标题： 非局域介质中孤子的Thouless泵浦 显示英文标题

标题： Thouless pumping of solitons in a nonlocal medium

摘要： 汤利思泵浦是一种被广泛认为存在于物理学多个领域的基本现象，其中光学占据特别显著的地位。 在这里，我们研究了在折射率由两个缓慢滑动的子晶格和非局域非线性响应所形成的介质中，光学孤子的这种效应。 这种势场的光谱带可以表现出非平凡的拓扑性质，占据这些带的激发态可以经历由线性谱的空间-时间陈数所控制的量化输运。 我们发现介质的非局域性对汤利思泵浦的动力学有深刻影响。 因此，我们表明，宽而低功率的基本孤子不表现出输运，因为它们仅激发光谱带的一小部分，而具有更宽光谱投影的高功率孤子则表现出稳定的量化输运。 这两种主要不同的光传播模式之间的转变点强烈依赖于非线性响应的非局域程度，并且随着非局域性的增加而向更高的功率移动。 值得注意的是，即使是中等水平的非局域性也足以防止在局域克尔介质中通常观察到的高功率下拓扑输运的破坏。 除了基本孤子之外，我们还证明了多极孤子，如偶极子和三极子状态也可以稳定地被泵浦。 这是首次展示这种复杂的孤子状态经历汤利思泵浦。 虽然基本孤子只需要超过一个功率阈值，但多极子只有在有限的功率窗口内才能表现出稳定的输运。 对于偶极子来说，这个窗口比三极子更宽，并且随着非局域性的增加而扩大，揭示了结构复杂性和稳定性之间的权衡。 显示英文摘要

摘要： Thouless pumping is a fundamental phenomenon recognized as being widespread across various areas of physics, with optics holding a particularly prominent role. Here, we study this effect for optical solitons in a medium where the refractive index is shaped by two slowly sliding sublattices and a nonlocal nonlinear response. The spectral bands of such a potential can exhibit nontrivial topology, and excitations occupying these bands can undergo quantized transport governed by the space -- time Chern indices of the linear spectrum. We find that nonlocality of the medium profoundly affects the dynamics of Thouless pumping. Thus, we show that broad, low-power fundamental solitons do not exhibit transport, as they excite only a small portion of the spectral band, while high-power solitons with broader spectral projections do demonstrate stable quantized transport. The transition point between these two principally different light propagation regimes strongly depends on the degree of nonlocality of the nonlinear response and shifts to larger powers with increasing nonlocality. Notably, even a moderate level of nonlocality is sufficient to prevent the breakdown of topological transport at high powers commonly observed in local Kerr media. Beyond fundamental solitons, we also demonstrate that multipole solitons, such as dipole and tripole states can be pumped stably. This is the first time such complex soliton states have been shown to undergo Thouless pumping. While fundamental solitons require only exceeding a power threshold, multipoles exhibit stable transport only within a finite power window. This window is broader for dipoles than for tripoles and expands with increasing nonlocality, revealing a trade-off between structural complexity and stability.