Excitation Gap of a Confined Chiral Mode Measures Critical Zero-Point Fluctuations

Shu He; Liwei Duan

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arXiv · 2609.34416

Excitation Gap of a Confined Chiral Mode Measures Critical Zero-Point Fluctuations

Shu He·Liwei Duan

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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 $η^{1/3}$. 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.

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Shu He, Liwei Duan. 2026-09-28. Excitation Gap of a Confined Chiral Mode Measures Critical Zero-Point Fluctuations. https://arxiv.org/abs/2609.34416

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