AI 中文总结
研究聚焦量子拉比模型中两个特殊情况，即具有显式\(U(1)\)对称性的Jaynes-Cummings模型和仅在整数偏置时具有参数依赖“隐藏”对称性的非对称量子拉比模型，用时均纠缠能力揭示光物质系统中对称结构，证明其可作算符诊断。
AI 中文摘要
量子拉比模型是光与物质相互作用研究中的标准有效哈密顿量，描述了一个量子比特与单个谐振子耦合的最简单非平凡情形。在更广泛的拉比家族中，我们关注两个特殊情况：具有显式\(U(1)\)对称性的Jaynes-Cummings（JC）模型，以及具有仅在整数偏置\(\varepsilon/\omega\in\mathbb{Z}\)时出现且在哈密顿量中不明显的参数依赖“隐藏”对称性的非对称量子拉比模型（AQRM）。我们用时均纠缠能力作为这些对称结构的算符级诊断。由于振子希尔伯特空间是无限维的，我们比较两个有限输入系综：福克空间截断后的哈尔平均和固定平均占据数\(\bar{n}\)时的相干态平均。两种诊断在AQRM的整数偏置点处都出现峰值，隐藏对称性存在于此。相比之下，JC点处的显式\(U(1)\)对称性反而给出一个弱凹陷。因此，时均纠缠能力对拉比家族中的隐藏对称性和\(U(1)\)对称性都有响应，响应的符号表明对称性如何重组谱展开。这些结果表明，纠缠能力可作为算符诊断，以揭示光物质系统中隐藏和显式对称性的存在及性质。
英文摘要
The quantum Rabi model is a standard effective Hamiltonian in studies of light-matter interaction, capturing the simplest nontrivial setting in which a qubit couples to a single harmonic oscillator. Within the broader Rabi family, we focus on two special cases: the Jaynes-Cummings (JC) model, which carries an explicit $U(1)$ symmetry, and the asymmetric quantum Rabi model (AQRM), which possesses a parameter-dependent "hidden'' symmetry that appears only at integer bias, $\varepsilon/ω\in\mathbb{Z}$, and is not manifest in the Hamiltonian. We use the time-averaged entangling power as an operator-level diagnostic of these symmetry structures. Since the oscillator Hilbert space is infinite-dimensional, we compare two finite input ensembles: a Haar average after Fock-space truncation and a coherent-state average at fixed mean occupation $\bar{n}$. Both diagnostics show peaks at the integer-bias points of the AQRM, where the hidden symmetry resides. In contrast, the manifest $U(1)$ symmetry at the JC point instead gives a weak dip. Thus, the time-averaged entangling power responds to both the hidden symmetry and the $U(1)$ symmetry in the Rabi family, with the sign of the response indicating how the symmetry reorganizes the spectral expansion. These results demonstrate that the entangling power can serve as an operator diagnostic to reveal the presence and properties of hidden and manifest symmetries in light-matter systems.
Comments17 pages, 5 figures
