发表机构
James C. Wyant College of Optical Sciences, University of Arizona（亚利桑那大学詹姆斯·C·怀安特光学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为驱动-耗散量子系统构建算符语言费曼规则，以高斯生成元为微扰基点，统一处理平均场与非高斯光子关联，并在Kerr腔、二能级原子及多格点链中验证其高效性与准确性。
AI 中文摘要
我们为量子光学算符语言中的林德布拉德主方程构建了费曼规则：一个固定的基本算符移动代数，以及关于一个精确可解（大多数情况下为高斯型）生成元的微扰论的闭式传播子。该展开分为运动学部分（Wick有序本征算符 $O_{mn}=:(c^\dagger)^m c^n:$ 上的移位代数，由此为指定相互作用组装顶点表）和动力学部分，后者仅通过未微扰生成元的预解式进入，对于任何稳定、可对角化的高斯 $L_0$（包括热库、压缩库和关联衰变）都是对角且可加的，并且同样适用于驱动或未驱动的二能级发射体。在驱动Kerr腔中，圈展开即为半经典展开，且级数是渐近的。在强驱动二能级原子中，缀饰线将有限半径的级数替换为深入饱和区仍精确的级数，每个Mollow分量对应一条线。对于Kerr环和链，在固定微扰阶数下，计算代价随格点数呈多项式增长。在三格点环上，图恢复了高斯累积量闭合所缺失的三光子关联的非高斯部分；推进到十阶时，在 $U\leq0.25\kappa$ 范围内，其给出的 $g^{(3)}$ 误差是所比较方法中最小的，且代价低于四阶闭合，而三阶和四阶闭合在中等耦合下更精确。相同的规则扩展到计数场倾斜生成元后，给出了无序八格点链的光子计数累积量，超越了直接对角化；在三个耦合强度下的量子跳跃轨迹与这些结果在 $1.6$ 个标准误差内一致，在最强耦合下误差在一个标准误差以内，此时第三累积量被置于高斯值之上六个标准误差处。
英文摘要
We construct Feynman rules for Lindblad master equations in the operator language of quantum optics: a fixed algebra of elementary operator moves and closed-form propagators for perturbation theory about an exactly solvable, in most cases Gaussian, generator. The expansion separates into a kinematic part (the shift algebra on the Wick-ordered eigenoperators $O_{mn}=:(c^\dagger)^m c^n:$, from which the vertex table for a specified interaction is assembled) and a dynamical part that enters only through the resolvent of the unperturbed generator, diagonal and additive for any stable, diagonalizable Gaussian $L_0$, including thermal and squeezed reservoirs and correlated decay, and equally available for a two-level emitter, driven or undriven. In the driven Kerr cavity the loop expansion is the semiclassical expansion and the series is asymptotic. In a strongly driven two-level atom, dressed lines replace a series of finite radius by one accurate deep into saturation, one line per Mollow component. For Kerr rings and chains the cost is polynomial in the number of sites at fixed perturbative order. On a three-site ring the diagrams recover the non-Gaussian part of the three-photon correlation that the Gaussian cumulant closure lacks; carried to tenth order they give the smallest $g^{(3)}$ error of the methods compared for $U\leq0.25κ$ at a cost below that of a fourth-order closure, and third- and fourth-order closures are more accurate at moderate coupling. The same rules, extended to the counting-field-tilted generator, give the photon-counting cumulants of a disordered eight-site chain beyond direct diagonalization; quantum-jump trajectories at three couplings agree with them to within $1.6$ standard errors, within one at the strongest coupling, where they place the third cumulant six standard errors above the Gaussian value.
