Topological invariance and global Berry phase in non-Hermitian systems

Liang, Shi‐Dong; Huang, Guang-Yao

doi:10.1103/physreva.87.012118

Cited by 214 publications

(135 citation statements)

References 44 publications

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“…To provide a complete description and proof, we start by considering a two-band, non-Hermitian -symmetric model which can be used to describe an array of subwavelength photonic resonators coated with gain media. The -symmetric eigenvalue problem is written in the generic form as2735…”

Section: Two-band -Symmetric Modelmentioning

confidence: 99%

“…Recently, many efforts have been put on extending topological band theory131415161718192021 to non-Hermitian -symmetric systems. For example, there have been different theoretical approaches to generalize topological invariants using bi-orthonormal basis22232425, redefining the inner product26, or using the global Berry phase27. Topological transition in the bulk of non-Hermitian system has also been realized28.…”

mentioning

confidence: 99%

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Anomalous Light Scattering by Topological PT-symmetric Particle Arrays

Ling

Choi

Mok

et al. 2016

Sci Rep

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Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological edge modes in a non-Hermitian -symmetric system can give rise to an anomalous sideway scattering when they are simultaneously excited by a plane wave. We propose a realization of such scattering state in a linear array of subwavelength resonators coated with gain media. The prediction is based on an analytical two-band model and verified by rigorous numerical simulation using multiple-multipole scattering theory. The result suggests an extreme situation where leakage of classical information is unnoticeable to the transmitter and the receiver when such a -symmetric unit is inserted into the communication channel.

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Section: Two-band -Symmetric Modelmentioning

confidence: 99%

mentioning

confidence: 99%

Anomalous Light Scattering by Topological PT-symmetric Particle Arrays

Ling

Choi

Mok

et al. 2016

Sci Rep

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“…Non-Hermitian Hamiltonians are widely used as effective models to describe open quantum and classical systems [4,5,6], or are introduced to provide complex extensions of the ordinary quantum mechanics such as in the PT -symmetric quantum mechanics [7,8,9,10]. The increasing interest devoted to non-Hermitian dynamics has motivated the extension of the arsenal of perturbation mathematical tools into the non-Hermitian realm 1 [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42]. Several results have been found concerning extensions and breakdown of the adiabatic theorem [13,15,16,34,38,39], Berry phase [12,14,…”

Section: Introductionmentioning

confidence: 99%

“…The increasing interest devoted to non-Hermitian dynamics has motivated the extension of the arsenal of perturbation mathematical tools into the non-Hermitian realm 1 [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42]. Several results have been found concerning extensions and breakdown of the adiabatic theorem [13,15,16,34,38,39], Berry phase [12,14,17,18,22,26,27,32,33] and shortcuts to adiabaticity [30,36,…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian time-dependent perturbation theory: Asymmetric transitions and transitionless interactions

Longhi

Valle

2017

Annals of Physics

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The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are symmetric with respect to the initial an final states. Here we extend time-dependent perturbation theory into the non-Hermitian realm and consider the transitions in a stationary Hermitian system, described by a self-adjoint HamiltonianĤ 0 , induced by a time-dependent non-Hermitian interaction f (t)Ĥ 1 . In the weak interaction (perturbative) limit, the transition probabilities generally turn out to be asymmetric for exchange of initial and final states. In particular, for a temporal shape f (t) of the perturbation with one-sided Fourier spectrum, i.e. with only positive (or negative) frequency components, transitions are fully unidirectional, a result that holds even in the strong interaction regime. Interestingly, we show that non-Hermitian perturbations can be tailored to be transitionless, i.e. the perturbation leaves the system unchanged as if the interaction had not occurred at all, regardless the form ofĤ 0 andĤ 1 . As an application of our results, we provide important physical insights into the asymmetric (chiral) behavior of dynamical encircling of an exceptional point in two-and three-level non-Hermitian systems.

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“…The observed complex Berry phase is directly related to Wannier-Stark ladders with complex energies in the presence of an external force 37 . The topological nature of the system is determined by the global Berry phase, corresponding to the summation of Berry phase in both lower and upper bands 28 . While Berry phase of each individual band continuously varies in different quantum phases, the global Berry phase remains quantized independent of onsite gain/loss, demonstrating the same topological nature of the system regardless of quantum phase transition.…”

mentioning

confidence: 99%

Robust Light State by Quantum Phase Transition in Non-Hermitian Optical Materials

Zhao

Longhi

Feng

2016

Conference on Lasers and Electro-Optics

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Robust light transport is the heart of optical information processing, leading to the search for robust light states by topological engineering of material properties. Here, it is shown that quantum phase transition, rather than topology, can be strategically exploited to design a novel robust light state. We consider an interface between parity-time (PT) symmetric media with different quantum phases and use complex Berry phase to reveal the associated quantum phase transition and topological nature. While the system possesses the same topological order within different quantum phases, phase transition from PT symmetry to PT breaking across the interface in the synthetic non-Hermitian metamaterial system facilitates novel interface states, which are robust against a variety of gain/loss perturbations and topological impurities and disorder. The discovery of the robust light state by quantum phase transition may promise fault-tolerant light transport in optical communications and computing.Metamaterials have offered a new paradigm of designing unprecedented material properties, revolutionizing our fundamental understanding in optics 1 . While in the past the design of metamaterials was mainly focused on the real permittivity-permeability plane, the emergence of parity-time (PT) symmetry 2 for non-Hermitian Hamiltonians in quantum field theory has been guiding the studies of metamaterials into the entire dielectric permittivity plane with a delicate interplay of index, gain and loss [3][4][5][6] . In spite of non-Hermiticity, completely real eigen spectra, corresponding to PT symmetric phase, can still be expected. By increasing the gain/loss contrast, the eigen spectra become complex and the system can transit into PT broken phase [3][4][5][6] . Recent investigations of PT symmetric metamaterials have enabled a variety of intriguing optical phenomena, including effective manipulation of cavity oscillating modes [7][8][9] and unidirectional light transport [10][11][12][13][14][15][16] , which promise new functionalities for integrated photonics information processing.To secure fault-tolerant light transport for optical communications, robust optical interface states, inspired by topological insulators and quantum Hall systems in condensed-matter physics, have been developed [17][18][19][20][21][22][23] . From a topological perspective, a system can acquire a non-negligible geometric phase (also called Berry phase) under a cyclic and adiabatic variation in a parameter space, which classifies the topological orders of matter 24 . An important signature of topological effects is the presence of topological states at the interface between two media with different topological orders. Because of the persistent Berry phase underlying each topological order, the interface states are topologically protected against local perturbations to the interface. In optics, topological light states are immune to backscattering of light 25 , promising applications in optical information processing 26 . Nevertheless, these robust light...

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Topological invariance and global Berry phase in non-Hermitian systems

Cited by 214 publications

References 44 publications

Anomalous Light Scattering by Topological PT-symmetric Particle Arrays

Anomalous Light Scattering by Topological PT-symmetric Particle Arrays

Non-Hermitian time-dependent perturbation theory: Asymmetric transitions and transitionless interactions

Robust Light State by Quantum Phase Transition in Non-Hermitian Optical Materials

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