{"paper":{"title":"Effective Hamiltonians in Cavity and Waveguide QED from Transition-Operator Diagrammatic Perturbation Theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Transition-operator diagrammatic perturbation theory enables systematic derivation of effective Hamiltonians in cavity and waveguide QED at arbitrary orders.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Louis Garbe, Maxime Federico, Mohamed Meguebel, Nadia Belabas, Nicolas Fabre","submitted_at":"2026-05-13T20:37:58Z","abstract_excerpt":"We propose an adiabatic-elimination formalism in the dispersive regime based on a transition-centric perturbation theory. The perturbative expansion is recast into a diagrammatic framework, while adiabatic elimination is implemented through controlled projections onto transition subspaces. Our approach applies systematically at arbitrary perturbation order, and is suited to multilevel systems and multiple qubits in both cavity and waveguide quantum electrodynamics. It ultimately enables the explicit construction of effective higher-order Hamiltonians while bypassing important limitations of ex"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our approach applies systematically at arbitrary perturbation order, and is suited to multilevel systems and multiple qubits in both cavity and waveguide quantum electrodynamics. It ultimately enables the explicit construction of effective higher-order Hamiltonians while bypassing important limitations of existing techniques.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The perturbative expansion remains valid and the projections onto transition subspaces remain controlled at arbitrary order in the dispersive regime for the targeted systems.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A transition-operator diagrammatic perturbation theory enables systematic construction of effective higher-order Hamiltonians in dispersive cavity and waveguide QED.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Transition-operator diagrammatic perturbation theory enables systematic derivation of effective Hamiltonians in cavity and waveguide QED at arbitrary orders.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"618760e6f86b821aed1e8b90ae4aa31e034e0bcbb727cf71293f4c84da490de8"},"source":{"id":"2605.14100","kind":"arxiv","version":1},"verdict":{"id":"e49b2ec6-8105-4dfe-b98e-25a34a56415a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T05:18:17.230992Z","strongest_claim":"Our approach applies systematically at arbitrary perturbation order, and is suited to multilevel systems and multiple qubits in both cavity and waveguide quantum electrodynamics. It ultimately enables the explicit construction of effective higher-order Hamiltonians while bypassing important limitations of existing techniques.","one_line_summary":"A transition-operator diagrammatic perturbation theory enables systematic construction of effective higher-order Hamiltonians in dispersive cavity and waveguide QED.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The perturbative expansion remains valid and the projections onto transition subspaces remain controlled at arbitrary order in the dispersive regime for the targeted systems.","pith_extraction_headline":"Transition-operator diagrammatic perturbation theory enables systematic derivation of effective Hamiltonians in cavity and waveguide QED at arbitrary orders."},"references":{"count":72,"sample":[{"doi":"","year":null,"title":"Recall the perturbative expansion Eq","work_id":"aa50844e-6f3d-4201-aa45-633d810dbec7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Computation with the resolvent In this subsection, we demonstrate how the time weightsv n(t) in Eq. (B13) may equivalently be retrieved by manipulating the resolventG(s) of the LiouvillianL G(s) = 1 s","work_id":"e8f6725d-5ca5-420d-b83f-099194d39fe7","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Computation of the reverse process’ weight This section provides a computation of the time weightv reverse n (t) of the reverse process of a givenn-th order JLM transition operator of time weightv n(t","work_id":"dd91b043-75d3-48d4-8a3b-481361c0c0f6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"1 (t)|γ⟩ ⟨α| ⊗ˆa† σj(ω′)ˆaσi(ω) + h.c,(C4) where the 1/2 factor stems from rule (R5) II B","work_id":"d88c2ad8-3e6e-4b7b-ac39-18d9f0b59898","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Stark-shift correction Employing the same procedure for the Stark-shift contributions lead to the total correction to the Hamiltonian at first order ∆ ˆH(1) int (t) ∆ ˆH(1) int (t) = 1 2 |γ⟩ ⟨α| ⊗ P Z","work_id":"e08d1552-90d9-413d-9095-e92437bdd79e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":72,"snapshot_sha256":"c090d91e7c87c9831df762bd2c026ecfa5c5ec7c68a874f447b22f859df5615b","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}