Schmid transition was introduced first as a superconductor-insulator transition in the zero-frequency response of a shunted Josephson junction in equilibrium at zero temperature. As it is typical for a quantum impurity problem, at finite frequencies the transition is broadened to a crossover. Modern attempts to find Schmid transition rely on finite-frequency measurements of a quantum circuit. We predict the frequency dependence of the admittance and reflection phase shift for a high-impedance transmission line terminated by a Josephson junction for a wide variety of devices, from a charge qubit to a transmon. Our results identify the circuit parameters needed for the experimental observation of universal scaling of the responses with frequency. On the insulating side of the transition, the full crossover from weak to strong coupling can only be observed in a transmon. On the contrary, observation of such crossover on the superconducting side of the transition is possible only with the charge qubit. The frequency dependence gets weaker and vanishes upon approaching the Schmid transition from either side.

中文翻译：

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施密德跃迁的微波光谱

施密德转变首先被引入作为零温度下平衡的分流约瑟夫森结的零频率响应中的超导体-绝缘体转变。由于这是典型的量子杂质问题，因此在有限频率下，跃迁会扩大到交叉。现代寻找施密德跃迁的尝试依赖于量子电路的有限频率测量。我们预测了由约瑟夫森结终止的高阻抗传输线的导纳和反射相移的频率依赖性，适用于从电荷量子位到传输mon的各种器件。我们的结果确定了响应随频率的通用缩放实验观察所需的电路参数。在过渡的绝缘侧，从弱耦合到强耦合的完全交叉只能在跨蒙中观察到。相反，只有通过电荷量子位才能观察到跃迁超导侧的这种交叉。当从任一侧接近施密德转变时，频率依赖性变弱并消失。