Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths

AbstractTopological on-chip photonics based on tailored photonic crystals (PhCs) that emulate quantum valley-Hall effects has recently gained widespread interest owing to its promise of robust unidirectional transport of classical and quantum information. We present a direct quantitative evaluation of topological photonic edge eigenstates and their transport properties in the telecom wavelength range using phase-resolved near-field optical microscopy. Experimentally visualizing the detailed sub-wavelength structure of these modes propagating along the interface between two topologically non-trivial mirror-symmetric lattices allows us to map their dispersion relation and differentiate between the contributions of several higher-order Bloch harmonics. Selective probing of forward- and backward-propagating modes as defined by their phase velocities enables direct quantification of topological robustness. Studying near-field propagation in controlled defects allows us to extract upper limits of topological protection in on-chip photonic systems in comparison with conventional PhC waveguides. We find that protected edge states are two orders of magnitude more robust than modes of conventional PhC waveguides. This direct experimental quantification of topological robustness comprises a crucial step toward the application of topologically protected guiding in integrated photonics, allowing for unprecedented error-free photonic quantum networks.

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Photonic topological insulator with broken time-reversal symmetry

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1525502113 ◽

2016 ◽

Vol 113 (18) ◽

pp. 4924-4928 ◽

Cited By ~ 104

Author(s):

Cheng He ◽

Xiao-Chen Sun ◽

Xiao-Ping Liu ◽

Ming-Hui Lu ◽

Yulin Chen ◽

...

Keyword(s):

Topological Insulator ◽

Time Reversal ◽

Magnetoelectric Coupling ◽

Electronic Systems ◽

Time Reversal Symmetry ◽

Edge States ◽

Protection Mechanism ◽

Fundamental Particles ◽

Left And Right ◽

Symmetry Protected

A topological insulator is a material with an insulating interior but time-reversal symmetry-protected conducting edge states. Since its prediction and discovery almost a decade ago, such a symmetry-protected topological phase has been explored beyond electronic systems in the realm of photonics. Electrons are spin-1/2 particles, whereas photons are spin-1 particles. The distinct spin difference between these two kinds of particles means that their corresponding symmetry is fundamentally different. It is well understood that an electronic topological insulator is protected by the electron’s spin-1/2 (fermionic) time-reversal symmetry Tf2=−1. However, the same protection does not exist under normal circumstances for a photonic topological insulator, due to photon’s spin-1 (bosonic) time-reversal symmetry Tb2=1. In this work, we report a design of photonic topological insulator using the Tellegen magnetoelectric coupling as the photonic pseudospin orbit interaction for left and right circularly polarized helical spin states. The Tellegen magnetoelectric coupling breaks bosonic time-reversal symmetry but instead gives rise to a conserved artificial fermionic-like-pseudo time-reversal symmetry, Tp (Tp2=−1), due to the electromagnetic duality. Surprisingly, we find that, in this system, the helical edge states are, in fact, protected by this fermionic-like pseudo time-reversal symmetry Tp rather than by the bosonic time-reversal symmetry Tb. This remarkable finding is expected to pave a new path to understanding the symmetry protection mechanism for topological phases of other fundamental particles and to searching for novel implementations for topological insulators.

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Direct quantification of robustness in topologically-protected photonic edge states at telecom wavelengths

Active Photonic Platforms XIII ◽

10.1117/12.2594527 ◽

2021 ◽

Author(s):

Sonakshi Arora ◽

Thomas A. Bauer ◽

René Barczyk ◽

Ewold Verhagen ◽

Laurens K. Kuipers

Keyword(s):

Edge States ◽

Direct Quantification

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Interacting edge states of fermionic symmetry-protected topological phases in two dimensions

SciPost Physics ◽

10.21468/scipostphys.9.2.016 ◽

2020 ◽

Vol 9 (2) ◽

Author(s):

Joseph Sullivan ◽

Meng Cheng

Keyword(s):

Two Dimensions ◽

Topological Phases ◽

Edge States ◽

Exactly Solvable ◽

Fermionic Systems ◽

Spatial Dimensions ◽

Translation Symmetry ◽

Interacting Systems ◽

Symmetry Transformations ◽

Symmetry Protected

Recently, it has been found that there exist symmetry-protected topological phases of fermions, which have no realizations in non-interacting fermionic systems or bosonic models. We study the edge states of such an intrinsically interacting fermionic SPT phase in two spatial dimensions, protected by \mathbb{Z}_4\times\mathbb{Z}_2^\mathsf{T}ℤ4×ℤ2𝖳 symmetry. We model the edge Hilbert space by replacing the internal \mathbb{Z}_4ℤ4 symmetry with a spatial translation symmetry, and design an exactly solvable Hamiltonian for the edge model. We show that at low-energy the edge can be described by a two-component Luttinger liquid, with nontrivial symmetry transformations that can only be realized in strongly interacting systems. We further demonstrate the symmetry-protected gaplessness under various perturbations, and the bulk-edge correspondence in the theory.

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Defective edge states and anomalous bulk-boundary correspondence for topological insulators under non-Hermitian similarity transformation

International Journal of Modern Physics B ◽

10.1142/s0217979220501465 ◽

2020 ◽

Vol 34 (09) ◽

pp. 2050146

Author(s):

C. Wang ◽

X.-R. Wang ◽

C.-X. Guo ◽

S.-P. Kou

Keyword(s):

Chiral Symmetry ◽

Topological Insulators ◽

Skin Effect ◽

Similarity Transformation ◽

Topological Invariant ◽

Inversion Symmetry ◽

Edge States ◽

Boundary Correspondence ◽

Zhang Model ◽

Symmetry Protected

It was known that for non-Hermitian topological systems due to the non-Hermitian skin effect, the bulk-edge correspondence is broken down. In this paper, by using one-dimensional Su–Schrieffer–Heeger model and two-dimensional (deformed) Qi–Wu–Zhang model as examples, the focus is on a special type of non-Hermitian topological system without non-Hermitian skin effect — topological systems under non-Hermitian similarity transformation. In these non-Hermitian systems, the defective edge states and the breakdown of bulk-edge correspondence are discovered. To characterize the topological properties, a new type of inversion symmetry-protected topological invariant — total [Formula: see text] topological invariant — has been introduced. In topological phases, defective edge states appear. With the help of the effective edge Hamiltonian, it was found that the defective edge states are protected by (generalized) chiral symmetry and thus the (singular) defective edge states are unstable against the perturbation breaking the chiral symmetry. In addition, the results are generalized to non-Hermitian topological insulators with inversion symmetry in higher dimensions. This work could help people to understand the defective edge states and the breakdown of bulk-edge correspondence for non-Hermitian topological systems.

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(d−2) -Dimensional Edge States of Rotation Symmetry Protected Topological States

Physical Review Letters ◽

10.1103/physrevlett.119.246402 ◽

2017 ◽

Vol 119 (24) ◽

Cited By ~ 291

Author(s):

Zhida Song ◽

Zhong Fang ◽

Chen Fang

Keyword(s):

Edge States ◽

Rotation Symmetry ◽

Topological States ◽

Symmetry Protected

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Operational entanglement of symmetry-protected topological edge states

Physical Review Research ◽

10.1103/physrevresearch.2.043191 ◽

2020 ◽

Vol 2 (4) ◽

Cited By ~ 3

Author(s):

Kyle Monkman ◽

Jesko Sirker

Keyword(s):

Edge States ◽

Symmetry Protected

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PC -symmetry-protected edge states in interacting driven-dissipative bosonic systems

Physical Review A ◽

10.1103/physreva.99.033801 ◽

2019 ◽

Vol 99 (3) ◽

Cited By ~ 4

Author(s):

E. Cancellieri ◽

H. Schomerus

Keyword(s):

Edge States ◽

Symmetry Protected

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Symmetry-protected solitons and bulk-boundary correspondence in generalized Jackiw–Rebbi models

Scientific Reports ◽

10.1038/s41598-021-01117-5 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Chang-geun Oh ◽

Sang-Hoon Han ◽

Sangmo Cheon

Keyword(s):

Internal Field ◽

Fermion Field ◽

Edge States ◽

Global Minima ◽

Rotation Symmetry ◽

Fermion Fields ◽

Boundary Correspondence ◽

Symmetry Protected ◽

Chiral Solitons

AbstractWe investigate the roles of symmetry and bulk-boundary correspondence in characterizing topological edge states in generalized Jackiw–Rebbi (JR) models. We show that time-reversal (T), charge-conjugation (C), parity (P), and discrete internal field rotation ($$Z_n$$ Z n ) symmetries protect and characterize the various types of edge states such as chiral and nonchiral solitons via bulk-boundary correspondence in the presence of the multiple vacua. As two representative models, we consider the JR model composed of a single fermion field having a complex mass and the generalized JR model with two massless but interacting fermion fields. The JR model shows nonchiral solitons with the $$Z_2$$ Z 2 rotation symmetry, whereas it shows chiral solitons with the broken $$Z_2$$ Z 2 rotation symmetry. In the generalized JR model, only nonchiral solitons can emerge with only $$Z_2$$ Z 2 rotation symmetry, whereas both chiral and nonchiral solitons can exist with enhanced $$Z_4$$ Z 4 rotation symmetry. Moreover, we find that the nonchiral solitons have C, P symmetries while the chiral solitons do not, which can be explained by the symmetry-invariant lines connecting degenerate vacua. Finally, we find the symmetry correspondence between multiply-degenerate global vacua and solitons such that T, C, P symmetries of a soliton inherit from global minima that are connected by the soliton, which provides a novel tool for the characterization of topological solitons.

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