标题： 分数拓扑泵浦晶格孤子的量子理论 显示英文标题

标题： Quantum theory of fractional topological pumping of lattice solitons

摘要： 拓扑量子系统的标志之一是粒子输运的鲁棒量化，这是整数量子霍尔电导率的起源。在存在相互作用的情况下，拓扑输运也可以变为分数形式。最近关于由光波导阵列构建的拓扑泵浦的实验已经展示了晶格孤子的整数和分数输运。这里背景介质通过Kerr非线性介导光子之间的相互作用，并导致自束缚复合物（称为晶格孤子）的形成。当这些孤子的相互作用强度增加时，在泵浦循环中从具有整数量子输运的相位经过不同分数输运的相位，最终到达无输运相位的一系列转变被观察到。我们在此提出了孤子拓扑泵浦的一个完整的量子描述。这种方法使我们能够识别一个拓扑不变量，即由孤子质心（COM）动量带结构决定的多体Chern数，它完全控制着它们的输运。增加相互作用会导致COM能带的相继合并，这解释了所观察到的一系列拓扑相变以及在中间相互作用强度下拓扑量化潜在失效的原因。 显示英文摘要

摘要： One of the hallmarks of topological quantum systems is the robust quantization of particle transport, which is the origin of the integer-valued Quantum Hall conductivity. In the presence of interactions the topological transport can also become fractional. Recent experiments on topological pumps constructed by arrays of photonic waveguides have demonstrated both integer and fractional transport of lattice solitons. Here a background medium mediates interactions between photons via a Kerr nonlinearity and leads to the formation of self-bound composites, called lattice solitons. Upon increasing the interaction strength of these solitons a sequence of transitions was observed from a phase with integer transport in a pump cycle through different phases of fractional transport to a phase with no transport. We here present a full quantum description of topological pumps of solitons. This approach allows us to identify a topological invariant, a many-body Chern number, determined by the band structure of the center-of-mass (COM) momentum of the solitons, which fully governs their transport. Increasing the interaction leads to a successive merging of COM bands which explains the observed sequence of topological phase transitions and also the potential for a breakdown of topological quantization for intermediate interaction strength