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 $\eta$: it closes as ${\eta }^{-2/3}$ while the variance grows as ${\eta }^{1/3}$. 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 ${\eta }^{-1}$ and ${\eta }^{-1/3}$ laws and to photon-number saturation.

arXiv comment4 pages, 2 figures; Supplemental Material: 8 pages, 3 figures, 4 tables. Source code available at Zenodo: https://doi.org/10.5281/zenodo.23005392