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Physical Review Letters

Observation of Non-Hermitian Edge Burst Effect in One-Dimensional Photonic Quantum Walk

Jiankun Zhu, Ya-Li Mao, Hu Chen, Kui-Xing Yang, Linhu Li, Bing Yang, Zheng-Da Li, Jingyun Fan

Published May 17, 2024• 21 citations
Publisher

Abstract

Non-Hermitian systems can exhibit unique quantum phases without any Hermitian counterparts. For example, the latest theoretical studies predict a new surprising phenomenon that bulk bands can localize and dissipate prominently at the system boundary, which is dubbed the non-Hermitian edge burst effect. Here we realize a one-dimensional non-Hermitian Su-Schrieffer-Heeger lattice with bulk translation symmetry implemented with a photonic quantum walk. Employing time-resolved single-photon detection to characterize the chiral motion and boundary localization of bulk bands, we determine experimentally that the dynamics underlying the non-Hermitian edge burst effect is due to the interplay of non-Hermitian skin effect and imaginary band gap closing. This new non-Hermitian physical effect deepens our understanding of quantum dynamics in open quantum systems.

DOI
10.1103/physrevlett.132.203801

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Non-Hermitian systems can exhibit unique quantum phases without any Hermitian counterparts. For example, the latest theoretical studies predict a new surprising phenomenon that bulk bands can localize and dissipate prominently at the system boundary, which is dubbed the non-Hermitian edge burst effect. Here we realize a one-dimensional non-Hermitian Su-Schrieffer-Heeger lattice with bulk translation symmetry implemented with a photonic quantum walk. Employing time-resolved single-photon detection to characterize the chiral motion and boundary localization of bulk bands, we determine experimentally that the dynamics underlying the non-Hermitian edge burst effect is due to the interplay of non-Hermitian skin effect and imaginary band gap closing. This new non-Hermitian physical effect deepens our understanding of quantum dynamics in open quantum systems.
We unveil an unexpected non-Hermitian phenomenon, dubbed edge burst, in non-Hermitian quantum dynamics. Specifically, in a class of non-Hermitian quantum walk in periodic lattices with open boundary condition, an exceptionally large portion of loss occurs at the system boundary. The physical origin of this edge burst is found to be an interplay between two unique non-Hermitian phenomena: non-Hermitian skin effect and imaginary gap closing. Furthermore, we establish a universal bulk-edge scaling relation underlying the non-Hermitian edge burst. Our predictions are experimentally accessible in various non-Hermitian systems including quantum-optical and cold-atom platforms.
The non-Hermitian skin effect, by which the eigenstates of the Hamiltonian are predominantly localized at the boundary, has revealed a strong sensitivity of non-Hermitian systems to the boundary condition. Here we experimentally observe a striking boundary-induced dynamical phenomenon known as the non-Hermitian edge burst, which is characterized by a sharp boundary accumulation of loss in non-Hermitian time evolutions. In contrast to the eigenstate localization, the edge burst represents a generic non-Hermitian dynamical phenomenon that occurs in real time. Our experiment, based on photonic quantum walks, not only confirms the prediction of the phenomenon, but also unveils its complete space-time dynamics. Our observation of edge burst paves the way for studying the rich real-time dynamics in non-Hermitian topological systems.
Non-Hermitian quantum walks on lossy lattices with open boundaries can exhibit an anomalous peak of the loss probability at the boundary, known as the non-Hermitian edge burst (NHEB). This phenomenon has been attributed to the combined effect of the non-Hermitian skin effect (NHSE) and a gapless imaginary spectrum. Here we investigate a class of models in which the NHSE is induced by magnetic flux while the loss is spatially nonuniform. We show that the spatial distribution of loss plays a crucial role in determining the emergence and strength of the NHEB. Notably, even in the absence of the NHSE, a weak boundary accumulation of the loss probability persists. We term this effect a quasi-non-Hermitian edge burst (quasi-NHEB). By analyzing the dependence of the loss probability on the initial position, we further demonstrate that the quasi-NHEB obeys a bulk-edge scaling relation distinct from that of conventional NHEB. Our results show that spatially nonuniform loss alone can generate boundary-localized loss anomalies even without the NHSE, providing new insight into non-Hermitian boundary phenomena and a broader platform for their exploration and potential applications.
In a class of non-Hermitian quantum walk in lossy lattices with open boundary conditions, an unexpected peak in the distribution of the decay probabilities appears at the edge, referred to as an edge burst. It is proposed that the edge burst originates jointly from the non-Hermitian skin effect (NHSE) and the imaginary gaplessness of the spectrum [W.-T. Xue et al., Phys. Rev. Lett. 128, 120401 (2022)]. Using a particular one-dimensional lossy lattice with a nonuniform loss rate, we show that the edge burst can occur even in the absence of skin localizations. Furthermore, we discuss that the edge burst may not appear if the spectrum satisfies the imaginary gapless condition. Aside from its fundamental importance, by removing the restrictions on observing the edge burst effect, our results open the door to broader design space for future applications of the edge burst effect.
A dynamical bulk-edge relation in quantum walks has been theoretically proposed and experimentally observed, in which a power-law dependence of the bulk loss probability is associated with a pronounced peak of loss probability at the edge. This behavior has been proven to arise from imaginary gap closing and the non-Hermitian skin effect in the infinite limit without boundary effects. However, in a finite-size chain, we find that boundary scattering can suppress this edge burst. Meanwhile, imaginary gap opening, together with the non-Hermitian skin effect, can also induce a large loss probability at the edge. Our results provide insights into finite-size quantum dynamics.