다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is described by a non-Hermitian Hamiltonian that encircles an exceptional point in momentum space. The winding number has a fractional value of 1/2. There is only one dynamically stable zero-energy edge state due to the defectiveness of the Hamiltonian. This edge state is robust to disorder due to protection by a chiral symmetry. We also discuss experimental realization with arrays of coupled resonator optical waveguides.

Anomalous Edge State in a Non-Hermitian Lattice

The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wave function. Here we address the Chern number of a two-dimensional insulator and we show that the corresponding topological order can be mapped by means of a ``topological marker,'' defined in $\\mathbf{r}$ space, and which may vary in different regions of the same sample. Notably, this applies equally well to periodic and open boundary conditions. Simulations over a model Hamiltonian validate our theory.

/pdf/mapping-topological-order-in-coordinate-space-i26vtwerdg.pdf

Mapping topological order in coordinate space

The non-Hermitian skin effect (NHSE), the accumulation of eigen--wave functions at boundaries of open systems, underlies a variety of exotic properties that defy conventional wisdom. While the NHSE and its intriguing impact on band topology and dynamics have been observed in classical or photonic systems, their demonstration in a quantum gas system remains elusive. Here we report the experimental realization of a dissipative Aharonov-Bohm chain---non-Hermitian topological model with NHSE---in the momentum space of a two-component Bose-Einstein condensate. We identify signatures of the NHSE in the condensate dynamics, and perform Bragg spectroscopy to resolve topological edge states against a background of localized bulk states. Our Letter sets the stage for further investigation on the interplay of many-body statistics and interactions with the NHSE, and is a significant step forward in the quantum control and simulation of non-Hermitian physics. 

Dynamic Signatures of Non-Hermitian Skin Effect and Topology in Ultracold Atoms

Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the conventional bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper, we construct a one-dimensional non-Hermitian Su-Schrieffer-Heeger model with periodic driving that exhibits the non-Hermitian skin effect: all the eigenstates are localized at the boundary of the systems, whether they are the bulk states or the zero and the $\ensuremath{\pi}$ modes. To capture the topological properties, the non-Bloch winding numbers are defined by the non-Bloch periodized evolution operators based on the generalized Brillouin zone. Furthermore, the non-Hermitian bulk-boundary correspondence is established: the non-Bloch winding numbers $({W}_{0,\ensuremath{\pi}})$ characterize the edge states with quasienergies $\ensuremath{\epsilon}=0,\ensuremath{\pi}$. In our non-Hermitian system, a novel phenomenon can emerge: the robust edge states can appear even when the Floquet bands are topological trivial with zero non-Bloch band invariant, which is defined in terms of the non-Bloch effective Hamiltonian. We also show the relation between the non-Bloch winding numbers $({W}_{0,\ensuremath{\pi}})$ and the non-Bloch band invariant $(\mathcal{W})$: $\mathcal{W}={W}_{0}\ensuremath{-}{W}_{\ensuremath{\pi}}$.

Non-Hermitian bulk-boundary correspondence in a periodically driven system

The authors proposed a dynamic detection scheme of non-Bloch topology in the presence of non-Hermitian skin effects.

https://link.aps.org/pdf/10.1103/PhysRevResearch.3.023022

Non-Bloch quench dynamics

We construct a two-dimensional, discrete-time quantum walk exhibiting non-Hermitian skin effects under open-boundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states are consistent with Floquet winding numbers calculated using a non-Bloch band theory invoking time-dependent generalized Billouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined through local biorthogonal eigen wave functions of the non-unitary Floquet operator. Our work would stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.

Two-Dimensional Quantum Walk with Non-Hermitian Skin Effects

We discuss the systematic engineering of quasicrystals in open quantum systems where quasiperiodicity is introduced through purely dissipative processes. While the resulting short-time dynamics is governed by non-Hermitian variants of the Aubry-Andr\'e-Harper model, we demonstrate how phases and phase transitions pertaining to the non-Hermitian quasicrystals fundamentally change the long-time, steady-state-approaching dynamics under the Lindblad master equation. Our schemes are based on an exact mapping between the eigenspectrum of the Liouvillian superoperator with that of the non-Hermitian Hamiltonian, under the condition of quadratic fermionic systems subject to linear dissipation. Our work suggests a systematic route toward engineering exotic quantum dynamics in open systems, based on insights of non-Hermitian physics.

Engineering Dissipative Quasicrystals.

Two-dimensional quantum walk with non-Hermitian skin effects

We study the quench dynamics of non-Hermitian topological models with non-Hermitian skin effects. Adopting the non-Bloch band theory and projecting quench dynamics onto the generalized Brillouin zone, we find that emergent topological structures, in the form of dynamic skyrmions, exist in the generalized momentum-time domain, and are correlated with the non-Bloch topological invariants of the static Hamiltonians. The skyrmion structures anchor on the fixed points of dynamics whose existence are conditional on the coincidence of generalized Brillouin zones of the pre- and post-quench Hamiltonians. Global signatures of dynamic skyrmions, however, persist well beyond such a condition, thus offering a general dynamic detection scheme for non-Bloch topology in the presence of non-Hermitian skin effects. Applying our theory to an experimentally relevant, non-unitary quantum walk, we explicitly demonstrate how the non-Bloch topological invariants can be revealed through the non-Bloch quench dynamics.

Yong-Sheng Zhang

Papers

Non-Bloch quench dynamics

Two-Dimensional Quantum Walk with Non-Hermitian Skin Effects

Engineering Dissipative Quasicrystals.

Two-dimensional quantum walk with non-Hermitian skin effects

Non-Bloch quench dynamics