Magnetic graphs for cavity quantum electrodynamics
Abstract
Strengthening light-matter coupling has become a central challenge in cavity quantum electrodynamics (QED), enabling ultrafast gate operations, qubit protection, and deterministic nonlinear optics. As the coupling increases, even the simplest configuration, a two-level atom interacting with a quantized field, requires careful treatment, as exemplified by the gauge-invariant quantum Rabi model (QRM). Here we propose a magnetic graph model for single-atom cavity QED, which enables the interpretation of quantum dynamics across the ultrastrong coupling regime through graph connectivity. We demonstrate that the generalized QRM maps onto a complex bipartite graph of identical sites under Floquet boundary conditions. This framework captures the crossover from weak to deep-strong coupling via a single metric: the cost of disconnecting a nonmagnetic subgraph. We examine the mechanism underlying this connectivity transition, establishing phase frustration induced by subgraph topology as the primary driver. Scalable to many-body systems, this approach bridges graph theory and cavity QED, revealing highly complex-graph dynamics even in the simplest setting.
Versions
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BibTeX
@misc{yu2026magnetic,
title = {{Magnetic graphs for cavity quantum electrodynamics}},
author = {Sunkyu Yu and Xianji Piao and Namkyoo Park},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.04736},
eprint = {2607.04736},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04736},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Magnetic graphs for cavity quantum electrodynamics
AU - Sunkyu Yu
AU - Xianji Piao
AU - Namkyoo Park
PY - 2026
DA - 2026/07/06
PB - arXiv
DO - 10.48550/arxiv.2607.04736
UR - https://arxiv.org/abs/2607.04736
AB - Strengthening light-matter coupling has become a central challenge in cavity quantum electrodynamics (QED), enabling ultrafast gate operations, qubit protection, and deterministic nonlinear optics. As the coupling increases, even the simplest configuration, a two-level atom interacting with a quantized field, requires careful treatment, as exemplified by the gauge-invariant quantum Rabi model (QRM). Here we propose a magnetic graph model for single-atom cavity QED, which enables the interpretation of quantum dynamics across the ultrastrong coupling regime through graph connectivity. We demonstrate that the generalized QRM maps onto a complex bipartite graph of identical sites under Floquet boundary conditions. This framework captures the crossover from weak to deep-strong coupling via a single metric: the cost of disconnecting a nonmagnetic subgraph. We examine the mechanism underlying this connectivity transition, establishing phase frustration induced by subgraph topology as the primary driver. Scalable to many-body systems, this approach bridges graph theory and cavity QED, revealing highly complex-graph dynamics even in the simplest setting.
ER -