Non-Hermitian non-reciprocal systems are known to be extremely sensitive to boundary conditions, exhibiting diverse localizing behaviors and spectrum structures when translational invariance is locally broken, either by tuning the boundary coupling strength, or by introducing an effective boundary using impurities or defects. In this work, we consider the single impurity problem in the Hatano-Nelson model and the Su-Schreieffer-Heeger model, which can be exactly solved with the single impurity being treated as an effective boundary of the system. From our exact solutions for finite-size systems, we unveil that increasing the impurity strength can lead to a transition of the bulk states from non-skin states to skin states, accompanied by the change of the spectrum structure from an ellipse in the complex plane to a segment along the real axis. These exact results indicate that the critical value of impurity strength is size-dependent, and increases exponentially with the lattice size when the impurity is strong or the system is large enough. OUr exact solutions are also useful for determining the point-gap topological transition in the concerned models.
Non-Hermiticity from non-reciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization in a \textit{non-reciprocal} quasiperiodic lattice, dubbed non-reciprocal Aubry-André model, and a \textit{rescaled} transition point is exactly proved. The non-reciprocity can induce not only the NHSE, but also the asymmetry in localized states with two Lyapunov exponents for both sides. Meanwhile, this transition is also topological, characterized by a winding nu…
Directional Dynamics of the Non-Hermitian Skin Effect
University of Electronic Science and Technology of China（电子科技大学）；Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学前沿与基础科学研究所）
This work develops a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with PBCs, OBCs and even their interpolations being special cases across a whole range of boundary impurity strengths. As the impurity strength is tuned, the localization of steady states can assume very rich behavior, including the expected non-Hermitian skin effect, Bloch-like states albeit broken translational invariance, and surprisingly, scale-free accumulation along or even against the direction of non-reciprocity. We further uncover the possibility of the co-existence of non-Hermitian ski…
A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if the spectrum under periodic boundary conditions is point gapped, by opening the lattice the non-Hermitian skin effect will necessarily occur. Finding the exact skin eigenstates may be demanding in general, and many methods in the literature are based on ansatzes and on recurrence equations for the eigenstates' components. Here we devise a general procedure based on the Green's function method to calculate the eigenstates of non-Hermitian tig…
We propose a realistic cold-atom quantum setting where nontrivial energy-band topology induces non-reciprocal pumping. This is an intriguing non-Hermitian phenomenon that illustrates how topology, when assisted with atom loss, can act as a "switch" for non-Hermitian skin effect (NHSE), rather than as a passive property that is modified by the NHSE. In particular, we present a lattice shaking scenario to realize a two-dimensional cold-atom platform, where non-reciprocity is switched on only in the presence of both atom loss and topological localization due to time-reversal symmetry breaking. Su…
Observation of Erratic Non-Hermitian Skin Effect in Phononic Crystals
Institute of Acoustics, School of Physics Science and Engineering, Tongji University（同济大学物理科学与工程学院声学研究所）；School of Advanced Manufacturing Engineering, Nanjing University（南京大学先进制造工程学院）
Robust boundary states have been the focus of much recent research, both as topologically protected states and as non-Hermitian skin states. In this work, we show that many-body effects can also induce analogs of these robust states in place of actual physical boundaries. Particle statistics or suitably engineered interactions i.e. in ultracold atomic lattices can restrict the accessible many-body Hilbert space, and introduce effective boundaries in a spatially periodic higher-dimensional configuration space. We demonstrate the emergence of topological chiral modes in a two-fermion hopping mod…
Non-Hermitian skin effect (NHSE) describes the exponential localization of all eigenstates toward boundaries in non-Hermitian systems, and has attracted intense research interest of late. Here we theoretically propose a scheme in which the NHSE significantly impacts the external motion of a single trapped ion through complex spin-motion dynamics. On the one hand, we show the competition between the NHSE and the coherent Bloch dynamics. On the other hand, since the NHSE manifests as a non-reciprocal flow in occupied phonon modes, we demonstrate that such dynamics can have potential applications…
The non-Hermitian skin effect (NHSE) is a phenomenon whereby certain non-Hermitian lattice Hamiltonians, particularly those with nonreciprocal couplings, can host an extensive number of eigenmodes condensed to the boundary, called skin modes. Although the NHSE has mostly been studied in the classical regime, we show that it can also manifest in quantum systems containing boson number nonconserving processes arising from uniform parametric driving. We study lattices of coupled nonlinear resonators that can function as reciprocal quantum amplifiers. A one-dimensional chain exhibiting NHSE can pe…
Institute for Condensed Matter Theory, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校凝聚态理论研究所）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；CeFEMA-LaPMET, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院物理系CeFEMA-LaPMET）
Confined non-Hermitian skin effect in a semi-infinite Fock-state lattice
College of Science, National University of Defense Technology（国防科技大学理学院）；Hunan Key Laboratory of Mechanism and Technology of Quantum Information（湖南省量子信息机制与技术重点实验室）；Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University（湖南师范大学低维量子结构与量子控制教育部重点实验室）
Noise-Induced Resurrection of Dynamical Skin Effects in Quasiperiodic Non-Hermitian Systems
School of Physics, Peking University（北京大学物理学院）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
Dissipative phase transition of interacting non-reciprocal fermions
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；JEIP, UAR 3573 CNRS, Collège de France, PSL Research University（法国国家科学研究中心联合研究单位3573，法兰西学院，巴黎文理研究大学）
Observation of Non-Hermitian Skin Dynamics in the Liouvillian Regime
The University of Hong Kong（香港大学）；HK Institute of Quantum Science and Technology（香港量子科学研究所）；State Key Laboratory of Optical Quantum Materials（光学量子材料国家重点实验室）
Critical Non-Hermitian Skin Effect and Scale-Free Localization Morphing in Bilocally Coupled Hatano-Nelson Chains
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心）；Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing & School of Physics and Astronomy, Sun Yat-Sen University (Zhuhai Campus)（中山大学（珠海校区）物理与天文学院 广东省量子精密测量与传感重点实验室）
Non-Hermitian models with real eigenenergies are highly desirable for their stability. Yet, most of the currently known ones are constrained by symmetries such as PT-symmetry, which is incompatible with realizing some of the most exotic non-Hermitian phenomena. In this work, we investigate how the non-Hermitian skin effect provides an alternative route towards enforcing real spectra and system stability. We showcase, for different classes of energy dispersions, various ansatz models that possess large parameter space regions with real spectra, despite not having any obvious symmetry. These min…
The breakdown of the conventional bulk-boundary correspondence due to non-Hermitian skin effect leads to the non-Bloch bulk-boundary correspondence in the generalized Brillouin zone. Inspired by the case of the equivalence between the non-reciprocal hopping and imaginary gauge field, we propose a method to construct the topological equivalent models of the non-Hermitian dimerized lattices with the similarity transformations. The idea of the constructions is from that the imaginary magnetic flux vanishes under the open boundary condition and the period boundary spectra can be well approximated …
Based on a general transport theory for non-reciprocal non-Hermitian systems and a topological model that encompasses a wide range of previously studied models, we (i) provide conditions for effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption, (ii) identify which effects are compatible and linked with each other, and (iii) determine by which levers they can be tuned independently. For instance, the directed amplification inherent in the non-Hermitian skin effect does not enter the spectral conditions for reflectionless transport, lasing, or coheren…
Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, University of Michigan Ann Arbor（密歇根大学安娜堡分校物理系）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Kavli Institute for Theoretical Sciences, Chinese Academy of Sciences（中国科学院理论科学卡弗里研究所）
