论文标题
时间依赖的Schrieffer-Wolff-lindblad扰动理论：分散读数的测量引起的分类和二阶变化
Time-dependent Schrieffer-Wolff-Lindblad Perturbation Theory: measurement-induced dephasing and second-order Stark shift in dispersive readout
论文作者
论文摘要
我们开发了时间依赖的Schrieffer-Wolff-Lindblad扰动理论，以研究驱动开放量子系统的有效相互作用。分析的起点是给定的lindblad方程，基于我们获得的有效（平均）图，该图描述了由于驱动器而导致的哈密顿量和崩溃算子的重新归一化。作为一个案例研究，我们将此方法应用于Transmon Qubit的分散读数，并得出了一个有效的异常图，该图描述了Transmon的测量引起的dephasing和Stark Shift。在绝热谐振器响应下，我们得出的有效图是完全积极和痕迹的。为了基准我们的方法，我们通过Lindbladian频谱对有效速率进行了良好的一致性。我们的结果也与Gambetta等人对这种影响的早期推导相吻合并扩展。 （Phys。Rev.A 74，042318（2006））使用谐振器场的正p-pressentation。
We develop a time-dependent Schrieffer-Wolff-Lindblad perturbation theory to study effective interactions for driven open quantum systems. The starting point of our analysis is a given Lindblad equation, based on which we obtain an effective (averaged) map that describes the renormalization of both the Hamiltonian and collapse operators due to the drive. As a case study, we apply this method to the dispersive readout of a transmon qubit and derive an effective disperive map that describes measurement-induced dephasing and Stark shift for the transmon. The effective map we derive is completely positive and trace-preserving under adiabatic resonator response. To benchmark our method, we demonstrate good agreement with a numerical computation of the effective rates via the Lindbladian spectrum. Our results are also in agreement with, and extend upon, an earlier derivation of such effects by Gambetta et al. (Phys. Rev. A 74, 042318 (2006)) using the positive P-representation for the resonator field.
