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arXiv:2408.07861 · IEEE Transactions on Applied Superconductivity

Modeling Flux-Quantizing Josephson Junction Circuits in Keysight ADS

Ofer Naaman, Mohamed H. Awida, T. White, Derek Slater, Sean Mcilvane, Edwin Yeung, Philip Krantz

Published Jan 15, 2025• 13 citations
arXivHTMLPDF

Abstract

We introduce Josephson junction and inductor models in Keysight Advanced Design System that feature an auxiliary flux port, and facilitate the expression of flux quantization conditions in simulation of superconducting microwave circuits. We present several examples that illustrate our methodology for constructing flux-quantizing circuits, including dc- andrf-SQUIDs, tunable couplers, and parametric amplifiers using superconducting nonlinear asymmetric inductive element and rf-SQUID arrays. We perform dc, S-parameter, and harmonic balance simulations to validate our models and methods against theory and published experimental results.

DOI
10.1109/tasc.2025.3528927

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Acta Physica Sinica•Jan 1, 2025•0 citations
We introduce Josephson junction and inductor models in Keysight Advanced Design System that feature an auxiliary flux port, and facilitate the expression of flux quantization conditions in simulation of superconducting microwave circuits. We present several examples that illustrate our methodology for constructing flux-quantizing circuits, including dc- andrf-SQUIDs, tunable couplers, and parametric amplifiers using superconducting nonlinear asymmetric inductive element and rf-SQUID arrays. We perform dc, S-parameter, and harmonic balance simulations to validate our models and methods against theory and published experimental results.
Josephson parametric amplifiers (JPAs) have become an important component of superconducting applications. Simulating these circuits is vital for optimizing their performance, including their gain and stability. Previously, simulating JPAs has been inefficient due to the limits of using SPICE-based simulators that work in the time domain. JPAs are better suited to frequency domain simulations over a broad frequency range and parameter space. We present JPA simulations using the recently released flux-aware Josephson junction (JJ) and inductor models in Keysight Advanced Design Systems (ADS). We simulate two different flux-driven JPAs: one based on an RF SQUID, and another based on a DC SQUID. We efficiently run harmonic balance simulations over a wide range of circuit parameters. We compare the use of RF and DC SQUIDs in these JPAs by analyzing their simulation results. This work provides a foundation for future SQUID-based JPA simulations in Keysight ADS.
Abstract This work presents an analysis of a flux-pumped Josephson parametric amplifier (JPA) with a detailed superconducting quantum interference device (SQUID) model, using the harmonic balance (HB) method in Keysight’s Advanced Design System. The model is built using the generalized resistively shunted junction model of a Josephson junction and the quantization condition of a SQUID, incorporating the effects of the geometric inductance and parasitic parameters. This approach is used to simulate the behavior of an unmatched lumped element JPA and an impedance-matched JPA, showing the necessity of the detailed SQUID model for the simulation of a broadband JPA by comparison with the results based on a widely used, simplified model. Gain profiles obtained from the approach are consistent with existing experiments in the literature, with reasonable accuracy. Due to the HB method, the simulation is of high efficiency, making it feasible to sweep and optimize parameters. This provides a useful method for the analysis of Josephson parametric amplification and the design of a JPA.
An improved tunable coupling element for building networks of coupled rf-superconducting quantum interference device (rf-SQUID) flux qubits has been experimentally demonstrated. This new form of coupler, based on the compound Josephson-junction rf-SQUID, provides a sign and magnitude tunable mutual inductance between qubits with minimal nonlinear crosstalk from the coupler tuning parameter into the qubits. Quantitative agreement is shown between an effective one-dimensional model of the coupler's potential and measurements of the coupler persistent current and susceptibility.
The 2ϕ-Josephson junctions (JJs), characterized by a dominant second harmonic in the current-phase relationship (CPR), are promising devices for low-power, high-density superconducting digital logic. These junctions eliminate the need for on-chip inductors to store magnetic flux and they reduce bias current requirements. In practical implementations, both first and second harmonic components are typically present in the CPR, affecting the junction dynamics and circuit operation. Understanding this behavior is essential for the reliable design of superconducting logic circuits utilizing these junctions, such as half flux quantum (HFQ) circuits. In this article, a compact Verilog-A model for 2ϕ-JJs is presented that captures the nonlinear behavior of the junctions, accounting for both harmonic contributions and their impact on damping. Two parameter sets are derived from experimental data corresponding to junctions with weak ferromagnetic barriers and ferromagnetic insulator barriers. Based on the inferred parameters, models of each junction type are developed. The model is validated against published experimental results and simulated within a D flip flop cell, demonstrating its use for superconducting circuit design and analysis, including evaluation of circuit behavior under nonideal junction conditions. Stability issues and failure mechanisms introduced by a nonzero first harmonic are analyzed, and underlying junction dynamics are examined to explain the reduction in circuit parameter margins.
Josephson junction, as the core nonlinear element underpinning superconducting electronics, is characterized by its current-phase relation (CPR), which fundamentally determines the dynamical properties and functional capabilities of superconducting quantum devices. Traditional Josephson junctions typically exhibit a traditional sinusoidal CPR; however, the junctions characterized by non-sinusoidal CPR have recently attracted considerable attention due to their distinctive physical properties and promising quantum device applications. In this work, a numerical model tailored specifically for junctions exhibiting non-sinusoidal CPR is developed by integrating experimentally measured current-voltage (I-V ) characteristics from Nb/Al-AlOx/Nb junctions into a resistively and capacitively shunted junction (RCSJ) framework. By leveraging this refined model, the influence of CPR skewness on Josephson junction dynamics is systematically investigated. Our results indicate that in underdamped junctions, the critical current significantly diminishes with the increase of CPR skewness, a behavior reminiscent of the adjustable critical currents typically observed in DC superconducting quantum interference devices (SQUIDs). Conversely, in overdamped junctions, the influence of CPR skewness on the I-V characteristics is found to be negligible. However, our numerical simulations under microwave irradiation indicate that nonsinusoidal CPRs readily promote the emergence of half-integer Shapiro steps in overdamped junctions, thereby establishing CPR skewness as a plausible microscopic origin for this phenomenon. In addition, the advanced design system (ADS) simulations is employed to model nonlinear resonators and DC SQUID circuits, offering a detailed investigation into how nonsinusoidal CPRs modulate the Josephson inductance and magnetic flux response. Our findings reveal that engineering the CPR of Josephson junctions provides substantial flexibility in the design of superconducting qubits, parametric amplifiers, and non-magnetic nonreciprocal devices. This tunability underscores significant opportunities for developing next-generation superconducting electronic components. The Josephson junctions with engineered CPR offer expanded functionality for superconducting quantum technologies. This study suggests that customized CPR can enhance control over the dynamical behavior of junctions, and promote the optimized designs of superconducting qubits, parametric amplifiers, and nonmagnetic nonreciprocal devices.