Non-Hermitian bulk-boundary correspondence in quantum dynamics
TLDR
In this paper, the non-Hermitian bulk-boundary correspondence was shown to hold for a wide range of open topological systems with effective non-Bloch Hamiltonians.Abstract:
Bulk–boundary correspondence, a guiding principle in topological matter, relates robust edge states to bulk topological invariants. Its validity, however, has so far been established only in closed systems. Recent theoretical studies indicate that this principle requires fundamental revisions for a wide range of open systems with effective non-Hermitian Hamiltonians. Therein, the intriguing localization of nominal bulk states at boundaries, known as the non-Hermitian skin effect, suggests a non-Bloch band theory in which non-Bloch topological invariants are defined in generalized Brillouin zones, leading to a general bulk–boundary correspondence beyond the conventional framework. Here, we experimentally observe this fundamental non-Hermitian bulk–boundary correspondence in discrete-time non-unitary quantum-walk dynamics of single photons. We demonstrate pronounced photon localizations near boundaries even in the absence of topological edge states, thus confirming the non-Hermitian skin effect. Facilitated by our experimental scheme of edge-state reconstruction, we directly measure topological edge states, which are in excellent agreement with the non-Bloch topological invariants. Our work unequivocally establishes the non-Hermitian bulk–boundary correspondence as a general principle underlying non-Hermitian topological systems and paves the way for a complete understanding of topological matter in open systems. Measurements of non-Hermitian photon dynamics show boundary-localized bulk eigenstates given by the non-Hermitian skin effect. A fundamental revision of the bulk–boundary correspondence in open systems is required to understand the underlying physics.read more
Citations
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Stochastic non-Hermitian skin effect.
TL;DR: A hallmark of photonic transport in non-Hermitian lattices with asymmetric hopping is the robust unidirectional flow of light, which can be induced by stochastic fluctuations in lattices that maintain a symmetric hopping on average.
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Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation
Zidong Lin,Li Zhang,Xinyue Long,Yu-ang Fan,Yishan Li,Kai Tang,Jun Jie Li,Xinfang Nie,Tao Xin,Xiong-Jun Liu,Dawei Liu +10 more
TL;DR: In this article , the authors developed a stochastic average approach to realize the non-Hermitian dissipative quantum dynamics, which has advantages in saving the quantum simulation sources and simplifying the implementation of quantum gates.
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Unconventional skin modes in generalized topolectrical circuits with multiple asymmetric couplings
TL;DR: In this article , the authors derived general conditions for the NHSE in a non-Hermitian superlattice in which the overall eigenmode localization is determined by the geometric mean of the cumulative contributions of all asymmetric coupling segments.
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Non-Hermitian Weyl semimetal and its Floquet engineering
TL;DR: In this article , the authors investigate the non-Hermitian Weyl semimental and its Floquet engineering in a system with skin effect, which breaks the bulk-boundary correspondence in its Hermitian counterpart.
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Persistence of topological phases in non-Hermitian quantum walks.
TL;DR: In this article, the authors investigated the behaviour of topological states in quantum walks in the presence of a lossy environment and showed that the topological phases of the quantum walks are robust against moderate losses.
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