量子液滴的非线性 Thouless 泵浦

Nonlinear Thouless Pumping in Quantum Droplet

摘要: 非线性 Thouless 泵浦是对传统 Thouless 泵浦理论的重要拓展，它揭示了非线性效应对拓扑系统中波包演化的影响。量子液滴作为超冷原子领域的新兴物态，因其在极稀薄环境中仍能稳定存在的独特性质，成为当前研究的焦点。因此，对量子液滴在超晶格中的非线性 Thouless 泵浦的研究具有极高的学术价值和应用前景。本文给出了量子液滴在不同相互作用强度下的非线性 Thouless 泵浦图。发现量子液滴中非线性项能够促使波包形成稳定的孤子结构，这些孤子在拓扑保护的作用下实现了空间上的拓扑输运，输运距离与系统的陈数紧密相关。随着非线性效应强度的增加，孤子不仅稳定存在，还发生了能带间的耦合，导致孤子在不同能带之间发生拉比振荡，影响了波包的传输行为。此外，本文通过改变相互作用系数，深入研究了量子液滴的陈数与相互作用强度之间的关系，得到了陈数随着相互作用系数的增大而增大，但是相互作用项对陈数的影响相对有限的结论。

Abstract: Nonlinear Thouless pumping represents a significant extension of the conventional Thouless pumping theory, revealing the influence of nonlinear effects on wave-packet evolution in topological systems. Quantum droplets, as an emerging quantum state in ultracold atomic systems, have become a focal point of current research due to their unique ability to remain stable in extremely dilute environments. Therefore, investigating the nonlinear Thouless pumping of quantum droplets in superlattices holds substantial academic value and application potential. This paper presents the nonlinear Thouless pumping diagrams of quantum droplets under varying interaction strengths. It is found that the nonlinear terms in quantum droplets facilitate the formation of stable solitonic structures, which achieve spatially quantized topological transport under topological protection, with the transport distance closely tied to the system’s Chern number. As the strength of nonlinearity increases, solitons not only remain stable but also exhibit interband coupling, leading to Rabi oscillations between distinct energy bands that modify the wave-packet dynamics. Furthermore, by tuning the interaction coefficients, this work systematically explores the relationship between the Chern number and interaction strength in quantum droplets. The results demon- strate that while the Chern number increases with interaction strength, the impact of nonlinear interactions on the Chern number remains relatively limited.