We theoretically demonstrate the effects of quantum interferences among valence electrons with various initial crystal momenta in the high-order harmonic generation (HHG) in solids. By investigating crystal-momentum-dependent harmonics from solids in linearly polarized laser fields, some unique radiation characteristics of the observed overall harmonics are attributed to the consequences of interferences among valence electrons with different crystal momenta. It is shown that the electron pairs with opposite crystal momenta result in the destructive interferences of even-order harmonics for a crystal with the inversion symmetry, which eventually leads to the only odd orders in observed overall harmonic spectra for a semiconductor material because of the complete pairing of all valence electrons. Additionally, each of the harmonic plateaus in the overall multiple-plateau harmonic spectrum is identified to be contributed by the valence electrons within different crystal momentum zones. We also find that the solid-phase HHG in the below-band-gap region is substantially suppressed due to the collective responses of multiple valence electrons. This work sheds light on the essential impacts of interferences among crystal-momentum-resolved electrons on the HHG in solids and is helpful to explore ultrafast coherent processes in condensed matter.

中文翻译：

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固体动量高次谐波产生中晶体动量分辨电子之间的量子干扰效应

我们从理论上证明了固体中高阶谐波产生（HHG）中具有各种初始晶体动量的价电子之间的量子干扰效应。通过研究线性偏振激光场中固体中与晶体动量有关的谐波，观察到的总谐波的某些独特辐射特性归因于具有不同晶体动量的价电子之间的干扰。结果表明，具有相反晶体矩的电子对对具有反转对称性的晶体产生偶次谐波的破坏性干扰，由于完全所有价电子配对。此外，整个多平台谐波谱中的每个谐波平台都被确定为由不同晶体动量区内的价电子贡献。我们还发现，由于多个价电子的集体响应，带隙以下区域中的固相HHG被显着抑制。这项工作揭示了晶体动量分解的电子之间的干扰对固体中HHG的本质影响，并有助于探索凝聚态物质的超快速相干过程。