AI 中文总结
研究泵浦锗中瞬态光学响应里非共振和单光子共振晶体动量的相关性，通过动态投影算符方法等计算介电函数微分虚部，发现共振区域主导光学响应，且瞬态光学权重非仅由实电荷动力学决定，还与虚拟泵浦贡献有关，建立了多光子共振与瞬态光学可观测量的动量分辨联系。
AI 中文摘要
泵浦诱导的瞬态光学性质结合了整个布里渊区电子态的贡献，但非共振和单光子共振晶体动量的相对相关性尚未得到探索。我们通过将瞬态吸收响应分解为相对于泵浦存在或不存在1、2和3光子共振定义的动量空间类别，来解决泵浦锗中的这个问题。使用动态投影算符方法和相关的广义线性响应理论，我们计算介电函数的微分虚部并评估每个共振类别的贡献。共振区域几乎占了整个光学响应，而识别出的共振集之外的点贡献可忽略不计。然而，双光子共振集虽然包含超过98%的残余（泵浦后）激发粒子数，但不能重现完整的瞬态光谱。相反，具有非常小的残余粒子数的共振类别对瞬态光学性质产生不可忽略的贡献。这种不匹配表明瞬态光学权重不仅仅由实电荷动力学决定，并且与大量虚拟泵浦诱导的贡献一致，其主要光学权重来自动量空间的共振区域。主导的2\(\omega_{\mathrm{pu}}\)振荡的类别分辨相位进一步表明，每当一个类别有明显贡献时，其振荡分量的相位跟随相应全信号的相位。由此产生的分解在实际材料中提供了多光子共振和瞬态光学可观测量之间的动量分辨联系。
英文摘要
Pump-induced transient optical properties combine contributions from electronic states throughout the Brillouin zone, but the relative relevance of off-resonant and l-photon resonant crystal momenta has remained unexplored. We address this issue in pumped germanium by resolving the transient absorptive response into momentum-space classes defined by the presence or absence of 1-, 2-, and 3-photon resonances with respect to the pump. Using the Dynamical Projective Operatorial Approach together with the related generalized linear response theory, we compute the differential imaginary part of the dielectric function and evaluate the contributions of each resonance class. Resonant regions account for nearly the entire optical response, whereas points outside the identified resonance sets contribute only negligibly. Nevertheless, the 2-photon-resonant set, although containing more than 98% of the residual (post-pump) excitation population, does not reproduce the full transient spectrum. Conversely, resonance classes with very small residual populations generate non-negligible contributions to the transient optical properties. This mismatch shows that the transient optical weight is not determined solely by the real-charge dynamics (which results in post-pulse residual excitation population) and is consistent with substantial virtual pump-induced contributions, whose dominant optical weight nevertheless arises from the resonant regions of momentum space. The class-resolved phase of the dominant 2$ω_{\mathrm{pu}}$ oscillations further shows that, whenever a class contributes appreciably, the phase of its oscillatory component follows that of the corresponding full signal. The resulting decomposition provides a momentum-resolved connection among multi-photon resonances and transient optical observables in a realistic material.
Comments10 pages, 6 figures, 19 panels, 1 table
