Observation of 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.

15 pages, 9 figures

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• New topological invariants in non-Hermitian systems
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• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
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• Non-Hermitian quantum gases: a platform for imaginary time crystals
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• Quasi-stationary solutions in non-Hermitian systems
• Non-Bloch Dirac Points and Phase Diagram in the Stacked Non-Hermitian SSH Model
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• Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model
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• Many-body critical non-Hermitian skin effect
• Liouvillian skin effect in quantum neural networks
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• Optical pumping through the Liouvillian skin effect
• Two-dimensional lattice with an imaginary magnetic field
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Dynamics of non-Hermitian Floquet Wannier-Stark system
• Non-Hermitian $C_{NH}=2$ Chern insulator protected by generalized rotational symmetry
• Loss-induced universal one-way transport in periodically driven systems
• Emergent non-Hermitian physics in generalized Lotka-Volterra model
• Spontaneous Formation of Exceptional Points at the Onset of Magnetism
• Controllable Floquet edge modes in a multi-frequency driving system
• Bulk-boundary correspondence in topological systems with the momentum dependent energy shift
• Winding Topology of Multifold Exceptional Points
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Optical non-Hermitian skin effect in two-dimensional uniform media
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Exceptional second-order topological insulators
• Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
• Impurity in a Fermi gas under non-Hermitian spin-orbit coupling
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Manipulating Spectral Windings and Skin Modes through Nonconservative Couplings
• Quantum Pontus-Mpemba Effect Enabled by the Liouvillian Skin Effect
• Antichiral and trap-skin dynamics in a nonreciprocal bosonic two-leg ladder with artificial magnetic flux
• Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics
• Phase transitions in non-Hermitian superlattices
• Topology and its detection in a dissipative Aharonov-Bohm chain
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations
• Entanglement entropy distinguishes PT-symmetry and topological phases in a class of non-unitary quantum walks
• Hermitian and non-Hermitian topology in active matter
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Alternating quantum-emitter chains: Exceptional-point phase transition, edge state, and quantum walks
• Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Quantum Reservoir Computing for Realized Volatility Forecasting
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Optical realization of one-dimensional generalized split-step quantum walks
• Controllable suppression of Non-Hermitian skin effects
• Polariton Chern Bands in 2D Photonic Crystals Beyond Dirac Cones
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Direct Measurement of a Non-Hermitian Topological Invariant in a Hybrid Light-Matter System
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• Multitype entanglement dynamics induced by exceptional points
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• Quantum walk for SU(1,1)
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Experimentally Probing Non-Hermitian Spectral Transition and Eigenstate Skewness
• Exceptional mode topological surface laser
• Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
• Chiral state conversion in a levitated micromechanical oscillator with in situ control of parameter loops
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Entanglement phases and phase transitions in monitored free fermion system due to localizations
• Non-Hermitian Hopf insulators
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Topological spin textures in electronic non-Hermitian systems
• Non-Hermitian magnetic moment
• Optimal spectral transport of non-Hermitian systems
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Non-Hermitian higher-order topological insulators enabled by altermagnet engineering
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Non-Hermitian topological wall modes in rotating Rayleigh-Benard convection
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Non-Hermitian topology of transport in the quantum Hall phases in graphene
• Dynamical transition in non-Hermitian Chern insulator
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Emergent non-Hermitian conservation laws at exceptional points
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks
• Quantifying non-Hermiticity using single- and many-particle quantum properties
• Supermetal-insulator transition in a non-Hermitian network model
• Non-Hermitian Higher-Order Dirac Semimetals
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• QFT Realization of Non-Unitary $\mathfrak{sl}(2,\mathbb{C})$ WRT Invariants and Their Galois Conjugations
• Winding-control mechanism of non-Hermitian systems
• Beyond characteristic equations: A unified one-dimensional non-Bloch band theory via wavefunction data
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Correspondence between non-Hermitian topology and directional amplification in the presence of disorder
• Dynamical Quantum Phase Transitions and Many-Body Backflow in Open Quantum Systems
• 1D Spontaneous Symmetry Breaking in thermal equilibrium via Non-Hermitian Construction
• Interacting many-body non-Hermitian systems as Markov chains
• Anomalous Point-Gap Interactions Unveil the Mirage Bath
• Reversing non-Hermitian skin accumulation with a non-local transverse switch
• Floquet spin textures in optically pumped non-Hermitian surface states
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Emergence of Hermitian topology from non-Hermitian knots
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices
• Scaling rule in critical non-Hermitian skin effect
• Self-healing of non-Hermitian topological skin modes
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
• One-directional polarization transport in electron/nuclear spin chains with loss and gain
• Probing phase transitions in non-Hermitian systems with quantum entanglement