Pith Number

pith:USILHEBN

pith:2026:USILHEBN3H4MGMPLYXUDHTTRKQ

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Effective Hamiltonians in Cavity and Waveguide QED from Transition-Operator Diagrammatic Perturbation Theory

Louis Garbe, Maxime Federico, Mohamed Meguebel, Nadia Belabas, Nicolas Fabre

Transition-operator diagrammatic perturbation theory enables systematic derivation of effective Hamiltonians in cavity and waveguide QED at arbitrary orders.

arxiv:2605.14100 v1 · 2026-05-13 · quant-ph

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Claims

C1strongest 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.

C2weakest 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.

C3one line summary

A transition-operator diagrammatic perturbation theory enables systematic construction of effective higher-order Hamiltonians in dispersive cavity and waveguide QED.

References

72 extracted · 72 resolved · 0 Pith anchors

[1] Recall the perturbative expansion Eq

[2] 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

[3] 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

[4] 1 (t)|γ⟩ ⟨α| ⊗ˆa† σj(ω′)ˆaσi(ω) + h.c,(C4) where the 1/2 factor stems from rule (R5) II B

[5] 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

Receipt and verification

First computed	2026-05-17T23:39:12.107630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a490b3902dd9f8c331ebc5e833ce7154385a832fb2b9a3d3bd801bc3438a3fa9

Aliases

arxiv: 2605.14100 · arxiv_version: 2605.14100v1 · doi: 10.48550/arxiv.2605.14100 · pith_short_12: USILHEBN3H4M · pith_short_16: USILHEBN3H4MGMPL · pith_short_8: USILHEBN

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/USILHEBN3H4MGMPLYXUDHTTRKQ \
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  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a490b3902dd9f8c331ebc5e833ce7154385a832fb2b9a3d3bd801bc3438a3fa9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea25a0243a7d5217e3a28efb2ddf8dc005028886644c7c0aa5e19810cd2a83c6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-13T20:37:58Z",
    "title_canon_sha256": "9e4e2ecbf72d1c4442d3e04ef84ecbd26316b81b634a83f6a8b88144793d2c04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14100",
    "kind": "arxiv",
    "version": 1
  }
}