发表机构
Chengdu University of Technology; Shanghai Jiao Tong University; Institute of Spectroscopy, Russian Academy of Sciences; Universidade de Lisboa（成都理工大学; 上海交通大学; 俄罗斯科学院光谱研究所; 里斯本大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二维二次孤子在周期性χ^(2)材料中的Thouless泵浦，发现大振幅孤子可实现稳定量子化输运，且输运方向由纵向周期之比的无理数极限决定。
AI 中文摘要
我们研究了由相干相互作用的基频（FF）和二次谐波（SH）分量组成的二维二次孤子在周期性χ^(2)材料中传播时的Thouless泵浦。泵浦由两个相互滑动的二维晶格诱导，这些晶格由浅的横向和纵向周期性折射率调制定义。聚焦于半无限带隙中的孤子，我们发现了三种不同的泵浦场景：小振幅孤子无输运、中等振幅下瞬态区域中的非量子化输运，以及相对大振幅孤子的稳定量子化输运。研究了滑动速度的不同方向，导致孤子中心的不同轨迹。发现向量子化输运区域的转变强烈依赖于FF和SH波之间的相位失配，这也影响二维χ^(2)晶格孤子的稳定性。我们还表明，x和y方向上的纵向周期之比近似为无理数的泵浦，会诱导量子化输运，其方向随着近似精度的提高而迅速收敛到由该无理数确定的极限泵浦方向，对应于真正不可公度的纵向周期。
英文摘要
We consider Thouless pumping of two-dimensional quadratic solitons composed from coherently interacting fundamental frequency (FF) and second harmonic (SH) components propagating in a periodic $χ^{(2)}$ material. The pumping is induced by two mutually sliding two-dimensional lattices defined by shallow transverse and longitudinal periodic refractive index modulation. Focusing on solitons in the semi-infinite gap, we find three distinct pumping scenarios: the absence of transport for small-amplitude solitons, non-quantized transport in a transient regime at intermediate amplitudes, and stable quantized transport for solitons with relatively large amplitudes. Different directions of the sliding velocity were investigated resulting in different trajectories of soliton center. The transition to the regime of quantized transport is found to depend strongly on phase mismatch between FF and SH waves that also influences stability properties of two-dimensional $χ^{(2)}$ lattice solitons. We also show that pumping with longitudinal periods in the x and y directions, whose ratio approximates an irrational number, induces quantized transport whose direction rapidly converges, with increase of the accuracy of the approximation, to a limiting pumping direction determined by this irrational number and corresponding to truly incommensurate longitudinal periods.
Comments29 pages, 6 figures
Journal refCommunications Physics 9, 47 (2026)
DOI：10.1038/s42005-025-02478-3
