Amplification of quantum signals by the non-Hermitian skin effect

Wang, Qiang; Zhu, Changyan; Wang, You; Zhang, Baile; Chong, Yidong

doi:10.1103/physrevb.106.024301

Cited by 13 publications

(3 citation statements)

References 84 publications

(148 reference statements)

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“…Non-Hermitian phenomena can be introduced into the quantum regime via several interesting avenues [287][288][289][290][291][292][293]. For example, certain particle non-conserving Hamiltonians, describing parametrically driven nonlinear systems [294], can be mapped to non-Hermitian Hamiltonians via the Bogoliubov-de Gennes transformation [295][296][297][298][299], which can be used to access phenomena such as non-Hermitian topological boundary states and the non-Hermitian skin effect [300][301][302][303]. The experimental implementation of quantum photonic lattices exhibiting non-Hermitian phenomena, though highly challenging, would provide new opportunities for realizing non-Hermitian bandstructures and exploiting their special properties.…”

Section: Discussionmentioning

confidence: 99%

Non-Hermitian photonic lattices: tutorial

Wang¹,

Chong²

2023

J. Opt. Soc. Am. B

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Non-Hermitian photonic lattices combine the peculiar consequences of energy non-conservation with the physics of bandstructures, giving rise to a variety of exotic properties not found in conventional materials or photonic metamaterials. In this tutorial, we introduce the key concepts in the design and implementation of non-Hermitian photonic lattices, including the general features of non-Hermitian lattice Hamiltonians and their bandstructures, the role of non-Hermitian lattice symmetries, and the topological chracterization of non-Hermitian bandstructures. We survey several important non-Hermitian lattice designs, as well as the photonics platforms on which they can be realized. Finally, we discuss the possibilities for future developments in the field.

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Section: Discussionmentioning

confidence: 99%

Non-Hermitian photonic lattices: tutorial

Wang¹,

Chong²

2023

J. Opt. Soc. Am. B

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“…We also expect our analytical approach to be practically useful for tuning to EPs and identifying conditions for NHSE in various experimental arenas. Finally, we note that, very recently, amoebas have been used to determine the generalized Brillouin zone for non-Hermitian systems ( 48 ). In summary, we have introduced and developed a framework to characterize EPs using tropical geometry.…”

Section: Conclusion and Further Directionsmentioning

confidence: 99%

A tropical geometric approach to exceptional points

Banerjee

Jaiswal

Manjunath

et al. 2023

Proc. Natl. Acad. Sci. U.S.A.

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Non-Hermitian systems have been widely explored in platforms ranging from photonics to electric circuits. A defining feature of non-Hermitian systems is exceptional points (EPs), where both eigenvalues and eigenvectors coalesce. Tropical geometry is an emerging field of mathematics at the interface between algebraic geometry and polyhedral geometry, with diverse applications to science. Here, we introduce and develop a unified tropical geometric framework to characterize different facets of non-Hermitian systems. We illustrate the versatility of our approach using several examples and demonstrate that it can be used to select from a spectrum of higher-order EPs in gain and loss models, predict the skin effect in the non-Hermitian Su–Schrieffer–Heeger model, and extract universal properties in the presence of disorder in the Hatano–Nelson model. Our work puts forth a framework for studying non-Hermitian physics and unveils a connection of tropical geometry to this field.

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“…Recent theoretical and experimental studies on non-Hermitian systems have revealed many interesting phenomena without Hermitian counterparts, which greatly expands our cognition of the laws of physics. [1][2][3][4][5][6][7][8][9][10][11][12][13] . One of the quintessential features of non-Hermitian systems is the skin modes [14][15][16][17][18][19][20][21] , namely, the accumulation of the majority of eigenstates at the boundaries of the system.…”

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confidence: 99%

Anomalous non-Hermitian skin effect: the topological inequivalence of skin modes versus point gap

Guo¹,

Bao²,

Zhu³

et al. 2023

Preprint

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Non-Hermitian skin effect, the localization of an extensive number of open boundary eigenstates at the boundaries of the system, has greatly expanded the frontier of physical laws. It has long been believed that the present of skin modes is equivalent to the topologically nontrivial point gap. However, we find that this concomitance can be broken, i.e., the skin modes can be present or absent whereas the point gap is topologically trivial or nontrivial, respectively, named anomalous non-Hermitian skin effect. This anomalous phenomenon arises whenever the unidirectional hopping amplitudes among subsystems are emergence, in which sub-chains have the decoupling-like behaviors and only contribute to the energy levels while without particle occupation. The occurrence of the anomalous non-Hermitian skin effect is accompanied by the mutations of the open boundary eigenvalues, whose structure exhibits the multifold exceptional point and can not be recovered by continuum bands. Moreover, an experimental setup using circuits is proposed to simulate this novel effect. Our results reveal the topologically inequivalent between skin modes and point gap. This new effect not only can give a deeper understanding of non-Bloch theory and the critical phenomenon in non-Hermitian systems, but may also inspire new applications such as in the sensors field.

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Amplification of quantum signals by the non-Hermitian skin effect

Cited by 13 publications

References 84 publications

Non-Hermitian photonic lattices: tutorial

Non-Hermitian photonic lattices: tutorial

A tropical geometric approach to exceptional points

Anomalous non-Hermitian skin effect: the topological inequivalence of skin modes versus point gap

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