发表机构
Steklov Mathematical Institute of Russian Academy of Sciences（俄罗斯科学院斯捷克洛夫数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个微扰框架，用于处理二次耦合到非高斯非幺正玻色子环境的系统，通过特征函数表示和递归构造生成器，并以量子比特双光子耦合为例展示四阶矩的影响。
AI 中文摘要
我们为二次耦合到具有二次哈密顿量和线性Lindblad算子的玻色子环境的系统开发了一个微扰框架。该方法适用于初始态可能为非高斯且非平稳的单模和多模环境。通过将加倍算子空间中的线性演化与特征函数表示相结合，我们将有序的多时间环境相关函数表示为初始特征函数导数的函数。这些相关函数进入时间卷积无生成器的任意有限阶递归构造。我们通过一个经由双光子相互作用耦合到阻尼模式的量子比特来展示该方法。具有相同一阶和二阶场矩的初始福克态和热态，通过它们的四阶矩产生不同的二阶生成器。
英文摘要
We develop a perturbative framework for systems coupled quadratically to bosonic environments with quadratic Hamiltonians and linear Lindblad operators. The method applies to both single-mode and multimode environments whose initial states may be non-Gaussian and nonstationary. By combining linear evolution in a doubled operator space with a characteristic-function representation, we express ordered multitime environmental correlation functions in terms of derivatives of the initial characteristic function. These correlation functions enter a recursive construction of the time-convolutionless generator at arbitrary finite order. We illustrate the method with a qubit coupled to a damped mode via a two-photon interaction. Initial Fock and thermal states with identical first and second field moments produce different second-order generators through their fourth moments.
