{"title":"Eigenoperator approach to Schrieffer-Wolff perturbation theory and dispersive interactions","authors":"Gabriel T. Landi","doi":"arxiv-2409.10656","DOIUrl":null,"url":null,"abstract":"Modern quantum physics is very modular: we first understand basic building\nblocks (``XXZ Hamiltonian'' ``Jaynes-Cummings'' etc.) and then combine them to\nexplore novel effects. A typical example is placing known systems inside an\noptical cavity. The Schrieffer-Wolff perturbation method is particularly suited\nfor dealing with these problems, since it casts the perturbation expansion in\nterms of operator corrections to a Hamiltonian, which is more intuitive than\nenergy level corrections, as in traditional time-independent perturbation\ntheory. However, the method lacks a systematic approach.% and has largely\nremained a niche topic. In these notes we discuss how \\emph{eigenoperator\ndecompositions}, a concept largely used in open quantum systems, can be\nemployed to construct an intuitive and systematic formulation of\nSchrieffer-Wolff perturbation theory. To illustrate this we revisit various\npapers in the literature, old and new, and show how they can instead be solved\nusing eigenoperators. Particular emphasis is given to perturbations that couple\ntwo systems with very different transition frequencies (highly off-resonance),\nleading to the so-called dispersive interactions.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10656","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.