Exceptional topology of non-Hermitian systems

Reviews of Modern Physics, Journal Year: 2021, Volume and Issue: 93(1)

Published: Feb. 24, 2021

Quantum systems that are coupled to an external bath can often be described in terms of a non-Hermitian effective Hamiltonian. In isolated with Hermitian Hamiltonians, topological aspects the band structure, and resulting phases, have been interest. The combination two concepts, i.e., properties open systems, leads qualitatively new effects. This review provides introduction these quantum mechanical concepts their classical analogs, discusses number applications ranging from metamaterials dissipative cold-atom systems.

Language: Английский

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

Physical Review Letters, Journal Year: 2019, Volume and Issue: 123(17)

Published: Oct. 21, 2019

One of the unique features non-Hermitian Hamiltonians is skin effect, namely, that eigenstates are exponentially localized at boundary system. For open quantum systems, a short-time evolution can often be well described by effective Hamiltonians, while long-time dynamics calls for Lindblad master equations, in which Liouvillian superoperators generate time evolution. In this Letter, we find exhibit and uncover its unexpected physical consequences. It shown effect dramatically shapes dynamics, such damping class systems algebraic under periodic conditions but exponential conditions. Moreover, non-Bloch bands cause chiral with sharp wave front. These phenomena beyond Hamiltonians; instead, they belong to physics full-fledged dynamics.

Language: Английский

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Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial

Proceedings of the National Academy of Sciences, Journal Year: 2020, Volume and Issue: 117(47), P. 29561 - 29568

Published: Nov. 9, 2020

Topological edge modes are excitations that localized at the materials' edges and yet characterized by a topological invariant defined in bulk. Such bulk-edge correspondence has enabled creation of robust electronic, electromagnetic mechanical transport properties across wide range systems, from cold atoms to metamaterials, active matter geophysical flows. Recently, advent non-Hermitian systems---wherein energy is not conserved---has sparked considerable theoretical advances. In particular, novel phases can only exist systems have been introduced. However, whether such be experimentally observed, what their are, remained open questions. Here, we identify observe form for particular phase. We find change bulk leads mode localisation together with peculiar purely properties. Using quantum-to-classical analogy, create metamaterial non-reciprocal interactions, which predicted correspondence, demonstrating its robustness. Our results new avenues field topology manipulating waves unprecedented fashions.

Language: Английский

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Non-Hermitian Bulk-Boundary Correspondence and Auxiliary Generalized Brillouin Zone Theory

Physical Review Letters, Journal Year: 2020, Volume and Issue: 125(22)

Published: Nov. 24, 2020

We provide a systematic and self-consistent method to calculate the generalized Brillouin zone (GBZ) analytically in one-dimensional non-Hermitian systems, which helps us understand bulk-boundary correspondence. In general, $n$-band Hamiltonian is constituted by $n$ distinct sub-GBZs, each of piecewise analytic closed loop. Based on concept resultant, we can show that all properties GBZ be characterized an algebraic equation, solution complex plane dubbed as auxiliary (aGBZ). also obtain from aGBZ. Two physical applications are discussed. Our provides approach spectral problem open boundary systems thermodynamic limit.

Language: Английский

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Non-reciprocal phase transitions

Nature, Journal Year: 2021, Volume and Issue: 592(7854), P. 363 - 369

Published: April 14, 2021

Language: Английский

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Probing non-Hermitian skin effect and non-Bloch phase transitions

Physical Review Research, Journal Year: 2019, Volume and Issue: 1(2)

Published: Sept. 11, 2019

This paper uncovers a bulk probing method to catch physical effects hindered in topological non-Hermitian crystals. The is based on Lyapunov exponent calculation of quantum walker the lattice and can reveal non-Bloch phase transitions, skin effect breakdown bulk-boundary correspondence.

Language: Английский

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Non-Hermitian Topological Sensors

Physical Review Letters, Journal Year: 2020, Volume and Issue: 125(18)

Published: Oct. 29, 2020

We introduce and study a novel class of sensors whose sensitivity grows exponentially with the size device. Remarkably, this drastic enhancement does not rely on any fine-tuning, but is found to be stable phenomenon immune local perturbations. Specifically, physical mechanism behind striking intimately connected anomalous boundary conditions observed in non-Hermitian topological systems. outline concrete platforms for practical implementation these ranging from classical metamaterials synthetic quantum materials.

Language: Английский

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Non-Hermitian topology and exceptional-point geometries

Nature Reviews Physics, Journal Year: 2022, Volume and Issue: 4(12), P. 745 - 760

Published: Oct. 19, 2022

Language: Английский

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Highlighting photonics: looking into the next decade

eLight, Journal Year: 2021, Volume and Issue: 1(1)

Published: June 7, 2021

Abstract Let there be light –to change the world we want to be! Over past several decades, and ever since birth of first laser, mankind has witnessed development science light, as light-based technologies have revolutionarily changed our lives. Needless say, photonics now penetrated into many aspects technology, turning an important dynamically changing field increasing interdisciplinary interest. In this inaugural issue eLight , highlight a few emerging trends in that think are likely major impact at least upcoming decade, spanning from integrated quantum computing, through topological/non-Hermitian topological insulator lasers, AI-empowered nanophotonics photonic machine learning. This Perspective is by no means attempt summarize all latest advances photonics, yet wish subjective vision could fuel inspiration foster excitement scientific research especially for young researchers who love .

Language: Английский

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Higher-order non-Hermitian skin effect

Physical review. B./Physical review. B, Journal Year: 2020, Volume and Issue: 102(20)

Published: Nov. 17, 2020

The non-Hermitian skin effect is a unique feature of systems, in which an extensive number boundary modes appear under the open conditions. Here, we discover higher-order counterparts that exhibit new physics. In two-dimensional systems with system size $L \times L$, while conventional (first-order) accompanies $O\,( L^{2} )$ modes, second-order L corner modes. This also contrasts Hermitian topological insulators, only 1 zero appear. Moreover, for third-order three dimensions, from all L^{3} We demonstrate originates intrinsic topology protected by spatial symmetry. show it modification non-Bloch band theory higher dimensions.

Language: Английский

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