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Parity-time (PT) symmetry was first studied in quantum mechanical systems with a non-Hermitian Hamiltonian whose observables are real-valued. Most existing designs of PT symmetric systems in electronics, optics, and acoustics rely on an exact balance of loss and gain in the media to achieve PT symmetry. However, the dispersive behavior of most loss and gain materials restricts the frequency range where the system is PT symmetric. This makes it challenging to access the exceptional points of the system to observe the PT symmetric transition dynamics. Here, we propose a new path to realize PT symmetric systems based on gyroscopic effects instead of using loss and gain units. We demonstrate that PT symmetry and the occurrence of exceptional points are preserved for inversive, counter-rotating gyroscopic systems even with dispersive sub-units. In a gyroscopic system with two circular rings rotating in opposite directions at the same speed, the spontaneous symmetry breaking across the exceptional points results in a phase transition from a moving maximum deformation location to a motionless maximum point. The motionless maximum point occurs despite the externally imposed rotation of the two rings. The results set the foundation to study nonlinear dispersive physics in PT symmetric systems, including solitary waves and inelastic wave scattering.
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PT-symmetry-enabled stable modes in a multicore fiber
Open systems with balanced gain and loss, described by parity-time reversal (PT) symmetric Hamiltonians have been deeply explored over the past decade. Most explorations are limited to finite discrete models (in real or reciprocal spaces) or continuum problems in one dimension. As a result, these models do not leverage the complexity and variability of two-dimensional continuum problems on a compact support. Here, we investigate eigenvalues of the Schrödinger equation on a disk with zero boundary condition, in the presence of constant, PT-symmetric, gain-loss potential that is confined to two mirror-symmetric disks. We find a rich variety of exceptional points, re-entrant PT-symmetric phases, and a nonmonotonic dependence of the PT-symmetry breaking threshold on the system parameters. By comparing results of two model variations, we show that this simple model of a multicore fiber supports propagating modes in the presence of gain and loss.
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- PAR ID:
- 10533006
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Research
- Volume:
- 6
- Issue:
- 3
- ISSN:
- 2643-1564
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Emergence of Exceptional Points in Periodic Metastructures With Hidden Parity-Time Symmetric DefectsAbstract We study the elastodynamics of a periodic metastructure incorporating a defect pair that enforces a parity-time (PT) symmetry due to judiciously engineered imaginary impedance elements—one having energy amplification (gain) and the other having an equivalent attenuation (loss) mechanism. We show that their presence affects the initial band structure of the periodic Hermitian metastructure and leads to the formation of numerous exceptional points (EPs) which are mainly located at the band edges where the local density of modes is higher. The spatial location of the PT-symmetric defect serves as an additional control over the number of emerging EPs in the corresponding spectra as well as the critical non-Hermitian (gain/loss) strength required to create the first EP—a specific defect location minimizes the critical non-Hermitian strength. We use both finite element and coupled-mode-theory-based models to investigate these metastructures and use a time-independent second-order perturbation theory to further demonstrate the influence of the size of the metastructure and the PT-symmetric defect location on the minimum non-Hermitian strength required to create the first EP in a band. Our findings motivate feasible designs for the experimental realization of EPs in elastodynamic metastructures.more » « less
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Abstract We introduce cascaded parity-time (PT)-symmetric artificial sheets (e.g. metasurfaces or frequency selective surfaces) that may exhibit multiple higher-order laser-absorber modes and bidirectional reflectionless transmission resonances within the PT-broken phase, as well as a unidirectional reflectionless transmission resonance associated with the exceptional point (EP). We derive the explicit expressions of the gain–loss parameter required for obtaining these modes and their intriguing physical properties. By exploiting the cascaded PT structures, the gain–loss threshold for the self-dual laser-absorber operation can be remarkably lowered, while the EP remains unaltered. We further study interferometric sensing based on such a multimodal laser-absorber and demonstrate that its sensitivity may be exceptionally high and proportional to the number of metasurfaces along the light propagation direction.more » « less
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Optical neural networks (ONNs), implemented on an array of cascaded Mach–Zehnder interferometers (MZIs), have recently been proposed as a possible replacement for conventional deep learning hardware. They potentially offer higher energy efficiency and computational speed when compared to their electronic counterparts. By utilizing tunable phase shifters, one can adjust the output of each of MZI to enable emulation of arbitrary matrix–vector multiplication. These phase shifters are central to the programmability of ONNs, but they require a large footprint and are relatively slow. Here we propose an ONN architecture that utilizes parity–time (PT) symmetric couplers as its building blocks. Instead of modulating phase, gain–loss contrasts across the array are adjusted as a means to train the network. We demonstrate that PT symmetric ONNs (PT-ONNs) are adequately expressive by performing the digit-recognition task on the Modified National Institute of Standards and Technology dataset. Compared to conventional ONNs, the PT-ONN achieves a comparable accuracy (67% versus 71%) while circumventing the problems associated with changing phase. Our approach may lead to new and alternative avenues for fast training in chip-scale ONNs.more » « less
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The dynamical behavior of broken symmetric coupled cavity lasers is theoretically investigated. The frequency response of this class of lasers is obtained using small signal analysis under direct modulation. Our model predicts a modulation bandwidth enhancement as a broken symmetric laser, operating in the parity-time (PT) symmetry and non-PT symmetry domains. This theoretical prediction is numerically examined in a laser system based on an InGaAs quantum dot platform. Our results clearly show that in these structures, in addition to the injection current, the gain-loss contrast can be used as a new degree of freedom in order to control the characteristic poles of the frequency response function.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevResearch.6.033025
