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National Science Review

Observation of dark edge states in parity-time-symmetric quantum dynamics

Peng Xue, Xingze Qiu, Kunkun Wang, Barry C. Sanders, Wei Yi

Published Jan 10, 2023• 7 citations
Publisher

Abstract

Topological edge states arise in non-Hermitian parity-time ([Formula: see text])-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken [Formula: see text] symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in [Formula: see text]-symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the [Formula: see text]-symmetry-unbroken and -broken regimes. Our results establish a unified framework for characterizing topology in [Formula: see text]-symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in [Formula: see text]-symmetric non-Hermitian systems in general.

DOI
10.1093/nsr/nwad005

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Topological edge states arise in non-Hermitian parity-time ([Formula: see text])-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken [Formula: see text] symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in [Formula: see text]-symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the [Formula: see text]-symmetry-unbroken and -broken regimes. Our results establish a unified framework for characterizing topology in [Formula: see text]-symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in [Formula: see text]-symmetric non-Hermitian systems in general.
Topology in quench dynamics gives rise to intriguing dynamic topological phenomena, which are intimately connected to the topology of static Hamiltonians yet challenging to probe experimentally. Here we theoretically characterize and experimentally detect momentum-time skyrmions in parity-time [Formula: see text]-symmetric non-unitary quench dynamics in single-photon discrete-time quantum walks. The emergent skyrmion structures are protected by dynamic Chern numbers defined for the emergent two-dimensional momentum-time submanifolds, and are revealed through our experimental scheme enabling the construction of time-dependent non-Hermitian density matrices via direct measurements in position space. Our work experimentally reveals the interplay of [Formula: see text] symmetry and quench dynamics in inducing emergent topological structures, and highlights the application of discrete-time quantum walks for the study of dynamic topological phenomena.
Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk-boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity-time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems.
Parity-time (PT\mathcal{P}\mathcal{T}PT) symmetry is extensively studied within non-Hermitian physical systems as it has the capability to ensure the presence of real eigenenergies of the systems characterized by non-Hermitian Hamiltonians. Previous studies have been mostly based on the Bloch band theory. Recent developments have unveiled intriguing phenomena which can only be explained by non-Bloch band theory. In this paper, we observe the PT\mathcal{P}\mathcal{T}PT phase transition in photonic quantum walks, which can only be explained by the non-Bloch band theory, which relies on the open boundary condition. Furthermore, we explore the impact of disorder on PT\mathcal{P}\mathcal{T}PT symmetry and demonstrate disorder-induced PT\mathcal{P}\mathcal{T}PT phase transitions. Our work provides a valuable perspective for further explorations on non-Hermitian physics.
We experimentally investigate topological phenomena in one-dimensional discrete-time photonic quantum walks using a combination of methods. We first detect winding numbers of the quantum walk by directly measuring the average chiral displacement, which oscillates around quantized winding numbers for finite-step quantum walks. Topological phase transitions can be identified as changes in the center of oscillation of the measured chiral displacement. The position of topological phase transition is then confirmed by measuring the moments of the walker probability distribution. Finally, we observe localized edge states at the boundary of regions with different winding numbers. We also confirm the robustness of edge states against chiral-symmetry-preserving disorder.
Steering the evolution of single spin systems is crucial for quantum computing and quantum sensing. The dynamics of quantum systems has been theoretically investigated with parity-time-symmetric Hamiltonians exhibiting exotic properties. Although parity-time symmetry has been explored in classical systems, its observation in a single quantum system remains elusive. We developed a method to dilate a general parity-time-symmetric Hamiltonian into a Hermitian one. The quantum state evolutions ranging from regions of unbroken to broken [Formula: see text] symmetry have been observed with a single nitrogen-vacancy center in diamond. Owing to the universality of the dilation method, our result provides a route for further exploiting and understanding the exotic properties of parity-time symmetric Hamiltonian in quantum systems.
We present a method to detect topological invariants in nonunitary parity-time-symmetric (PT-symmetric) quantum walks (QWs). The topological phases of a PT-symmetric QW can be characterized by the mean position of the walk, which is an experimentally observable quantity. This method can also be applied to reveal topological phases in the unitary split-step QW and lattice model. We also explore the selection of topological interface modes in the PT-symmetric QW. The introduction of nonunitarity into the PT-symmetric QW can render the eigenvalue of the topological interface mode larger than the bulk region modes, which leads to the selective excitation of the corresponding topological interface mode during the evolution. Contrary to the Su--Schrieffer--Heeger (SSH) lattice model, in the PT-symmetric QW, the transition between the amplification and the suppression of the topological interface mode may not occur. Our study of the selection of topological interface modes in the PT-symmetric QW provides a route to realize the lasing of specific modes within the system.