标题： 原子蒸汽中的Liouvillian和Hamiltonian例外点：量子跃迁的光谱特征 显示英文标题

标题： Liouvillian and Hamiltonian exceptional points of atomic vapors: The spectral signatures of quantum jumps

摘要： 我们研究了用四条以及有效三条超精细态建模的碱金属原子蒸气中的谱奇异点。 通过比较非厄米哈密顿量（NHH）和李约维安超算符的本征值谱，我们分析了半经典和量子 exceptional 点的出现及其特性。 我们的结果显示，对于原子系统而言，单独使用 NHH 方法可能不足以完全捕捉系统的谱属性。 尽管 NHH 在某些情况下可以得出准确的预测，但全面描述通常需要李约维安形式主义，该形式主义支配着林德布洛姆主方程，并明确包含了导致重新布居动力学的量子跃迁过程。 我们证明了量子跃迁的引入从根本上改变了系统的谱结构。 特别是，我们给出了两个方法之间在谱退化存在性、参数空间中的位置甚至阶数上存在显著差异的例子，从而突出了量子跃迁的影响以及 NHH 方法的局限性。 最后，利用混合型李约维安形式主义，我们展示了量子跃迁如何重塑由 NHH 预测的初始谱特征，最终确定完整的李约维安谱。 显示英文摘要

摘要： We investigate spectral singularities in an alkali-metal atomic vapor modeled using four and effectively three hyperfine states. By comparing the eigenvalue spectra of a non-Hermitian Hamiltonian (NHH) and a Liouvillian superoperator, we analyze the emergence and characteristics of both semiclassical and quantum exceptional points. Our results reveal that, for atomic systems, the NHH approach alone may be insufficient to fully capture the system's spectral properties. While NHHs can yield accurate predictions in certain regimes, a comprehensive description typically requires the Liouvillian formalism, which governs the Lindblad master equation and explicitly incorporates quantum jump processes responsible for repopulation dynamics. We demonstrate that the inclusion of quantum jumps fundamentally alters the spectral structure of the system. In particular, we present examples in which the existence, location in parameter space, or even the order of spectral degeneracies differ significantly between the two approaches, thereby highlighting the impact of quantum jumps and the limitations of the NHH method. Finally, using the hybrid-Liouvillian formalism, we show how quantum jumps reshape spectral features initially predicted by the NHH, ultimately determining the full Liouvillian spectrum.