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
More filters
Journal ArticleDOI
Topological photonics: Where do we go from here?
TL;DR: Topological photonics is currently one of the most active research areas in optics as discussed by the authors and is also the spearhead of research in topological physics at large, more than a decade after it started.
Journal ArticleDOI
Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
Nobuyuki Okuma,Masatoshi Sato +1 more
TL;DR: In this article, the role of non-Hermitian topology in spectral properties and entanglement structures of open systems was investigated in terms of symmetry-protected and higher-dimensional skin effects.
Journal ArticleDOI
Skin effect and winding number in disordered non-Hermitian systems
Jahan Claes,Taylor L. Hughes +1 more
TL;DR: In this paper, the authors extend the definition of the winding number to disordered NH Hamiltonians by generalizing established results on disordered Hermitian topological insulators, and verify that their real-space formula still predicts the NH skin effect.
Journal ArticleDOI
Observation of higher-order non-Hermitian skin effect
TL;DR: In this paper, the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional acoustic higher order topological insulators was shown to drive wave localizations toward opposite edges upon different spin polarizations.
Journal ArticleDOI
Two-dimensional non-Hermitian Skin Effect in a Synthetic Photonic Lattice
TL;DR: In this paper, a two-dimensional non-Hermitian skin effect (NHSE) was realized in a synthetic photonic lattice composed of a spatial dimension and a synthetic frequency dimension by introducing gain and loss and dynamically modulating the complex refractive index in a one-dimensional ring-resonator array.
References
More filters
Journal ArticleDOI
Colloquium: Topological insulators
M. Z. Hasan,Charles L. Kane +1 more
TL;DR: In this paper, the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topologically insulators have been observed.
Journal ArticleDOI
Topological insulators and superconductors
Xiao-Liang Qi,Shou-Cheng Zhang +1 more
TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Journal ArticleDOI
Non-Hermitian physics and PT symmetry
Ramy El-Ganainy,Konstantinos G. Makris,Mercedeh Khajavikhan,Ziad H. Musslimani,Stefan Rotter,Demetrios N. Christodoulides +5 more
TL;DR: In this paper, the interplay between parity-time symmetry and non-Hermitian physics in optics, plasmonics and optomechanics has been explored both theoretically and experimentally.
Journal ArticleDOI
Edge States and Topological Invariants of Non-Hermitian Systems.
Shunyu Yao,Zhong Wang +1 more
TL;DR: This work obtains the phase diagram of the non-Hermitian Su-Schrieffer-Heeger model, whose topological zero modes are determined by theNon-Bloch winding number instead of the Bloch-Hamiltonian-based topological number.
Journal ArticleDOI
Topological insulator laser: Experiments
Miguel A. Bandres,Steffen Wittek,Gal Harari,Midya Parto,Jinhan Ren,Mordechai Segev,Demetrios N. Christodoulides,Mercedeh Khajavikhan +7 more
TL;DR: This work demonstrates an all-dielectric magnet-free topological insulator laser, with desirable properties stemming from the topological transport of light in the laser cavity, and demonstrates higher slope efficiencies compared to those of the topologically trivial counterparts.