Non-Hermitian bulk–boundary correspondence in quantum dynamics

By Lei Xiao, Tian-Shu Deng, Kunkun Wang, Gaoyan Zhu, Zhong Wang, W. Yi, Peng Xue. Nature Physics, 2019

860 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/5f5a27ea6be78c445e4768ed32364cfdc7deea6d

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Citations in the corpus

Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class (2020, background): “Recent experimental observations confirmed it in mechanical metamaterials [68], electrical circuits [69], and quantum walk [70].”
A review on non-Hermitian skin effect (2022, methodology): “[115,128], acoustics [121,124], mechanics [132,161–163] and electric circuits [130,131,133–135,137] have exploited their unique characteristics to facilitate the peculiar NHSE, but also the quantum-walk [129], cold-atom [136] and active matter [165] systems are thriving on demonstrating various non-”
Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect (2022, background): “The skin effect has recently been observed in classical experiments of mechanical metamaterials [123], electrical circuits [124, 125], photonic lattices [126], and active particles [127], as well as quantum experiments of single photons [128] and ultracold atoms [129].”
Higher-order non-Hermitian skin effect (2020, neutral): “[111] L.”