标题： 超导电路中的腔量子电动力学：高温下的极化率 显示英文标题

标题： Cavity QED in superconducting circuits: susceptibility at elevated temperatures

摘要： 我们研究超导电路的性质，实现腔量子电动力学。 特别是我们探索强耦合、低耗散和高温条件，这与当前和未来的实验相关。 我们专注于腔的电 susceptibility，因为它可以直接通过实验测量，即腔的阻抗或反射系数。 为此，我们在高温下研究强耦合 regime 中的耗散 Jaynes-Cummings 模型。 动力学是在 Bloch-Redfield 形式下进行研究的。 在低温下，当只有少数最低能级被占据时，susceptibility 可以表示为独立跃迁贡献的总和。 这对应于 Bloch-Redfield 形式中的主项（随机相位）近似。 当温度与振荡器频率相当或更高时，许多跃迁变得重要，并出现多峰结构。 我们表明，在这个 regime 中，只要峰开始重叠，主项近似就会失效。 换句话说，susceptibility 不再是独立跃迁贡献的总和。 我们通过精确对角化 qubit 加上最多 200 个振荡器状态的哈密顿量来数值处理系统的动力学。 我们将使用和不使用主项近似得到的结果进行比较，发现即使在中等温度下也存在定性差异。 显示英文摘要

摘要： We study the properties of superconducting electrical circuits, realizing cavity QED. In particular we explore the limit of strong coupling, low dissipation, and elevated temperatures relevant for current and future experiments. We concentrate on the cavity susceptibility as it can be directly experimentally addressed, i.e., as the impedance or the reflection coefficient of the cavity. To this end we investigate the dissipative Jaynes-Cummings model in the strong coupling regime at high temperatures. The dynamics is investigated within the Bloch-Redfield formalism. At low temperatures, when only the few lowest levels are occupied the susceptibility can be presented as a sum of contributions from independent level-to-level transitions. This corresponds to the secular (random phase) approximation in the Bloch-Redfield formalism. At temperatures comparable to and higher than the oscillator frequency, many transitions become important and a multiple-peak structure appears. We show that in this regime the secular approximation breaks down, as soon as the peaks start to overlap. In other words, the susceptibility is no longer a sum of contributions from independent transitions. We treat the dynamics of the system numerically by exact diagonalization of the Hamiltonian of the qubit plus up to 200 states of the oscillator. We compare the results obtained with and without the secular approximation and find a qualitative discrepancy already at moderate temperatures.