Non-Hermitian bulk–boundary correspondence in quantum dynamics

Abstract

Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we theoretically predict and experimentally observe non-Hermitian bulk-boundary correspondence, a fundamental generalization of the conventional bulk-boundary correspondence, in discrete-time non-unitary quantum-walk dynamics of single photons. We experimentally demonstrate 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 match excellently with non-Bloch topological invariants calculated from localized bulk-state wave functions. 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.

Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems

“…Broader implications of NHSE have been under investigations [25,32,33,37,58,[88][89][90][91][92][93][94][95][96][97][98][99]. Very recently, NHSE has been observed in experiments [100][101][102].…”

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

“…A particular point of interest is the observation of the non-Hermitian skin effect [65][66][67][68][69][70][71], whereby all Eigen states of one-dimensional (1D) systems are localized at a boundary, in sharp contrast with the extend Bloch modes of Hermitian counterparts. This intriguing feature of non-Hermitian lattices has recently been experimentally demonstrated using topo electrical circuits [72] and quantum walks of single photons [73]. Further theoretical investigations have also shown higher order skin modes localized at corners and edges of 2D and 3D non-Hermitian lattices [74,75].…”

Perspective on topological states of non-Hermitian lattices

“…The non-Hermitian skin effect presents a conceptual obstacle for building a bulk-boundary correspondence as typically the topological invariants are based on the bulk eigenstates of the system, which in these cases may have a completely different character than the eigenstates of the finite system, no matter how large [47]. We note that, after submission of this article, different experiments have put forward realizations of this anomalous localization in topoelectrical circuits [106,107], quantum walks [108] mechanical systems [109] and magnons [110].…”