Topological invariants play a key role in the characterization of topological states. Due to the existence of exceptional points, it is a great challenge to detect topological invariants in non-Hermitian systems. We put forward a dynamic winding number, the winding of realistic observables in long-time average, for exploring band topology in both Hermitian and non-Hermitian two-band models via a unified approach. We build a concrete relation between dynamic winding numbers and conventional topological invariants. In one-dimension, the dynamical winding number directly gives the conventional winding number. In two-dimension, the Chern number relates to the weighted sum of dynamic winding numbers of all phase singularity points. This work opens a new avenue to measure topological invariants not requesting any prior knowledge of system topology via time-averaged spin textures.
Quantized response is one distinguishing feature of a topological system. In non-Hermitian systems, the spectral winding topology yields quantized steady-state response. By considering two weakly coupled non-Hermitian chains, we discover that the spectral winding topology of one chain can be probed by a steady-state response defined solely on the other chain, even when other important properties, e.g., {energetics} and entanglement entropy, indicate that eigen-solutions are effectively {not hybridized} between the two chains. This intriguing phenomenon, as carefully investigated in a large par…
Nontrivial topology in lattices is characterized by invariants--such as the Zak phase for one dimensional (1D) lattices--derived from wave functions covering the Brillouin zone. We realized the 1D bipartite Rice-Mele (RM) lattice using ultracold $^{87}$Rb and focus on lattice configurations possessing various combinations of chiral, time-reversal and particle-hole symmetries. We quenched between configurations and used a form of quantum state tomography, enabled by diabatically tuning lattice parameters, to directly follow the time evolution of the Zak phase as well as a chiral winding number.…
Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge modes as their topological winding. In this work, we disc…
Linear-optical systems can implement photonic quantum walks that simulate systems with nontrivial topological properties. Here, such photonic walks are used to jointly entangle polarization and winding number. This joint entanglement allows information processing tasks to be performed with interactive access to a wide variety of topological features. Topological considerations are used to suppress errors, with polarization allowing easy measurement and manipulation of qubits. We provide three examples of this approach: production of two-photon systems with entangled winding number (including t…
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play complementary roles: the Fubini-Study metric, which introduces a notion of distance between quantum states defined over a parameter space, and the Berry curvature associated with Berry-phase effects and topological band structures. In fact, recent studies have revealed direct relations between these two important quantities, suggesting that topological properties…
Controlling Liouvillian topological phases via Hamiltonian band topology under chiral symmetry
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心）；School of Physics and Astronomy & Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-Sen University (Zhuhai Campus)（中山大学珠海校区物理与天文学院及广东省量子计量与传感重点实验室）；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
Curvature-Flux Representation of Local Dirac-Node Topology from Non-Hermitian Zeeman Quantum Geometry
College of Physics and Optoelectronic Engineering, Shenzhen University（深圳大学物理与光电工程学院）；Quantum Science Center of Guangdong-Hongkong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Department of Physics, The University of Hong Kong（香港大学物理系）
Exploring pathways towards quantum advantage in quantum chemistry: the case of a molecule with half-Möbius topology
IBM Research Europe – Zurich（IBM 欧洲苏黎世研究中心）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Éidgenössische Technische Hochschule Zürich (ETHZ)（苏黎世联邦理工学院）；University of Regensburg（雷根斯堡大学）；The University of Manchester（曼彻斯特大学）；Oxford University（牛津大学）
This work unveils how geometric features of two-band non-Hermitian Hamiltonians can completely classify the topology of their eigenstates and energy manifolds. Our approach generalizes the Bloch sphere visualization of Hermitian systems to a ``Bloch torus'' picture for non-Hermitian systems, where a singularity ring (SR) captures the degeneracy structure of generic exceptional points. The SR picture affords convenient visualization of various symmetry constraints and reduces their topological characterization to the classification of simple intersection or winding behavior, as detailed by our …
Tuning the topological winding number by rolling up graphene
National Cheng Kung University（国立成功大学）；Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University（国立成功大学量子前沿研究与技术中心）；Institute for Theoretical Solid State Physics, IFW Dresden（德累斯顿亥姆霍兹研究所理论固态物理研究所）；Würzburg-Dresden Cluster of Excellence ct.qmat（维尔茨堡-德累斯顿卓越集群 ct.qmat）；Program on Key Materials, Academy of Innovative Semiconductor and Sustainable Manufacturing, National Cheng Kung University（国立成功大学创新半导体与可持续制造学院关键材料计划）
Liouvillian topology and nonreciprocal dynamics in open Floquet chains
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Institute of Theoretical Physics, Technische Universität Dresden and Würzburg-Dresden Cluster of Excellence ctd.qmat（德累斯顿工业大学理论物理学院和维尔茨堡-德累斯顿卓越集群ctd.qmat）
The topology of one-dimensional chiral systems is captured by the winding number of the Hamiltonian eigenstates. Here we show that this invariant can be read-out by measuring the mean chiral displacement of a single-particle wavefunction that is connected to a fully localized one via a unitary and translational-invariant map. Remarkably, this implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases. We confirm experimentally these results in a quantum walk of structured light.
Topological insulators host topology-linked boundary states, whose spin and charge degrees of freedom could be exploited to design topological devices with enhanced functionality. We experimentally observe that dissipationless chiral edge states in a spin-orbit coupled anomalous Floquet topological phase exhibit topological spin texture on boundaries, realized via a two-dimensional quantum walk. Our experiment shows that, for a walker traveling around a closed loop along the boundary in real space, its spin evolves and winds through a great circle on the Bloch sphere, which implies that edge-s…
We construct an artificial U(1) gauge field in the cold atom system to form a monopole along with vortices. It is supposed that the cold atoms are confined on a spherical surface, and two sets of identical laser beams in the opposite propagating directions shine on two sides of the sphere. Arbitrary Chern number CN, proportional to the quantized magnetic flux, can be obtained by selecting proper laser modes. This construction meets the condition of Chern's theorem, so that the vortices of the atom wave function will emerge on the sphere, whose winding number equals CN. It is found that a geome…
We study the interplay between disorder and topology for the localized edge states of light in topological zigzag arrays of resonant dielectric nanoparticles. We characterize topological properties by the winding number that depends on both zigzag angle and spacing between nanoparticles in the array. For equal-spacing arrays, the system may have two values of the winding number $ν=0$ or $1$, and it demonstrates localization at the edges even in the presence of disorder, being consistent with experimental observations for finite-length nanodisk structures. For staggered-spacing arrays, the syst…
Exploring nontrivial topology at quantum criticality in a superconducting processor
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Zhejiang University（浙江大学物理学院、ZJU-杭州全球科创中心及浙江省微纳量子芯片与量子控制重点实验室）；Institute for Advanced Study in Physics and School of Physics, Zhejiang University（浙江大学物理学高等研究院及物理学院）
Interferometric Readout of Momentum-Space Topology in a Programmable Dissipative Photonic Circuit
KTH Royal Institute of Technology（皇家理工学院）；Stockholm University（斯德哥尔摩大学）；Singapore University of Technology and Design（新加坡科技设计大学）；Huazhong University of Science and Technology（华中科技大学）
