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Acta Physica Sinica

Numerical analysis of dynamical behavior in Josephson junctions with non-sinusoidal current-phase relations

Liangliang Yang, HE Kaiyong, Genting Dai, CHANG Jinlin, JIANG Linpan, SUN Zhenyuan, Jianshe Liu, Wei CHEN

Published Jan 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.74.20250723

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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.
Superconducting quantum interference devices (SQUIDs) based on nanobridge junctions (NBJs) are promising platforms for highly sensitive magnetic detection. The SQUID performance is influenced by the non-sinusoidal current-phase relation (CPR) of NBJs. In this work, we measured the flux modulation of 10 asymmetric Nb SQUIDs based on three-dimensional NBJs, along with the CPR response in each device, which is mainly determined by the junction with the smaller critical current. By studying the CPR parameters (skewness Δ θ , critical current I c1 , and effective junction inductance L j ), together with the SQUID modulation characteristics (voltage modulation amplitude Δ I c R n and current modulation ratio Δ I c /2 I c1 ), we found that as I c1 increases from 0.6 μA to 6.6 μA and L j correspondingly decreases from 106 pH to 70 pH, the CPR skewness Δ θ increases from 0.2 rad to 1.5 rad. Over this range, Δ I c /2 I c1 decreases from 1.2 to 0.5, while Δ I c R n increases from about 0.06 mV to 0.22 mV. More specifically, Δ I c R n increases while Δ I c /2 I c1 decreases with increasing I c1 , whereas both quantities decrease with increasing L j . These results reveal a trade-off between intrinsic SQUID response and tolerance to readout noise, suggesting that improved performance can be achieved by engineering NBJs with increased I c1 and smaller L j .
In this work, we develop a comprehensive numerical analysis of the dynamic response of a Josephson Traveling Wave Parametric Amplifier (JTWPA) by varying the driving parameters, with a focus on the pathways leading to chaotic behavior. By tuning the working conditions, we capture the broad spectrum of dynamical regimes accessible to JTWPAs, delineating the settings under which transition to chaos occurs. Furthermore, we extend our investigation to device formed by junctions characterized by a non--sinusoidal current phase relation (CPR) and exploring the impact of its shape on the amplifier's performance. Through the study of gain characteristics, Poincaré sections, and Fourier spectra, we provide an in-depth understanding of how non-linearity and CPR nonsinusoidality influence the JTWPAs' operational effectiveness and stability. This investigation offers insights into optimizing the device designs for enhanced performance and robustness against chaotic disruptions, in order to establish a framework for predicting and controlling JTWPA behavior in practical applications. This effort will pave the way for the development of devices with tailored dynamic responses and for advancements in quantum computing and precision measurement technologies, where stability and high fidelity are of paramount importance.
Hybrid superconductor(S)-semiconductor(Sm) devices bring a range of functionalities into superconducting circuits. In particular, hybrid parity-protected qubits and Josephson diodes were recently proposed and experimentally demonstrated. Such devices leverage the nonsinusoidal character of the Josephson current-phase relation (CPR) in highly transparent S-Sm-S junctions. Here, we report an experimental study of superconducting quantum-interference devices (SQUIDs) embedding Josephson field-effect transistors fabricated from a SiGe/Ge/SiGe heterostructure grown on a 200-mm silicon wafer. The single-junction CPR shows up to three harmonics with gate-tunable amplitude. In the presence of microwave irradiation, the ratio of the first two dominant harmonics, corresponding to single and double Cooper-pair transport processes, is consistently reflected in relative weight of integer and half-integer Shapiro steps. A combination of magnetic-flux and gate-voltage control enables tuning the SQUID functionality from a nonreciprocal Josephson-diode regime with 27% asymmetry to a π -periodic Josephson regime suitable for the implementation of parity-protected superconducting qubits. These results illustrate the potential of Ge-based hybrid devices as versatile and scalable building blocks of superconducting quantum circuits. Published by the American Physical Society 2024
A comprehensive numerical analysis of the dynamical response of Josephson Traveling Wave Parametric Amplifiers (JTWPA) under varying driving conditions is presented. The primary goal is to examine the effects of a current–phase relation (CPR) incorporating a second-harmonic contribution. The analysis further investigates how parameters such as pump intensity, signal frequency, and DC bias current influence the transition to chaos. The results reveal a wide range of dynamical regimes in JTWPAs, offering insights into optimizing device performance and stability. Notably, the shape of the CPR is shown to have a significant impact on the operational effectiveness and stability of JTWPAs. To obtain results closer to real devices, numerical modeling of JTWPAs implementing Resonant Phase Matching (RPM) circuitry has been performed. We have verified that the introduction of RPM allows a significant increase in the amplifier gain also in the case of non-sinusoidal CPR. These findings may have important implications for the development of next-generation JTWPAs, which are essential components in quantum computing and precision measurement applications.
We tackled the numerical analysis of the dynamic response of a Josephson Traveling Wave Parametric Amplifier (JTWPA) by varying the driving parameters, with a focus on the pathways leading to chaotic behavior. By tuning the working conditions, we explore the broad spectrum of dynamical regimes accessible to JTWPAs, delineating the conditions under which transition to chaos occurs. Furthermore, we extend our investigation to junctions characterized by a non-sinusoidal current phase relation (CPR) and explore the consequences on the amplifier’s performance. Through the study of gain characteristics, Poincaré sections, and Fourier spectra, we provide an in-depth understanding of how CPR nonlinearity and nonsinusoidality influence the operational effectiveness and stability of JTWPAs. This investigation offers insights into optimizing the device for enhanced performance and robustness against chaotic disruptions, in order to establish a framework for predicting and controlling JTWPA behavior in practical applications. In fact, we identify the regions in the parameter space where the input signal is maximally amplified without excessive noise or undesired harmonics. This effort paves the way for the development of devices with tailored dynamic responses and for advancements in quantum computing and precision measurement technologies, where stability and high fidelity are of paramount importance.
Controlling the current-phase relation (CPR) of Josephson elements is essential for tailoring the eigenstates of superconducting qubits, tuning the properties of parametric amplifiers, and designing nonreciprocal superconducting devices. Here, we introduce the hybrid Josephson rhombus, a highly tunable superconducting circuit containing four semiconductor-superconductor hybrid Josephson junctions embedded in a loop. Combining magnetic frustration with gate-voltage-controlled tuning of individual Josephson couplings provides deterministic control of the harmonic content of the rhombus CPR. We show that, for balanced Josephson couplings at full frustration, the hybrid rhombus displays a π -periodic cos ( 2 φ ) potential, indicating coherent charge- 4 e transport. Tuning away from the balanced configuration, we observe a superconducting diode effect with efficiency exceeding 25%. These results showcase the potential of hybrid Josephson rhombi as fundamental building blocks for noise-resilient qubits and quantum devices with custom transport properties.