约瑟夫森电路中的强驱动极限：从混沌到无界共振阈值

中文摘要 AI 辅助

强微波驱动可实现超导电路的快速测量与参数控制，但也可能诱导系统脱离预期的低能流形。我们针对磁通驱动和电荷驱动约瑟夫森电路，在驱动频率与直流磁通偏置范围内，建立了强驱动极限的统一描述。通过经典相空间分析与Floquet-Markov模拟，我们识别出低频与高频两种不同机制：低频下，我们表征了束缚态共振与 separatrix 混沌，发现磁通驱动的混沌阈值强烈依赖于直流磁通偏置；高频下，上述机制被抑制，耗散稳态从中心束缚态区转移至由势垒上方运行轨迹形成的外部共振区，所产生的无界共振阈值在研究范围内几乎与驱动频率、电路参数无关，主要由直流磁通偏置控制。相干模拟显示，参数操作可在该阈值之外继续进行，但速率会降低，从而为可实现的操作速度设定了有效上限。我们推导了两种阈值的解析判据，通过数值验证，并在磁通驱动SQUID中实验证实了低频阈值的直流偏置依赖关系。此外，我们还确定了向无界共振区转移以及驱动移除后弛豫回束缚态流形的时间尺度，最后将稳定性极限与基于结临界电流的互补图像关联，并将该框架扩展至多音驱动与电感分流电路。综上，这些结果明确了限制强驱动的机制，并为扩展约瑟夫森电路的稳定工作范围提供了途径。

英文摘要

Strong microwave drives enable fast measurement and parametric control in superconducting circuits but can induce transitions out of the intended low-energy manifold. We develop a unified description of strong-drive limits in flux- and charge-driven Josephson circuits across drive frequency and dc flux bias. Using classical phase-space analysis and Floquet--Markov simulations, we identify distinct low- and high-frequency mechanisms. At low frequency, we characterize bound-state resonances and separatrix chaos and find that the flux-drive chaos threshold depends strongly on dc flux bias. At high frequency, these mechanisms are suppressed, and the dissipative steady state transfers from the central bound-state sector to outer resonances formed by above-barrier running trajectories. The resulting unbound-resonance threshold is nearly independent of drive frequency and circuit parameters over the regime studied and is controlled primarily by dc flux bias. Coherent simulations show that parametric operation persists beyond this threshold, but at a reduced rate, setting an effective upper bound on the achievable operation speed. We derive analytical criteria for both thresholds, validate them numerically, and experimentally confirm the predicted dc-bias dependence of the low-frequency threshold in a flux-driven SQUID. We also determine the timescales for transfer into the unbound-resonance regime and relaxation back to the bound-state manifold after the drive is removed. Finally, we relate the stability limits to a complementary picture based on the junction critical current and extend the framework to multitone drives and inductively shunted circuits. Together, these results identify the mechanisms limiting strong driving and suggest routes to extend the stable operating range of Josephson circuits.

发表机构

• Fermi National Accelerator Laboratory (FNAL)（费米国家加速器实验室）
• Yale University（耶鲁大学）
• Yale Quantum Institute, Yale University（耶鲁大学量子研究所）

机构由 AI 辅助整理，请以论文原文为准。

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41 pages, 15 figures