石墨烯阿秒瞬态吸收光谱中的鱼骨共振结构
Fishbone resonance structure in the attosecond transient absorption spectroscopy of graphene
摘要：
通过数值求解四带密度矩阵方程，研究了石墨烯的阿秒瞬态吸收光谱，得到了明显的鱼骨共振结构。为了深入了解这些有趣的结构，我们利用一个简化的模型，只考虑电子的$Γ$和M点的布里渊区。利用该模型，我们可以将ATAS谱解析地表示为以红外泵浦场的强度和频率以及$Γ$和M点处电子的有效质量为变量的零阶和一阶贝塞尔函数之和。讨论了吸收光谱中的洛伦兹线和法诺线的形状。鱼骨结构由周期性的V形结构组成，可以用一阶贝塞尔函数来解释，并且其倾斜角仅由泵浦激光的频率决定。鱼骨中V形结构的周期性源于吸收光谱的洛伦兹和法诺线形对泵浦和探测激光器之间的时间延迟的周期性依赖。与数值结果相比，我们的解析理论可以定性甚至定量地预测ATAS光谱的鱼骨结构中的零阶和一阶条纹。对数值模拟中的规范问题也进行了讨论。
英文摘要：
We investigate the attosecond transient absorption spectroscopy (ATAS) of graphene by numerically solving four-band density-matrix equations, which demonstrates apparent fish bone resonance structures. To gain insight into these interesting structures, we exploit a simplified model that only considers the electrons of $Γ$ and M points in the Brillouin zone. With the help of this model, we can analytically express the ATAS spectrum as the sum of zeroth- and first-order Bessel functions in the variables of the strength and frequency of the infrared pump field as well as the effective mass of electrons at the $Γ$ and M points. Lorentzian and Fano line shapes in the absorption spectrum are addressed. The fish bone structure consists of periodic V-shaped structure that can be explained by first-order Bessel functions and its tilt angle is solely determined by the frequency of the pump laser. The periodicity of the V-shaped structure in the fish bone originates from the periodic dependence of the Lorentzian and Fano line shapes of the absorption spectrum on the time delay between the pump and probe lasers. Compared with the numerical results, our analytical theory can qualitatively or even quantitatively predict the zeroth- and first-order fringes in the fish bone structures of the ATAS spectrum. The gauge issues in the numerical simulations are also discussed.
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