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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Exceptional topology of non-Hermitian systems
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Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial.
TL;DR: In this paper, the authors identify and observe a form of bulk-edge correspondence for a particular non-Hermitian topological phase and show that a change in the bulk topological invariant leads to a change of topological edge-mode localization together with peculiar purely non-hermitian properties.
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Non-Hermitian Bulk-Boundary Correspondence and Auxiliary Generalized Brillouin Zone Theory
TL;DR: In this article, the generalized Brillouin zone (GBZ) is calculated analytically in one-dimensional non-Hermitian systems, which helps us to understand the non-hermitian bulk-boundary correspondence.
Journal ArticleDOI
Reciprocal skin effect and its realization in a topolectrical circuit
Tobias Hofmann,Tobias Helbig,Frank Schindler,Frank Schindler,Nora Salgo,Marta Brzezińska,Marta Brzezińska,Martin Greiter,Tobias Kiessling,D. Wolf,Achim Vollhardt,Anton Kabaši,Ching Hua Lee,Ching Hua Lee,Ante Bilušić,Ronny Thomale,Titus Neupert +16 more
TL;DR: The reciprocal skin effect as discussed by the authors describes the conspiracy of non-Hermiticity and non-reciprocity to yield extensive anomalous localization of all eigenmodes in a (quasi) one-dimensional geometry.
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Non-Hermitian Skin Modes Induced by On-Site Dissipations and Chiral Tunneling Effect
Yifei Yi,Zhesen Yang +1 more
TL;DR: A no-go theorem for the emergence of skin modes is revealed and paves the way for searching for quantum systems with skin modes and studying their novel physical responses.
References
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Non-Bloch ${\cal P}{\cal T}$PT symmetry breaking in non-Hermitian photonic quantum walks.
TL;DR: It is unveiled that non-unitary discrete-time quantum walks of photons in systems involving gain and loss show rather generally non-Bloch parity-time symmetry-breaking phase transitions and a bulk probing method to detect such boundary-driven phase transitions is suggested.