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Physical Review Applied

Graphical impedance-matching method for a superconducting parametric amplifier

Kaiyong He, Qing Yu, Liangliang Yang, Yongcheng He, Jianshe Liu, Wei Ren Chen

Published Mar 26, 2024• 4 citations
Publisher

Abstract

This work proposes a graphical impedance-matching method for superconducting parametric amplifiers with quantum-limited noise performance using a modified Smith chart. It enables one to quickly apply the impedance-matching methods in microwave engineering to the design of parametric amplifiers. When the matching networks are composed of resonators and their equivalents, the matching of a parametric amplifier can be reduced to that of a negative-resistance amplifier, which is generally invalid due to the connection between the signal-frequency and idler-frequency networks introduced by the parametrically modulated component. Several examples are presented to demonstrate the effective and efficient matching of parametric amplifiers using this method, circumventing the need for complex calculations. This method also offers intuitive insight into how variations in pump strength and bias affect the amplification behavior of the circuit, which is useful in characterizing the parametric amplifier and finding the optimal operating state.

DOI
10.1103/physrevapplied.21.034055

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This work proposes a graphical impedance-matching method for superconducting parametric amplifiers with quantum-limited noise performance using a modified Smith chart. It enables one to quickly apply the impedance-matching methods in microwave engineering to the design of parametric amplifiers. When the matching networks are composed of resonators and their equivalents, the matching of a parametric amplifier can be reduced to that of a negative-resistance amplifier, which is generally invalid due to the connection between the signal-frequency and idler-frequency networks introduced by the parametrically modulated component. Several examples are presented to demonstrate the effective and efficient matching of parametric amplifiers using this method, circumventing the need for complex calculations. This method also offers intuitive insight into how variations in pump strength and bias affect the amplification behavior of the circuit, which is useful in characterizing the parametric amplifier and finding the optimal operating state.
Broadband quantum-limited amplifiers play a critical role in the single-shot readout of superconducting qubits, but a popular implementation, the traveling wave parametric amplifier, involves a complex design and fabrication process. Here, we present a simple design for a Josephson parametric amplifier, using a lumped element resonator comprising a superconducting quantum interference device whose useful bandwidth is enhanced with an on-chip impedance-matching circuit. We demonstrate a flux-coupling geometry that maximizes the coupling to the Josephson loop and minimizes spurious excitation of the amplifier resonant circuit. The amplifier, which operates in a flux-pumped mode, is demonstrated with a power gain of more than 20 dB over a bandwidth of about 300 MHz, where approximate noise measurements indicate quantum-limited performance. A procedure is given for optimizing the bandwidth for this kind of amplifier, using a linearized circuit simulation while minimizing non-linearities.
In this Master thesis, I present a theoretical description and experimental measurements of a tunable microwave resonator operated as a parametric amplifier. Superconducting parametric amplifiers have attracted great interest in recent years as it has been demonstrated that they can operate with a noise performance at the standard quantum limit. \nParametric amplification is achieved in the devices by modulating the electrical length of the resonator at twice the resonance frequency. The device measured in this thesis consists of a quarter-wavelength microwave resonator fabricated in a thin-film aluminum coplanar waveguide geometry. With a termination to ground through a Superconducting Quantum Interference Device (SQUID), the boundary condition of the resonator becomes sensitive to an applied magnetic field. This enables the tuning of the resonance frequencies, using a DC magnetic field, over a wide frequency range of 670MHz. Similarly, an AC magnetic field then allows for the modulation of the resonator electrical length at microwave frequencies. \nWe characterized the device by first measuring the DC tuning curves of the 2nd and 3rd harmonics of the resonator, around 4 GHz and 6 GHz respectively. We then studied parametric amplification in the device when the electrical length was modulated at approximately twice the resonance frequency of one of the modes. We scanned the pump frequency and pump power over a wide range to study the region in parameters which gives parametric gain. We performed an in-depth parameter sweep over this region, identifying pump parameters that provided maximum gain and maximum system noise improvements compared the following HEMT amplifier. \nWe find that the use of the parametric amplifier can improve the system noise temperature by more than 10 dB compared to a start-of-the-art commercial HEMT amplifier. This implies a performance near the standard quantum limit.
We report the lowest noise temperature of any microwave amplifier except the maser. This amplifier is a nearly degenerate superconducting parametric amplifier at X-band consisting of a low β, thin film, single junction SQUID, a monolithic 50 Ω to 1 Ω impedance matching network, and a cooled circulator. Nb/Nb2O5/Pb alloy junctions were incorporated into Nb and Pb-in circuitry on 1×2 cm silicon chips. The SQUID was phase-biased near 90° and driven by an external pump at approximately twice the operating frequency. The self-resonance frequency of the SQUID inductance and junction capacitance was set at the operating frequency of 8.2GHz. The operating charac teristics depended on the pump amplitude, the junction phase bias, and the SQUID parameters. For small values of\beta < 1, the maximum gain in both the signal and idler channels was ≈10dB, the bandwidth = 170MHz, and the single-sidehand noise temperature was 6K with an uncertainty of (+15 to -7)K. For higher β, the gain increased to nearly 30dB with increased noise and parametric oscillations occurring near the pump subharmonic frequency.
It has been recently demonstrated that a single Josephson junction with a properly engineered impedance environment can be used as a reflection amplifier approaching the quantum limit at microwave frequencies. In this article the authors describe an improved microwave setup for such a device. Voltage-tunable capacitors enable precise impedance matching across a wide range of operating points. Also, a branch-line coupler instead of a microwave circulator is used for the separation of the input and the output signals to make the system more compact and affordable. Furthermore, a custom-designed bias tee is introduced. The authors present characterization results of individual components as well as of the complete system. In particular, noise spectroscopy is used to study amplifier stability as a function of input matching.
In this thesis, we study two topics on superconducting circuits. \nThe first topic is the tunable coupler for resonators. \nThis coupler is implemented with a superconducting circuit coupling with resonators in the dispersive regime. \nIt possesses a high on/off ratio and the coupling between two degenerate resonators can be turned off by tuning the frequency of the coupler via the biasing flux. \nWe present the design, the simulation, \nand the fabrication of the chip implementing this coupler. \nWe derive the Hamiltonian of the chip via formal circuit quantization. \nWe also present numerical results of the eigenenergies and the eigenstates of the chip. \nFrom the numerical results, \nwe show that the tunable coupling and the turn-off point can be realized on the chip. \n \nThe second topic is impedance engineering for enhancing the bandwidth of a Josephson parametric amplifier. \nBy transforming the input impedance seen by the Josephson parametric amplifier, \nthe frequency dependence of the gain function can be decreased and the bandwidth of the Josephson parametric amplifier can be enhanced. \nWe study impedance engineering for two different types of flux pumping Josephson parametric amplifier. \nFor each type of amplifier, \nwe develop a corresponding method of impedance engineering, \nand study implementing the method with transmission lines.
Quantum-limited noise amplifiers based on superconducting Josephson junction elements are essential components for measuring low-power signals in a wide range of applications. The gain bandwidth of a flux-pumped Josephson parametric amplifier can be broadened by coupling junction elements with an impedance-matching network. Well-known modeling methods for these amplifiers typically assume ideal lumped-element circuits for passive components, but often overlook unexpected resonant modes arising from the bulk geometric features. To address this challenge, flux-pumped junction elements can be simulated using finite-element analysis (FEA) combined with the pumpistor modeling method, which accurately accounts for the geometric features of arbitrary impedance-matching circuits. Here, we present a benchmark study using a circuit topology to compare different modeling methods: (1) the coupled mode network method, (2) the harmonic balance method, (3) the analytical pumpistor method, and (4) the FEA-assisted pumpistor method. Our results highlight the importance of accurately reflecting geometric features to prevent unexpected resonant modes and avoid detuning from the target flux bias values.