小量子霍尔样品中的拓扑相位

SU(N) fractional quantum Hall effects in topological flat bands

We study $N$-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU$(N)$-invariant interactions based on density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU$(N)$ fractional quantum Hall states can emerge at fractional filling factors $ν=N/(N+1)$ for bosons ($ν=N/(2N+1)$ for fermions) in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characte…

Laughlin's topological charge pump in an atomic Hall cylinder

The quantum Hall effect occuring in two-dimensional electron gases was first explained by Laughlin, who envisioned a thought experiment that laid the groundwork for our understanding of topological quantum matter. His proposal is based on a quantum Hall cylinder periodically driven by an axial magnetic field, resulting in the quantized motion of electrons. We realize this milestone experiment with an ultracold gas of dysprosium atoms, the cyclic dimension being encoded in the electronic spin and the axial field controlled by the phases of laser-induced spin-orbit couplings. Our experiment prov…

Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry

We study the many-body ground states of SU($N$) symmetric hardcore bosons on the topological flat-band model by using controlled numerical calculations. By introducing strong intracomponent and intercomponent interactions, we demonstrate that a hierarchy of bosonic SU($N$) fractional quantum Hall (FQH) states emerges at fractional filling factors $ν=N/(MN+1)$ (odd $M=3$). In order to characterize this series of FQH states, we figure the effective $\mathbf{K}$ matrix from the inverse of the Chern number matrix. The topological characterization of the $\mathbf{K}$ matrix also reveals quantized d…

拓扑泵浦的玻色子整数量子霍尔效应

Bosonic integer quantum Hall effect as topological pumping

基于薄环面上量子霍尔态的准一维极限，我们构造了一个相互作用诱导拓扑泵浦模型，该模型模拟了玻色整数量子霍尔（BIQH）态的霍尔响应。BIQH态的准一维对应物被确定为由形成有效自旋- $1$自由度的两分量玻色子组成的Haldron相。在Halcohol相和平凡莫特绝缘体之间的绝热变化构成{ \it非对角}拓扑泵浦，其中一个组件的晶格势的平移在另一个组件中感应电流。这种泵送的机制被解释在偏振之间的变化的保护量子化值。

用二维拓扑电荷泵探索四维量子霍尔物理

Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump

物质拓扑态的发现，深刻地增进了我们对物理系统中相变的理解。代替局部序参量，拓扑相位由全局拓扑不变量描述，因此对扰动是鲁棒的。其突出的例子是二维整数量子霍尔效应。它的特征在于第一陈数，该陈数表现在由外部电场诱导的量子化霍尔响应中。将量子霍尔效应推广到四维系统导致了一种新的非线性霍尔响应的出现，这种响应也是量子化的，但由四维拓扑不变量--第二陈氏数描述。在这里，我们报告的第一个观察到的散装响应与内在的4D拓扑结构和测量相关的第二陈数。通过在倾斜光学超晶格中利用超冷玻色子原子实现二维拓扑电荷泵，实现了四维整数量子霍尔效应的动力学版本。使用一个小的原子云作为本地探针，我们充分表征系统的非线性响应的原位成像和现场分辨带映射。我们的研究结果铺平了道路，实验探测高维量子霍尔系统，其中新的拓扑相位与奇异的激发预测。

Scheme to Equilibrate the Quantized Hall Response of Topological Systems from Coherent Dynamics

Two-dimensional topologically distinct insulators are separated by topological gapless points, which exist as Weyl points in three-dimensional momentum space. Slowly varying parameters in the two-dimensional Hamiltonian across two distinct phases therefore necessarily experiences the gap closing process, which prevents the intrinsic physical observable, the Hall response, from equilibrating. To equilibrate the Hall response, engineered laser noises were introduced at the price of destroying the quantum coherence. Here we demonstrate a new scheme to equilibrate the quantized Hall response from …