发表机构
Sichuan Normal University; Zhejiang Normal University（四川师范大学; 浙江师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究量子拉比环中手性模式的激发间隙，发现其与均匀零点方差成正比，随频率比按幂律闭合，并通过四次薛定谔方程和自旋-光子对角化验证，同时推广到具有Dzyaloshinskii-Moriya交换的自旋三角形。
AI 中文摘要
在量子拉比环中，均匀超辐射边界与手性超辐射边界相遇之处，二次理论留下一个具有有限径向宽度的简并手性阶梯。我们表明，添加一个手性量子会加宽阶梯的径向波函数；随后四次耦合会提高均匀二次系数。由此产生的间隙与均匀零点方差除以原子-腔频率比$\eta$成正比：当方差按$\eta^{1/3}$增长时，间隙按$\eta^{-2/3}$闭合。一个四次薛定谔方程同时确定这两个可观测量及其比值的首阶修正，这一点通过完整的自旋-光子对角化得到证实。具有Dzyaloshinskii-Moriya交换的集体自旋三角形满足相同关系，但系数不同且修正符号相反。环的三坐标谱将该间隙与相邻的$\eta^{-1}$和$\eta^{-1/3}$定律以及光子数饱和联系起来。
英文摘要
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.
Comments4 pages, 2 figures; Supplemental Material: 8 pages, 3 figures, 4 tables. Source code available at Zenodo: https://doi.org/10.5281/zenodo.23005392
