Excitation Gap of a Confined Chiral Mode Measures Critical Zero-Point Fluctuations
Abstract
Where uniform and chiral superradiant boundaries meet in a quantum Rabi ring, the quadratic theory leaves a degenerate chiral ladder with finite radial width. We show that adding one chiral quantum widens the ladder's radial wave function; the quartic coupling then raises the uniform quadratic coefficient. The resulting gap is proportional to the uniform zero-point variance divided by the atomic-to-cavity frequency ratio η: it closes as η−2/3 while the variance grows as η1/3. A quartic Schrödinger equation fixes both observables and the first correction to their ratio, as confirmed by full spin-photon diagonalization. A triangle of collective spins with Dzyaloshinskii-Moriya exchange obeys the same relation, with a different coefficient and a correction of opposite sign. The ring's three-coordinate spectrum connects this gap to the neighboring η−1 and η−1/3 laws and to photon-number saturation.
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BibTeX
@misc{he2026excitation,
title = {{Excitation Gap of a Confined Chiral Mode Measures Critical Zero-Point Fluctuations}},
author = {Shu He and Liwei Duan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34416},
eprint = {2609.34416},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34416},
}
RIS
TY - UNPB
TI - Excitation Gap of a Confined Chiral Mode Measures Critical Zero-Point Fluctuations
AU - Shu He
AU - Liwei Duan
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34416
UR - https://arxiv.org/abs/2609.34416
AB - Where uniform and chiral superradiant boundaries meet in a quantum Rabi ring, the quadratic theory leaves a degenerate chiral ladder with finite radial width. We show that adding one chiral quantum widens the ladder's radial wave function; the quartic coupling then raises the uniform quadratic coefficient. The resulting gap is proportional to the uniform zero-point variance divided by the atomic-to-cavity frequency ratio η: it closes as η^−2/3 while the variance grows as η^1/3. A quartic Schrödinger equation fixes both observables and the first correction to their ratio, as confirmed by full spin-photon diagonalization. A triangle of collective spins with Dzyaloshinskii-Moriya exchange obeys the same relation, with a different coefficient and a correction of opposite sign. The ring's three-coordinate spectrum connects this gap to the neighboring η^−1 and η^−1/3 laws and to photon-number saturation.
ER -