 3 dB-bandwidth centred near 10 GHz. Our design utilises a unilateral planar circuit structure which requires only a single layer of thin superconductor film deposited on a supporting substrate to reduce the fabrication complexity. The nonlinear medium of the device is provided by a series of Josephson junctions embedded in a coplanar waveguide with integrated shunt capacitor, and the dispersion of the transmission line is controlled by quarter wavelength resonators coupled capacitively to the feedline. Here, we describe in detail the electromagnetic designs of the various components of the amplifier, and the coupled-mode equations model that governs the three-wave mixing process. We extract the required circuit parameters of the amplifier through electromagnetic modelling, and determine the parametric gain-bandwidth product of the amplifier using an analytical model. Finally, we discuss the various design aspects that affect the overall performance of the amplifier.
In this paper, we present the design of a resonance phase-matched Josephson travelling-wave parametric amplifier that have a 12 GHz 3 dB-bandwidth centred near 10 GHz. Our design utilises a unilateral planar circuit structure which requires only a single layer of thin superconductor film deposited on a supporting substrate to reduce the fabrication complexity. The nonlinear medium of the device is provided by a series of Josephson junctions embedded in a coplanar waveguide with integrated shunt capacitor, and the dispersion of the transmission line is controlled by quarter wavelength resonators coupled capacitively to the feedline. Here, we describe in detail the electromagnetic designs of the various components of the amplifier, and the coupled-mode equations model that governs the three-wave mixing process. We extract the required circuit parameters of the amplifier through electromagnetic modelling, and determine the parametric gain-bandwidth product of the amplifier using an analytical model. Finally, we discuss the various design aspects that affect the overall performance of the amplifier.
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.
We propose and realize a multi-resonator coupled impedance-matched Josephson parametric amplifier. Parallel plate capacitors serve as couplers to achieve coupling between the nonlinear resonator containing the Josephson loop and the half-wavelength resonator, and between the half-wavelength resonators themselves. By precisely designing each coupling strength, we effectively extend the amplifier's bandwidth. Through a combination of circuit-level and electromagnetic field simulations, we optimize the structural parameters of the resonators and capacitors. The two measured devices have 15 dB gain with a bandwidth of 1.3 GHz and 20 dB gain with a bandwidth of 1.1 GHz, respectively, with near-quantum-limited noise temperatures.
We propose a technique to overcome phase mismatch in Josephson-junction traveling wave parametric amplifiers in order to achieve high gain over a broad bandwidth. Using "resonant phase matching," we design a compact superconducting device consisting of a transmission line with subwavelength resonant inclusions that simultaneously achieves a gain of 20 dB, an instantaneous bandwidth of 3 GHz, and a saturation power of -98 dBm. Such an amplifier is well suited to cryogenic broadband microwave measurements such as the multiplexed readout of quantum coherent circuits based on superconducting, semiconducting, or nanomechanical elements, as well as traditional astronomical detectors.
We develop a concept of traveling-wave Josephson parametric amplifier based on a ladder-type superconducting transmission line containing serial array of one-junctions SQUIDs. The circuit operates in a three-wave mixing mode and exploits both quadratic and cubic (Kerr) nonlinearities in the current-phase relation of the SQUIDs controlled by external magnetic flux. These two types of nonlinearities allow efficient three-wave mixing and perfect phase matching, respectively. The transmission line exhibits a power gain with exponential dependence on its length (number of cells N) in the widest frequency range, 0≲fs,fi≲fp, where fs, fi and fp are the signal, idler and pump frequencies, respectively, obeying relation fs+fi=fp. Estimation of the amplifier characteristics with typical experimental parameters, number of cells N = 700, length of 28 mm and pump frequency of 12.5 GHz yields a flat (-3 dB) gain of about 20 dB in the bandwidth from 3.35 GHz to 9.15 GHz and a saturation power of -90 dBm.
This work presents the design, fabrication strategy, and numerical modeling of niobium-based Josephson traveling-wave parametric amplifiers (JTWPAs) for quantum microwave readout. These devices are designed as nonlinear transmission lines composed of more than two thousand Josephson junction unit cells, with periodically embedded resonators enabling phase matching. The use of Nb trilayer technology (Nb/AlO[Formula: see text]/Nb) with respect to Al-based devices ensures higher junction uniformity, lower losses, and higher resilience to stray magnetic fields. We developed a multi-scale modeling framework combining harmonic balance methods and time-domain simulations of nonlinear coupled differential equations to describe wave propagation, parametric amplification, and spectral dynamics. Numerical results predict broadband gain up to 20[Formula: see text]dB over multi-GHz bandwidths. These results demonstrate the potential of Nb-based JTWPAs as scalable components for quantum applications.
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.