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Instruments and Experimental Techniques

Four-Photon Josephson Traveling Wave Parametric Amplifier

A. A. Lomonosov, Roman Kubrakov, Lyudmila V. Filippenko, R. K. Kozulin, Крупенин Владимир Александрович, Victor K. Kornev, Michael A. Tarasov

Published Oct 1, 2024• 1 citation
Publisher

Abstract

Abstract Josephson traveling wave parametric amplifiers can have high gain and wide frequency range, high sensitivity, and low noise, which makes them promising for quantum computing, array receiver readout systems, spectroscopy, single-photon detectors, etc. In this paper, the authors investigate samples of traveling wave parametric amplifiers based on a three-layer Nb/AlO x /Nb superconductor–insulator–superconductor (SIS) structure with a SNAIL (Superconducting Nonlinear Asymmetric Inductive Elements) series array. Each SNAIL cell consists of the kinetic inductance of four SIS junctions and the nonlinear inductance of a smaller SIS junction. The cells are alternately connected in antiphase with respect to the magnetic flux, which ensures a change in the sign of the Kerr nonlinearity and a reduction in the phase mismatch for the pump frequency, signal frequency, and idler frequency. The transmission spectra of the samples were measured at temperatures of 4.2 and 2.8 K in the frequency range of 0.1–6 GHz.

DOI
10.1134/s0020441224701586

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Abstract Josephson traveling wave parametric amplifiers can have high gain and wide frequency range, high sensitivity, and low noise, which makes them promising for quantum computing, array receiver readout systems, spectroscopy, single-photon detectors, etc. In this paper, the authors investigate samples of traveling wave parametric amplifiers based on a three-layer Nb/AlO x /Nb superconductor–insulator–superconductor (SIS) structure with a SNAIL (Superconducting Nonlinear Asymmetric Inductive Elements) series array. Each SNAIL cell consists of the kinetic inductance of four SIS junctions and the nonlinear inductance of a smaller SIS junction. The cells are alternately connected in antiphase with respect to the magnetic flux, which ensures a change in the sign of the Kerr nonlinearity and a reduction in the phase mismatch for the pump frequency, signal frequency, and idler frequency. The transmission spectra of the samples were measured at temperatures of 4.2 and 2.8 K in the frequency range of 0.1–6 GHz.
This article presents the results of a study of samples of Josephson traveling wave parametric amplifiers (JTWPA) based on a three-layer superconductor-insulator-superconductor (SIS) type structure: Nb/ AI-OxlNb. The unit cell of the studied amplifiers was a SNAIL type element (Superconducting Nonlinear Asymmetric Inductive eLements) representing the nonlinear inductance of one or more SIS junctions and the kinetic inductance of four larger SIS junctions. The transmission spectra of the samples were measured at temperatures of4.2K4.2K4.2Kand2.8K2.8K2.8Kat frequency range of 0.1-6 GHz.
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 NNN) in the widest frequency range, 0≲fs,fi≲fp0 \lesssim f_s, f_i \lesssim f_p0≲fs​,fi​≲fp​, where fsf_sfs​, fif_ifi​ and fpf_pfp​ are the signal, idler and pump frequencies, respectively, obeying relation fs+fi=fpf_s + f_i = f_pfs​+fi​=fp​. Estimation of the amplifier characteristics with typical experimental parameters, number of cells NNN = 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.
Josephson parametric amplifiers are an important part of a modern superconducting quantum computing platform and squeezed quantum states generation devices. Traveling wave and impedance-matched parametric amplifiers provide broad bandwidth for high-fidelity single-shot readout of multiple qubit superconducting circuits. Here, we present a quantum-limited 3-wave-mixing parametric amplifier based on superconducting nonlinear asymmetric inductive elements (SNAILs), whose useful bandwidth is enhanced with an on-chip two-section impedance-matching circuit based on microstrip transmission lines. The amplifier dynamic range is increased using an array of 67 SNAILs with 268 Josephson junctions, forming a nonlinear quarter-wave resonator. Operating in a current-pumped mode, we experimentally demonstrate an average gain of 17 dB across 300 MHz bandwidth, along with an average saturation power of –100 dBm, which can go as high as −97 dBm with quantum-limited noise performance. Moreover, the amplifier can be fabricated using a simple technology with just one e-beam lithography step.
Abstract A Josephson traveling-wave parametric amplifier (JTWPA) is indispensable for the high-fidelity readout of superconducting qubits, owing to its broadband gain and near-quantum-limited noise performance. Conventional JTWPAs implemented with 0-Josephson junctions (0-JTWPAs) avoid magnetic-flux bias but rely on Kerr nonlinearity, which leads to pump-power-dependent phase mismatch, gain ripple, and a limited dynamic range. More recently, three-wave-mixing (3WM) JTWPAs employing flux-biased rf-SQUIDs have been proposed to suppress Kerr effects. However, these designs require a significant external flux bias per unit cell, which complicates cryogenic hardware, introduces sensitivity to flux noise, and limits scalability in large arrays. In this study, we propose and analyze a π -junction-based JTWPA ( π -JTWPA) in which the intrinsic π phase shift of the junction effectively displaces the operating point of the current–phase relation. This approach aims to realize 3WM-type nonlinearity with reduced flux bias while preserving broadband amplification, thereby simplifying flux-bias distribution, enhancing robustness against flux noise, and providing a pathway toward scalable, multiplexed quantum readout architectures. In addition, we examine the potential applicability of the π -JTWPA in four-wave-mixing (4WM) operation.
Investigating the χ(3)\chi ^{(3)}χ(3) Nonlinearity of a Josephson Junction Array for Travelling-Wave Parametric Amplification in the W-Band
At microwave frequencies, Josephson junction arrays have been widely employed to create metamaterials exhibiting a third-order (χ(3)\chi ^{(3)}χ(3)) nonlinearity, analogous to the Kerr effect in optics. These nonlinear metamaterials enable parametric amplification, as in Josephson Travelling-Wave Parametric Amplifiers (JTWPAs), which achieve quantum-limited noise performance over multi-gigahertz bandwidths. The exceptional properties of JTWPAs make them ideal for the sensitive readout of weak microwave signals, with applications in quantum computing, astrophysics, and fundamental physics experiments. Extending JTWPAs to higher frequencies, such as the W-band (70–110 GHz), holds promise for first-stage amplification in astronomical receivers, lowering system noise; as well as for reading out emerging superconducting qubit architectures at these frequencies. In this work, we investigate theχ(3)\chi ^{(3)}χ(3)nonlinear properties of Josephson arrays operating in the W-band as a step toward realising parametric gain at these frequencies. We designed and fabricated an array composed of 704 Nb/Al-AlOx_{\mathrm{x}}x​/Nb tunnel junctions and experimentally demonstrated four-wave mixing via idler tone generation, providing clear evidence of third-order nonlinearity. These results mark an important step toward novel millimetre-wave and sub-millimetre-wave parametric-amplifier-based receiver technologies.
We develop a novel concept of a Josephson traveling-wave parametric amplifier with three-wave mixing. The proposed amplifier consists of a microwave transmission line formed by a serial array of nonhysteretic one-junction SQUIDs. These SQUIDs are flux-biased such that the phase drops across the Josephson junctions are equal to 90°. This one-dimensional metamaterial possesses large quadratic nonlinearity and minimal cubic (Kerr-like) nonlinearity. This property allows phase matching and exponential power gain in a wide frequency range. The proof-of-principle measurements performed at temperature T = 4.2 K on Nb trilayer samples have demonstrated the validity of our concept of a practical Josephson parametric amplifier with great promise for quantum-limited performance.