arXiv 2409.106562024-09-16quant-phcond-mat.quant-gascond-mat.stat-mechcond-mat.str-elhep-th

Schrieffer-Wolff微扰理论与色散相互作用的本征算符方法

Eigenoperator approach to Schrieffer-Wolff perturbation theory and dispersive interactions

Gabriel T. Landi

AI总结：

本研究将开放量子系统的本征算符分解概念引入Schrieffer-Wolff微扰理论，构建了直观系统的表述形式，并用该方法重新求解了多篇文献中的问题，重点分析了高度失谐系统耦合产生的色散相互作用。

摘要：

现代量子物理学具有很强的模块化特征：我们首先理解基本构建单元（如“XXZ哈密顿量”“Jaynes-Cummings模型”等），再将它们组合起来探索新效应。一个典型例子是将已知系统置于光学腔内。Schrieffer-Wolff微扰方法特别适合处理这类问题，因为它以哈密顿量的算符修正形式展开微扰，比传统定态微扰理论的能级修正更直观，但该方法缺乏系统性的研究路径。在本讲义中，我们讨论如何利用开放量子系统中广泛使用的本征算符分解概念，构建直观且系统的Schrieffer-Wolff微扰理论表述。为说明这一点，我们重新梳理了文献中多篇新旧论文，展示如何用本征算符求解这些问题。我们重点关注耦合两个跃迁频率差异极大（高度失谐）的系统的微扰，这类微扰会产生所谓的色散相互作用。

英文摘要：

Modern quantum physics is very modular: we first understand basic building blocks (``XXZ Hamiltonian'' ``Jaynes-Cummings'' etc.) and then combine them to explore novel effects. A typical example is placing known systems inside an optical cavity. The Schrieffer-Wolff perturbation method is particularly suited for dealing with these problems, since it casts the perturbation expansion in terms of operator corrections to a Hamiltonian, which is more intuitive than energy level corrections, as in traditional time-independent perturbation theory. However, the method lacks a systematic approach.% and has largely remained a niche topic. In these notes we discuss how \emph{eigenoperator decompositions}, a concept largely used in open quantum systems, can be employed to construct an intuitive and systematic formulation of Schrieffer-Wolff perturbation theory. To illustrate this we revisit various papers in the literature, old and new, and show how they can instead be solved using eigenoperators. Particular emphasis is given to perturbations that couple two systems with very different transition frequencies (highly off-resonance), leading to the so-called dispersive interactions.

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