发表机构
Università degli Studi di Napoli Federico II; Scuola Superiore Meridionale（那不勒斯费德里科二世大学; 南方高等学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示公共玻色子库中谱扭转效应，量化其导致两量子比特暗态保护泄漏的机制，并发现弱扭转下泄漏与谱交叉点参数呈二次标度关系。
AI 中文摘要
两个量子比特与公共玻色子库的相互作用由谱密度矩阵 $\mathbf{J}(\omega)$ 表征，其对角元 $J_{11}(\omega)$ 和 $J_{22}(\omega)$ 描述局部谱，而非对角元编码交叉关联。对于最大关联库，$\mathbf{J}(\omega)$ 的秩为1，因此在每个频率上存在一个局部暗耦合方向。然而，如果 $J_{22}(\omega)/J_{11}(\omega)$ 随频率变化，亮方向和暗方向会发生旋转，且 $\ker\mathbf{J}(\omega)$ 依赖于频率。我们将此称为谱扭转，并通过亮谱投影算符的Fubini-Study速度 $\tau(\omega)$ 来量化。我们研究谱扭转如何影响耦合两量子比特动力学和暗态保护。我们通过存活泄漏 $P_{\mathrm{leak}}(t)$ 来量化保护损失，对于仅在频率上局部为暗的态，该泄漏可以变为有限值。通过比较旋转波动力学和未扭转的不对称库，以及分析量子比特失谐，我们将扭转与耦合不对称性、热吸收、反旋过程和哈密顿量对称性破缺区分开来。对于失配的Drude-Lorentz谱，我们的非微扰层次运动方程计算表明，扭转会从单重态诱导泄漏，该单重态在由 $J_{11}(\omega_\times)=J_{22}(\omega_\times)$ 定义的谱交叉点 $\omega_\times$ 处局部为暗。扭转还会移动最优保护态并加速Werner态并发度的衰减。在固定观测时间下，我们发现弱扭转二次标度 $P_{\mathrm{leak}}(t)\propto[\omega_\times\tau(\omega_\times)]^2$。这些结果可能指导结构化库中的暗态工程，对关联噪声谱学和无退相干编码具有重要意义。
英文摘要
The interaction of two qubits with a common bosonic reservoir is encoded by a matrix-valued spectral density $\mathbf{J}(ω)$, whose diagonal entries describe the local spectra, while the off-diagonal entries encode cross-correlations. Even when \(\mathbf{J}(ω)\) has rank one, a frequency-independent dark channel need not exist because the family \(\{\mathbf{J}(ω)\}_ω\) may have a trivial common kernel. We term the frequency-dependent rotation of the bright and dark directions \textit{spectral twisting} and quantify it through the Fubini--Study speed $τ(ω)$ of the bright spectral projector. We analyze how twisting modifies two-qubit dynamics and quantify the loss of dark-state protection through the leakage \(P_{\mathrm{leak}}(t)\). Comparisons with untwisted asymmetric reservoirs and rotating-wave dynamics, together with detuned and finite-temperature calculations, distinguish spectral twisting from coupling asymmetry, counter-rotating processes, and thermal absorption. For resonant qubits tuned to the crossing of the two local spectra $ω_\times$, the singlet is locally dark at the transition frequency but couples to off-resonant components whose bright directions are rotated. In the weak-twisting regime, the fixed-time leakage scales as $P_{\mathrm{leak}}(t)\propto[ω_\timesτ(ω_\times)]^2$. We test this prediction for mismatched Drude-Lorentz spectra using nonperturbative hierarchical equations of motion generalized to cross-correlated bath forces. These results provide a geometric framework for dark-state engineering in structured reservoirs.
