Parity-time Symmetry Research Articles

Strain-Induced Frequency Splitting in PT Symmetric Coupled Silicon Resonators.

When two resonators of coupled silicon resonators are identical and the gain on one side is equal to the loss on the other side, a parity-time (PT) symmetric-coupled silicon resonator is formed. As non-Hermitian systems, the PT-symmetric systems have exhibited many special properties and interesting phenomena. This paper proposes the strain-induced frequency splitting in PT symmetry-coupled silicon resonators. The frequency splitting of the PT system caused by strain perturbations is derived and simulated. Theory and simulation both indicate that the PT system is more sensitive to strain perturbation near the exceptional point (EP) point. Then, a feedback circuit is designed to achieve the negative damping required for PT symmetry. Based on a simple silicon-on-insulator (SOI) process, the silicon resonator chip is successfully fabricated. After that, the PT-symmetric-coupled silicon resonators are successfully constructed, and the frequency splitting phenomenon caused by strain is observed experimentally.

Dynamic transition of the density-matrix topology under parity-time symmetry

Dynamic transition of the density-matrix topology under parity-time symmetry

Observation of parity-time symmetry for evanescent waves

Parity-time (PT) symmetry has enabled the demonstration of fascinating wave phenomena in non-Hermitian systems characterized by precisely balanced gain and loss. Until now, the exploration and observation of PT symmetry in scattering settings have largely been limited to propagating waves. Here, we demonstrate a versatile coupled-resonator acoustic waveguide (CRAW) system that enables the observation of PT-symmetric scattering responses for evanescent waves within a bandgap. By examining the generalized scattering matrix in the evanescent wave regime, we observe hallmark PT-symmetric phenomena—including phase transitions at an exceptional point, anisotropic transmission resonances, and laser-absorber modes—in systems that do not require balanced distributions of gain and loss. Owing to the peculiar energy transfer features of evanescent waves, our results not only demonstrate a distinct pathway for observing PT symmetry, but also enable strategies for exotic energy tunneling mechanisms, paving fresh directions for wave engineering grounded in non-Hermitian physics.

Transmission enhancement mechanism of PT symmetric photonic crystal coupled with grooved sub-wavelength grating

In order to enhance the sensing characteristics of the sensor, based on the periodic sub-wavelength grating(SWG), a groove structure is introduced to make the Fano resonance waveform sharper. At the same time, based on the Parity-Time(PT) symmetry principle, by making the periodic photonic crystal meet the PT symmetry condition, the structure can absorb the energy of the emitted light on the original basis, produce the transmission enhancement effect, and make the transmission peak of the structure exceed 1. The sensing is realized by using the property that the different refractive indices of the detected medium corresponds to different transmission. When the incident light is 1550 nm, the sensitivity and FOM (Figure of Merit) value of the proposed structure reach 5.702 × 105RIU−1and 1.9 × 107 respectively, which greatly improves the performance of the sensor.

Realizing Multi-Parameter Measurement Using PT-Symmetric LC Sensors.

With the rapid development in sensor network technology, the complexity and diversity of application scenarios have put forward more and more new requirements for inductor-capacitor (LC) sensors, for instance, multi-parameter simultaneous monitoring. Here, the parity-time (PT) symmetry concept in quantum mechanics is applied to LC passive wireless sensing. Two or even three parameters can be monitored simultaneously by observing the frequency response of the reflection coefficient at the end of the readout circuit. In particular, for three-parameter detection, a novel detection method is studied to extract the three resonant frequencies of the system through the phase-frequency characteristics of the reflection coefficient, which has never appeared in the previous literature on PT symmetry. The changes in three resonant frequencies are in response to changes in the three parameters in the environment. We show theoretically and demonstrate experimentally that the PT-symmetric LC sensor can realize multi-parameter measurement using a series LCR circuit as the sensor and a symmetric adjustable LCR circuit as the readout circuit. Our work paves the way for applying PT symmetry in multi-parameter detection.

Low-gain generalized PT symmetry for electromagnetic impurity-immunity via non-Hermitian doped zero-index materials

Parity-time-symmetric (PT-symmetric) metasurfaces exhibit a plethora of fascinating exceptional-point-induced phenomena, including unidirectional negative refraction and electromagnetic impurity-immunity. However, practical realization of these effects is often impeded by the high demand for gain metasurfaces (gain tangent ∼102). Here, we propose a solution to this challenge by constructing a low-gain generalized PT-symmetric system. This is achieved by transforming the high-gain metasurface into a bulky slab and then realizing it utilizing zero-index materials doped with low-gain dopants. Within this generalized PT-symmetric system, the required gain tangent of the dopants is only ∼10−1 for the emergence of a coalesced exceptional point, where the remarkable property of electromagnetic impurity-immunity effect—perfect wave transmission regardless of impurities—appears. Furthermore, we observe a further decrease in demand for gain materials in an asymmetric environment. To validate this approach, a microwave implementation is demonstrated in full-wave simulations. This work provides a feasible strategy for substantially reducing requirements on gain materials in PT-symmetric systems, thereby enabling advanced electromagnetic wave control.

Time-variant parity-time symmetry in frequency-scanning systems.

Parity-time (PT) symmetry is an active research area that provides a variety of new opportunities for different systems with novel functionalities. For instance, PT symmetry has been used in lasers and optoelectronic oscillators to achieve single-frequency lasing or oscillation. A single-frequency system is essentially a static PT-symmetric system, whose frequency is time-invariant. Here we investigate time-variant PT symmetry in frequency-scanning systems. Time-variant PT symmetry equations and eigenfrequencies for frequency-scanning systems are developed. We show that time-variant PT symmetry can dynamically narrow the instantaneous linewidth of frequency-scanning systems. The instantaneous linewidth of a produced frequency-modulated continuous-wave (FMCW) waveform is narrowed by a factor of 14 in the experiment. De-chirping and radar imaging results also show that the time-variant PT-symmetric system outperforms a conventional frequency-scanning one. Our study paves the way for a new class of time-variant PT-symmetric systems and shows great promise for applications including FMCW radar and lidar systems.

Switchable Dual-Wavelength Fiber Laser with Narrow-Linewidth Output Based on Parity-Time Symmetry System and the Cascaded FBG

In this paper, a dual-wavelength narrow-linewidth fiber laser based on parity-time (PT) symmetry theory is proposed and experimentally demonstrated. The PT-symmetric filter system consists of two optical couplers (OCs), four polarization controllers (PCs), a polarization beam splitter (PBS), and cascaded fiber Bragg gratings (FBGs), enabling stable switchable dual-wavelength output and single longitudinal-mode (SLM) operation. The realization of single-frequency oscillation requires precise tuning of the PCs to match gain, loss, and coupling coefficients to ensure that the PT-broken phase occurs. During single-wavelength operation at 1548.71 nm (λ1) over a 60-min period, power and wavelength fluctuations were observed to be 0.94 dB and 0.01 nm, respectively, while for the other wavelength at 1550.91 nm (λ2), fluctuations were measured at 0.76 dB and 0.01 nm. The linewidths of each wavelength were 1.01 kHz and 0.89 kHz, with a relative intensity noise (RIN) lower than −117 dB/Hz. Under dual-wavelength operation, the maximum wavelength fluctuations for λ1 and λ2 were 0.03 nm and 0.01 nm, respectively, with maximum power fluctuations of 3.23 dB and 2.38 dB. The SLM laser source is suitable for applications in long-distance fiber-optic sensing and coherent LiDAR detection.

Defected photonic crystal as propylene glycol THz sensor using parity-time symmetry

Detecting unsafe levels of chemical gases and vapors is essential in improving and maintaining a healthy environment for all to enjoy. Propylene glycol is a colorless, synthetic gas commonly used in medications, fragrances, and cosmetics. It causes side effects such as headaches, lightheadedness, nausea, and fainting. So, monitoring of propylene glycol is critically vital. This study uses a defected photonic crystal as a propylene glycol THz sensor. Due to the high absorption of propylene glycol, the intensity of the resonant confined mode is very small. As a result, the performance of the designed sensor seems unsatisfactory. We will use parity-time symmetry for the first time in THz to magnify the resonant confined mode to detect propylene glycol. The effect of microcavity thickness, incident angle, and gain/loss factor will be studied. The optimized sensor recorded distinguished results compared to other studies for the detection of propylene glycol.

ANALYTICAL SOLUTIONS OF THE NONLOCAL NONLINEAR SCHRÖDINGER-TYPE EQUATIONS

In physics, nonlinear equations are applіed to characterize the varied phenomena. Usually, the nonlinear equations are presented by nonlinear partial differential equations, that can be received as conditions for the compatibility of two linear differentіal equations, named the Lax pairs. The presence of the Lax pair determines integrability for the nonlinear partial differentіal equation. Linked to this development was the realization that certаіn coherent structures, known as solіtons, which play a fundamental role in nonlinear phenomena as lattice dynamics, nonlinear optіcs, and fluіd mechanics. One of the famous equations is the nonlinear Schrödinger equation which is associated with various physical phenomena in nonlinear optics and Bose-Einstein condensates. This equation allows the Lax pair thus it is integrable. This work investigates nonlocal nonlinear Schrödinger-type equations with PT symmetry. Nonlocal nonlinear equations arise in various physical contexts as fluid dynamics, condensed matter physics, optics, and so on. We introduce the Lax pair formulation for the nonlocal nonlinear Schrödinger-type equations. The method of the Darboux transformation is applied to receive analytical solutions.

Effect of parity–time symmetry operation on entanglement distribution in two parallel Heisenberg spin chains

Abstract The effect of the parity–time ( PT ) symmetry operation on the entanglement transfer in two parallel Heisenberg spin chains is investigated. We give two schemes, i.e. pre- and post- PT symmetric operations, to demonstrate the performance of the PT symmetric operation on the entanglement dynamics of two qubits. In our investigation, we find that the effect of pre- PT symmetric operation schemes on the protection of entanglement of two qubits in the case of double spin chains is superior to that of the single spin chain case. Conversely, the effect of the post- PT symmetric operation scheme on the protection of entanglement of two qubits in the single spin chain case is better than that in the double spin chain case.

Percolation-Induced PT Symmetry Breaking.

We propose a new avenue in which percolation, which has been much associated with critical phase transitions, can also dictate the asymptotic dynamics of non-Hermitian systems by breaking PT symmetry. Central to it is our newly designed mechanism of topologically guided gain, where chiral edge wave packets in a topological system experience non-Hermitian gain or loss based on how they are topologically steered. For sufficiently wide topological islands, this leads to irreversible growth due to positive feedback from interlayer tunneling. As such, a percolation transition that merges small topological islands into larger ones also drives the edge spectrum across a real to complex transition. Our discovery showcases intriguing dynamical consequences from the triple interplay of chiral topology, directed gain, and interlayer tunneling, and suggests new routes for the topology to be harnessed in the control of feedback systems.

Nonreciprocal transmission in silicon micromechanical resonators via parity-time symmetry breaking

Nonreciprocal transmission in silicon micromechanical resonators via parity-time symmetry breaking

PT Symmetry Breaking Induced Anomalous Valley Hall Effect in 2D Antiferromagnetic Semiconductor.

Realizing the anomalous valley Hall (AVH) effect in two-dimensional (2D) materials is of crucial importance for information processing and recording technology. While the research in this field mainly focuses on ferromagnetic systems, little is known about antiferromagnetic systems. Here, using k·p model analysis, we report a novel mechanism of realizing the AVH effect in 2D antiferromagnetic materials. This physics is related to the PT symmetry breaking induced by intrinsic staggered sublattice potential, which is introduced by asymmetric magnetic ions located at different sublattices. With reversal of the magnetic orientation on different sublattices, the AVH effect can be reversed. Based on first-principles calculations, we further demonstrate this mechanism in an antiferromagnetic monolayer of NiRuCl6. Intriguingly, due to the d orbital mismatch near the Fermi level, monolayer NiRuCl6 simultaneously owns zero net magnetization and large spin splitting and valley polarizations, which facilitates the observation of the AVH effect. Our findings greatly enrich the research on valley physics in antiferromagnetic systems.

Angular excitation of exceptional points and pseudospetra of photonic lattices

Abstract Optical parity-time ( PT ) symmetry has triggered a plethora of theoretical and experimental studies, and as a result non-Hermitian photonics is one of the frontiers of optics today. From unidirectional invisibility and coherent perfect absorbers to wireless power transfer and ultrasensitive sensors, non-hermiticity led to numerous important applications that rely on gain-loss synthetic structures. In particular, one such structure is that of complex photonic lattices that may exhibit exceptional points (EPs) around which the corresponding sensitivity is increased by orders of magnitude. Here, we investigate a new multiparametric family of non-Hermitian lattices that respects PT -symmetry, and examine their spectral sensitivity in terms of pseudospectra, as well, the angular excitation of the underlying EPs.

Storing light near an exceptional point

Photons with zero rest mass are impossible to be stopped. However, a pulse of light can be slowed down and even halted through strong light-matter interaction in a dispersive medium in atomic systems. Exceptional point (EP), a non-Hermitian singularity point, can introduce an abrupt transition in dispersion. Here we experimentally observe room-temperature storing light near an exceptional point induced by nonlinear Brillouin scattering in a chip-scale 90-μm-radius optical microcavity, the smallest platform up to date to store light. Through nonlinear coupling, a Parity-Time (PT) symmetry can be constructed in optical-acoustical hybrid modes, where Brillouin scattering-induced absorption (BSIA) can lead to both slow light and fast light of incoming pulses. A subtle transition of slow-to-fast light reveals a critical point for storing a light pulse up to half a millisecond. This compact and room-temperature scheme of storing light paves the way for practical applications in all-optical communications and quantum information processing.

𝒫𝒯 and anti-𝒫𝒯 symmetries for astrophysical waves

Context. Discrete symmetries have found numerous applications in photonics and quantum mechanics, but remain little studied in fluid mechanics, particularly in astrophysics. Aims. We aim to show how 𝒫𝒯 and anti-𝒫𝒯 symmetries determine the behaviour of linear perturbations in a wide class of astrophysical problems. They set the location of ‘exceptional points’ in the parameter space and the associated transitions to instability, and are associated with the conservation of quadratic quantities that can be determined explicitly. Methods. We study several classical local problems: the gravitational instability of isothermal spheres and thin discs, the Schwarzschild instability, the Rayleigh-Bénard instability and acoustic waves in dust–gas mixtures. We calculate the locations and the order of the exceptional points using the resultant of two univariate polynomials, as well as the conserved quantities in the different regions of the parameter space using Krein theory. Results. All problems studied here exhibit discrete symmetries, even though Hermiticity is broken by different physical processes (self-gravity, buoyancy, diffusion, and drag). This analysis provides genuine explanations for certain instabilities, and for the existence of regions in the parameter space where waves do not propagate. Those two aspects correspond to regions where 𝒫𝒯 and anti-𝒫𝒯 symmetries are broken respectively. Not all instabilities are associated to symmetry breaking (e.g. the Rayleigh-Benard instability).

Ginzburg-Landau description for multicritical Yang-Lee models

We revisit and extend Fisher’s argument for a Ginzburg-Landau description of multicritical Yang-Lee models in terms of a single boson Lagrangian with potential φ2(iφ)n. We explicitly study the cases of n = 1, 2 by a Truncated Hamiltonian Approach based on the free massive boson perturbed by PT symmetric deformations, providing clear evidence of the spontaneous breaking of PT symmetry. For n = 1, the symmetric and the broken phases are separated by the critical point corresponding to the minimal model M25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M}\\left(2,5\\right) $$\\end{document}, while for n = 2, they are separated by a critical manifold corresponding to the minimal model M25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M}\\left(2,5\\right) $$\\end{document} with M27\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{M}\\left(2,7\\right) $$\\end{document} on its boundary. Our numerical analysis strongly supports our Ginzburg-Landau descriptions for multicritical Yang-Lee models.

Edge-wave phase shifts versus normal-mode phase tilts in an Eady problem with a sloping boundary

One mechanistic interpretation of baroclinic instability is that of mutual constructive interference of Rossby edge waves. The suppression of baroclinic instability over slopes has been widely established, where previous research argues that a sloping boundary modifies the properties of these Rossby edge waves, but does not provide a mechanistic explanation for the suppression that is valid over all parameter space. In the context of an Eady problem modified by the presence of a sloping boundary, we provide a mechanistic rationalization for baroclinic instability in the presence of slopes that is valid over all parameter space, via an equivalent formulation explicitly in terms of Rossby edge waves. We also highlight the differences between edge-wave phase shifts and normal-mode phase tilts, showing that the edge-wave phase shifts should be the ones that are mechanistically relevant, and normal-mode phase tilt is a potentially misleading quantity to use. Further, we present evidence that the edge-wave phase shifts but not normal-mode phase tilts are well correlated with geometric quantities diagnosed from an analysis framework based on eddy variance ellipses. The result is noteworthy in that the geometric framework makes no explicit reference to the edge-wave structures in its construction, and the correlation suggests the geometric framework can be used in problems where edge-wave structures are not so well defined or readily available. Some implications for parametrization of baroclinic instability and relevant eddy-mean feedbacks are discussed. For completeness, we also provide an explicit demonstration that the linear instability problem of the present modified Eady problem is parity-time symmetric, and speculate about some suggestive links between parity-time symmetry, shear instability, and the edge-wave interaction mechanism. Published by the American Physical Society 2024

Polariton-polariton interaction induced by the hopping effect between two monolayers

Investigating the quantum many-body interaction in microcavity semiconductor systems is a significant objective in current research. Hence, in this study, Green’s function was employed to investigate the hopping effect between two monolayers denoted as L and R. The interaction between excitons in L monolayer and R monolayer, characterized by spin-like properties, leads to the generation of Josephson currents and emergence of two quasiparticle branches, known as LP+ and LP− polaritons (i.e., two low polariton states). And compared with other papers, such as reference 5, the research shows that presence of hopping interaction and many-body interaction between monolayers causes significant enhancement phenomenon of residue Z, which will further reduce the effective mass. This is more conducive to Bose–Einstein condensates (BEC). Furthermore, we investigated the Parity-Time symmetry (PT symmetry) of the system. The PT broken phase transition point will appear when the condition of PT symmetry is satisfied.