Exceptional points and dynamics of a non-Hermitian two-level system without PT symmetry

Wang, Qiu; Wang, Jiao; Shen, H. Z.; Hou, S. C.

doi:10.1209/0295-5075/131/34001

Cited by 8 publications

(3 citation statements)

References 99 publications

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“…In addition to that, new powerful stimuli to the development in this field have been coming from the works on non-Hermitian Hamiltonians having PT symmetry. Pioneered by Bender and Boettcher with the demonstration of real spectra of such operators (see, e.g., [264] and references therein), we have been witnessing new experimental results and applications that have appeared in this field during recent years [265], including the works on PT-symmetry breaking non-Hermitian operators which are relevant to both classical and quantum regimes [266,267].…”

Section: Discussion and Generalizationsmentioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

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Section: Discussion and Generalizationsmentioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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“…Non-Hermitian physics [1-6] is opening up new possibilities in photonics from the creation of omnipolarizers [7][8][9] to sensing applications [10][11][12] and tailoring laser output [13][14][15]. In general, non-Hermitian matrices do not guarantee orthogonal eigenvectors [16][17][18] and have real eigenvalues (PT-symmetric) [19][20][21], imaginary eigenvalues (anti-PT-symmetric) [22][23][24] or complex eigenvalues throughout [25,26]. Ultra narrowband magneto-optical filters [27], which rely on complex refractive indices, are perfect candidates for non-Hermitian physics but have not yet been studied in this domain.…”

Section: Introductionmentioning

confidence: 99%

Exploiting non-orthogonal eigenmodes in a non-Hermitian optical system to realize sub-100 MHz magneto-optical filters.

Logue¹,

Briscoe²,

Pizzey³

et al. 2023

Preprint

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Non-Hermitian physics is responsible for many of the counter-intuitive effects observed in optics research opening up new possibilities in sensing, polarization control and measurement. A hallmark of non-Hermitian matrices is the possibility of non-orthogonal eigenvectors resulting in coupling between modes. The advantages of propagation mode coupling have been little explored in magneto-optical filters and other devices based on birefringence. Magneto-optical filters select for ultra-narrow transmission regions by passing light through an atomic medium in the presence of a magnetic field. Passive filter designs have traditionally been limited by Doppler broadening of thermal vapors. Even for filter designs incorporating a pump laser, transmissions are typically less than 15% for sub-Doppler features. Here we exploit our understanding of non-Hermitian physics to induce non-orthogonal propagation modes in a vapor and realize better magneto-optical filters. We construct two new filter designs with ENBWs and maximum transmissions of 181 MHz, 42 % and 140 MHz, 17% which are the highest figure of merit and first sub-100 MHz FWHM passive filters recorded respectively. This work opens up a range of new filter applications including metrological devices for use outside a lab setting and commends filtering as a new candidate for deeper exploration of non-Hermitian physics such as exceptional points of degeneracy.

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“…[7][8][9] While this configuration is relatively difficult to implement in experiment, non-PT -symmetric systems represented by the ultra-compact metalinsulator-metal (MIM) plasmonic waveguides have aroused extensive attentions in the past few years. 2,3,5,[10][11][12][13][14][15][16] Plasmonic waveguides based on MIM structure have shown capability in guiding and manipulating lightwave at deep subwavelength scale. Zhang et al has proposed an optimized non-PT-symmetric MIM waveguide coupled with two unidentical stub resonators to realize destructive interfere between them, which forms an EP and asymmetric reflection.…”

mentioning

confidence: 99%

High-contrast tunable unidirectional reflectionless phenomenon near the exceptional points in integrated bulk Dirac semimetal waveguide

Wu¹,

Zeng²,

Liu³

et al. 2021

Appl. Phys. Express

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We realize the unidirectional reflectionless light propagation in metal-insulator-metal plasmonic waveguide side-coupled with two resonators based on bulk Dirac semimetal (BDS). This phenomenon is observed at exceptional points where the parity-time symmetry is broken, and near perfect absorption is obtained. Based on the dynamic tunability of BDS, the ultra-compact structure with adjustable unidirectional reflectionlessness can be achieved due to low scattering loss. Our results show a potential for developing integrated plasmonic devices such as active mid-infrared sensors, diodes, and absorbers.

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Exceptional points and dynamics of a non-Hermitian two-level system without PT symmetry

Cited by 8 publications

References 99 publications

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Exploiting non-orthogonal eigenmodes in a non-Hermitian optical system to realize sub-100 MHz magneto-optical filters.

High-contrast tunable unidirectional reflectionless phenomenon near the exceptional points in integrated bulk Dirac semimetal waveguide

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