PT-symmetry Breaking Research Articles

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.

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.

PT -symmetry-enabled stable modes in a multicore fiber

Open systems with balanced gain and loss, described by parity-time (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. Published by the American Physical Society 2024

Observation of parity-time symmetry in diffusive systems.

Phase modulation has scarcely been mentioned in diffusive physical systems because the diffusion process does not carry the momentum like waves. Recently, non-Hermitian physics provides a unique perspective for understanding diffusion and shows prospects in thermal phase regulation, exemplified by the discovery of anti-parity-time (APT) symmetry in diffusive systems. However, precise control of thermal phase remains elusive hitherto and can hardly be realized, due to the phase oscillations. Here we construct the PT-symmetric diffusive systems to achieve the complete suppression of thermal phase oscillation. The real coupling of diffusive fields is readily established through a strong convective background, and the decay-rate detuning is enabled by thermal metamaterial design. We observe the phase transition of PT symmetry breaking with the symmetry-determined amplitude and phase regulation of coupled temperature fields. Our work shows the existence of PT symmetry in dissipative energy exchanges and provides unique approaches for harnessing the mass transfer of particles, wave dynamics in strongly scattering systems, and thermal conduction.

Probing PT-Symmetry Breaking of Non-Hermitian Topological Photonic States via Strong Photon-Magnon Coupling.

Light-matter interaction is crucial to both understanding fundamental phenomena and developing versatile applications. Strong coupling, robustness, and controllability are the three most important aspects in realizing light-matter interactions. Topological and non-Hermitian photonics have provided frameworks for robustness and control flexibility, respectively. How to engineer the properties of the edge state such as photonic density of state by using non-Hermiticity while ensuring topological protection has not been fully studied. Here we construct a parity-time-symmetric dimerized photonic lattice and probe the spontaneous PT-symmetry breaking of the edge states by utilizing the strong coupling between the photonic mode and a spin ensemble. Our Letter presents an accurate and almost noninvasive approach for investigating non-Hermitian topological states, while also offering methodologies for the implementation and manipulation of topological light-matter interactions.

From digital to quantum epidemiology: The Quantum Data Lake concept for big data related to viral infectious diseases

The development of quantum epidemiology represents the next anticipated phase in epidemiology transformation, driven by the emergence of new quantum technologies. Epidemiology is currently transitioning into the digital era and undergoing a paradigm shift from a data-driven to a value-driven strategy. Epidemiology data are characterized by uncertainty, multidimensionality, and disconnection, thereby correlating with the preferential quantum approach for data exposition, value creation, and modeling. Examples of such complex epidemiology data include the data on DNA viruses with associated symptoms and diseases. The Quantum Data Lake concept is proposed and consists of several layers and quantum tools, including Robson semantic triples, Quantum Universal Exchange Language, Hyperbolic Dirac Net, “quantum ribosome” structure, quantum random access memory, teleportation, Quantum Query Language, non-Hermitian gates, and tensor networks (e.g., matrix product state, projected entangled pair state, and multiscale entanglement renormalization ansatz [MERA]), alongside PT-symmetry properties. PT-symmetry can serve as an intuitive modeling tool, and PT-symmetry breaking can detect the hidden shift in the information that is permanently updated in the Data Lake. The computational output is presented as PT-symmetry gain/loss equilibrium breaking in the form of a complex number, i.e., two possible variants of epidemic modeling. For MERA, non-Hermiticity with spontaneous PT-symmetry breaking can theoretically appear as a violation of the entanglement monotonicity and local entanglement gain, leading to a non-reversible character of the coarse-graining transformation. The duality of PT-symmetry equilibrium breaking can be compared to, for example, the estimation of the best and worst scenarios simultaneously, or the gain of entanglement can display a significant correlation between some studied parameters embedded into the data. The fundamental difference between digital and quantum epidemiology is the implementation of quantum logic and reliance on a quantum theory.

Investigation of partial parity- time reversal symmetry in cesium atomic system

<sec>Parity-time reversal (PT) in atomic systems is of great significance for exploring exotic phenomena in non-Hermitian physics and non-Hermitian systems. It has been found that if PT symmetry is satisfied only in a certain spatial direction, then the Hamiltonian of the system still has a spectrum with eigenvalues of real numbers, which is called partial PT symmetry. In this paper, we use a Λ-type three-level atomic system, which is composed of two ground states <inline-formula><tex-math id="M6">\begin{document}$\left| {6{{\mathrm{S}}_{1/2}}, F = 3} \right\rangle $\end{document}</tex-math></inline-formula>,<inline-formula><tex-math id="M7">\begin{document}$\left| {6{{\mathrm{P}}_{3/2}}, F' = 4} \right\rangle $\end{document}</tex-math></inline-formula>and an excited state <inline-formula><tex-math id="M8">\begin{document}$\left| {6{{\mathrm{P}}_{3/2}}, F' = 4} \right\rangle $\end{document}</tex-math></inline-formula>of cesium atom, to investigate the partial PT symmetry. A probe laser with the detuning of <i>Δ</i><sub>3</sub> = 607 MHz and a couple laser satisfy the condition of two-photon Raman absorption of cesium atom, forming a loss channel. In order to construct the gain channel, we add the repumping laser that resonates during the transition of <inline-formula><tex-math id="M9">\begin{document}$\left| {6{{\mathrm{S}}_{1/2}}, F = 3} \right\rangle $\end{document}</tex-math></inline-formula>to <inline-formula><tex-math id="M10">\begin{document}$\left| {6{{\mathrm{P}}_{3/2}}, F' = 4} \right\rangle $\end{document}</tex-math></inline-formula>, changing the population of the two ground state energy levels, thus reducing the absorption of the Λ level system and forming the gain channel of the atomic system under certain conditions. In order to obtain the equilibrium condition of the partial PT-symmetric system, firstly, the light spot of the repumping laser in the experiment is covered by the probe laser, and then the repumping laser is moved to overlap with half of the probe laser of the detection light. When the gain and loss are balanced, the partial PT-symmetric system is in equilibrium.</sec><sec>By changing the beam-waist ratio <i>σ</i> of the coupling laser to the probe laser, the transition from symmetry to broken phase is observed in partial PT-symmetric systems. By measuring the asymmetry of the detection-beam intensity distribution <i>D</i><sub>asym</sub>, we can accurately determine the partial PT symmetry breaking point, and the breaking point is located at <inline-formula><tex-math id="M11">\begin{document}$\sigma = {\sigma _{cr}} \approx 3.8$\end{document}</tex-math></inline-formula>. The theoretical calculations are in good agreement with the experimental measurements. The results of partial PT symmetry and its phase transition, reported in this study, open up a way to actively manipulate multidimensional laser beams in non-Hermitian systems and have potential applications in the design of optical devices for laser amplification and attenuation in different parts of the laser.</sec>

Vorticity wave interaction, Krein collision, and exceptional points in shear flow instabilities.

We relate the model of vorticity wave interaction to Krein collision, PT-symmetry breaking, and the formation of exceptional points in shear flow instabilities. We show that the dynamical system of coupled vorticity waves is a pseudo-Hermitian system with nonreciprocal coupling terms. Krein signatures of the eigenvalues are illustrated as the signs of the action of the vorticity waves. Interaction between positive-action and negative-action vorticity waves then corresponds to the Krein collision between eigenvalues with opposite Krein signatures, the spontaneous breaking of PT symmetry, and the formation of exceptional points. The control parameter of the PT-symmetry-breaking bifurcation is the ratio between frequency detuning and coupling strength of the vorticity waves. The critical behavior near the exceptional points is described as a transition between phase-locking and phase-slip dynamics of the vorticity waves. The phase-slip dynamics correspond to nonmodal, transient growth of perturbations in the regime of unbroken PT symmetry, and the phase-slip frequency Ω∝|k-k_{c}|^{1/2} shares the same critical exponent with the phase rigidity of system eigenvectors.

Stationary states and switching dynamics of the self-defocusing nonlinear coupled system with PT-symmetric [formula omitted]-wavenumber Scarf II potential

The stationary states and switching dynamics of the parity-time (PT) symmetric coupled system with k-wavenumber Scarf II potential in the self-defocusing nonlinear regime have been analysed. The eigenmodes with central peaks are evolved in the linear regime, whereas those with central dips are evolved in the defocusing nonlinear regime, for ground, 2nd, and 4th excited states. The threshold condition of the PT-symmetry breaking and the effect of coupling, self-defocusing nonlinearity, and width of the potential on the high and low-frequency modes of the ground and excited states have been analysed. The stability of the eigenmodes is verified using the linear stability analysis. The power-switching dynamics between the gain and lossy channels of the system has been analysed. The input power-dependent switching and the effects of gain/loss and potential width on the switching are discussed.

Optical limiter based on PT-symmetry breaking of reflectionless modes

The application of parity–time (PT) symmetry in optics, especially PT-symmetry breaking, has attracted considerable attention as an approach to controlling light propagation. Here, we report optical limiting by two coupled optical cavities with a PT-symmetric spectrum of reflectionless modes. The optical limiting is related to broken PT symmetry due to light-induced changes in one of the cavities. Our experimental implementation involves a three-mirror resonator of alternating layers of ZnS and cryolite with a PT-symmetric spectral degeneracy of two reflectionless modes. The passive optical limiting is demonstrated by measurements of single 532 nm 6 ns laser pulses and thermo-optical simulations. At fluences below 10mJ/cm2, the multilayer exhibits a flattop passband at 532 nm. At higher fluences, laser heating combined with the thermo-optic effect in ZnS leads to cavity detuning and PT-symmetry breaking of the reflectionless modes. As a result, the entire multilayer structure quickly becomes highly reflective, protecting itself from laser-induced damage. The cavity detuning mechanism can differ at much higher limiting thresholds and include nonlinearity.

Anti-Parity-Time Symmetry in a Su-Schrieffer-Heeger Sonic Lattice.

The Su-Schrieffer-Heeger (SSH) model is an important cornerstone in modern condensed-matter topology, yet it is the simplest one-dimensional (1D) tight binding approach to dwell into the characteristics of spinless electrons in chains of staggered bonds. Moreover, the chiral symmetry assures that its surface-confining states pin to zero energy, i.e., they reside midgap in the energy dispersion. Symmetry is also an attribute related to artificial media that are subject to parity P and time-reversal T operations. This non-Hermitian family has been thoroughly nourished in a wave-based context, where anti-PT (APT) symmetric systems are the youngest belonging members, permitting refractionless optics, inverse PT-symmetry breaking transition, and asymmetric mode switching. Here, we report the first extension of APT symmetry in an acoustic setting by endowing a SSH lattice with gain and loss components. We show that the in-gap topological defect state hinges on the non-Hermitian phase, in that the broken symmetry suppresses it, yet when PT or APT symmetry is intact, it is observed with either damped or evanescent decay, respectively. Our experiments showcase how the non-Hermitian SSH lattice serves as a utile platform to investigate topological properties across various PT symmetric phases using sound.

A multifunctional layered photonic structure with NOR logical operation and multiscale detection based on the PT-symmetry breaking

In this paper, a multifunctional layered photonic structure (LPS) with NOR logical operation and multiscale detection based on the parity-time (PT) symmetry breaking composed of magnetized yttrium iron garnet (YIG) is proposed in theory. The accurate NOR logical operation is completed by properly modulating the target resonant absorption peak (AP) by the external magnetic field and using the peak to ascertain the logical operation. Given the high-quality factor of the resulting APs, the proposed structure can be used to detect four important physical quantities, which are angle, magnetic field, the thickness of ferrite1, and refractive index (RI). YIG is a typical representative of ferrite. Due to the magneto-optical effect, the PT-symmetry is broken, resulting in a nonreciprocal phenomenon, thereby further realizing NOR logic operation and multi-physical quantity detection on the front and rear scales. Since the RI of YIG is modulated by the magnetic field, the change of the magnetic field can cause the AP generated by the resonance to shift, so that the magnetic field can be detected.

Non-reciprocal transmission of coupled LC resonators through parity-time symmetry breaking

Non-reciprocal devices that allow a signal to be transmitted only in one direction are important for full-duplex communications. Due to the requirements of miniaturized systems, there has been an increase interest in non-magnetic non-reciprocal devices in recent years. Based on parity-time (PT) symmetric inductors-capacitors (LC) resonators, this paper has proposed non-reciprocal transmission configurations by PT-symmetry breaking. In the configuration, the coupled capacitance between the two coupled LC resonators can be adjusted so that the transmission frequency is tunable. At the same time, the resonant frequency and transmission frequency have been discriminated to optimize the non-reciprocal transmission. The configuration has been implemented by utilizing discrete components on a printed circuit board (PCB). It demonstrates that the center operation frequency of 14.05 MHz with the bandwidth 4 MHz, the insertion loss 0.32 dB, and the isolation 11 dB is adjusted to the center operation frequency of 14.95 MHz with the bandwidth 4.6 MHz, the insertion loss 0.716 dB, and the isolation 14.5 dB.

Volume-to-area law entanglement transition in a non-Hermitian free fermionic chain

We consider the dynamics of the non-Hermitian Su-Schrieffer-Heeger model arising as the no-click limit of a continuously monitored free fermion chain where particles and holes are measured on two sublattices. The model has \mathcal{PT}𝒫𝒯-symmetry, which we show to spontaneously break as a function of the strength of measurement backaction, resulting in a spectral transition where quasiparticles acquire a finite lifetime in patches of the Brillouin zone. We compute the entanglement entropy’s dynamics in the thermodynamic limit and demonstrate an entanglement transition between volume-law and area-law scaling, which we characterize analytically. Interestingly we show that the entanglement transition and the \mathcal{PT}𝒫𝒯-symmetry breaking do not coincide, the former occurring when the entire decay spectrum of the quasiparticle becomes gapped.

Organic Synthetic Photonic Systems with Reconfigurable Parity-Time Symmetry Breaking for Tunable Single-Mode Microlasers.

Synthetic photonic materials exploiting the quantum concept of parity-time (PT) symmetry lead to an emerging photonic paradigm-non-Hermitian photonics, which is revolutionizing the photonic sciences. The non-Hermitian photonics dealing with the interplay between gain and loss in PT synthetic photonic material systems offers a versatile platform for advancing microlaser technology. However, current PT-symmetric microcavity laser systems only manipulate imaginary parts of the refractive indices, suffering from limited laser spectral bandwidth. Here, an organic composite material system is proposed to synthesize reconfigurable PT-symmetric microcavities with controllable complex refractive indices for realizing tunable single-mode laser outputs. A grayscale electron-beam direct-writing technique is elaborately designed to process laser dye-doped polymer films in one single step into microdisk cavities with periodic gain and loss distribution, which enables thresholdless PT-symmetry breaking and single-mode laser operation. Furthermore, organic photoisomerizable compounds are introduced to reconfigure the PT-symmetric systems in real-time by tailoring the real refractive index of the polymer microresonators, allowing for a dynamically and continuously tunable single-mode laser output. This work fundamentally enhances the PT-symmetric photonic systems for innovative design of synthetic photonic materials and architectures.

Scaling laws of out-of-time-order correlators in a non-Hermitian kicked rotor model

We investigate the dynamics of the out-of-time-order correlators (OTOCs) via a non-Hermitian extension of the quantum kicked rotor model, where the kicking potential satisfies PT-symmetry. The spontaneous PT-symmetry breaking emerges when the strength of the imaginary part of the kicking potential exceeds a threshold value. We find, both analytically and numerically, that in the broken phase of PT symmetry, the OTOCs rapidly saturate with time evolution. Interestingly, the late-time saturation value scales as a pow-law in the system size. The mechanism of such scaling law results from the interplay between the effects of the nonlocal operator in OTOCs and the time reversal induced by non-Hermitian-driven potential.

Exceptional point in tunable terahertz metasurface based on bulk Dirac semimetal

In this study, we designed a tunable metasurface using bulk Dirac semimetal, whose periodic unit consisted of two orthogonally oriented split rings with identical dimensions in resonator mode, to observe and study exceptional points (EPs). By changing the Fermi level of the Dirac semimetal, the PT symmetry phase transitioned to the PT symmetry-breaking phase, which enabled the observation of an EP. The proposed method exploits the sensitivity of EPs to the perturbations in the system. The results calculated using the coupled mode theory were consistent with the results of simulations and have significant implications in polarization detection, manipulation, and ultrasensitive sensing.

Nonlinear twisted multicore fibers with PT-symmetry

We investigate linear and nonlinear modes of parity-time (PT)-symmetric multicore fibers with a twist of peripheral cores with gain and loss around the lossless central core. We determine the spectral properties of such a light guiding system and demonstrate that the presence of the lossless central core combined with the fiber twist may significantly change the supermode structure, as well as the PT-symmetry breaking threshold of the multicore fiber with gain and loss. We also construct stationary nonlinear modes of the fiber and verify their stability.

Band structure of the one-dimensional spin–orbit-coupled Su–Schrieffer–Heeger lattice with [formula omitted]-symmetric onsite imaginary potentials

Energy band structures of one-dimensional non-Hermitian spin–orbit-coupled Su–Schrieffer–Heeger (SSH) model are theoretically investigated, by introducing imaginary potentials with gain and loss effects. It is found that the imaginary potentials can promote the occurrence of PT-symmetry breaking. In the topologically-nontrivial regions, the different imaginary parts of the edge-state energies leads to the different localization degrees of such states. Moreover, gapless phase regions arise between the topologically-nontrivial and -trivial regions, in which edge states are allowed to survive. Therefore, these results are helpful to understand the band-structural and topological properties of PT-symmetric non-Hermitian systems.

Dynamics of 1D and 3D quantum droplets in parity-time-symmetric harmonic-Gaussian potentials with two competing nonlinearities

In this paper, we investigate stable quantum droplet (alias soliton) propagations in the one- and three-dimensional (1D and 3D) amended Gross–Pitaevskii equations (alias nonlinear Schrödinger equations) with two competing nonlinearities and PT-symmetric harmonic-Gaussian potentials. Especially, in the 1D case, we demonstrate that the PT potential can admit fully-real linear spectra in certain potential parameter region, with apparent PT symmetry breaking behaviors. And, the stabilities of exact and numerical solitons are investigated. It can be found that the stabilities of solitons depend on not only the gain-and-loss strength (the condensate norm) but also the chemical potential. Then the relationship between two competing nonlinearities is adjusted by changing the strength of nonlinearity. It is concluded that the Lee–Huang–Yang (LHY) correction plays an active role in droplet stabilization Furthermore, collisions between solitons with unequal norms are explored in the PT potential in detail, and there exist elastic collisions for certain parameters. And the strong LHY correction term will ensure the stable dynamical behaviors of the droplets. Finally, we explore the excitation initialized by density-modulation and find that some excited droplets can propagate like breathers. And the adiabatic excitations by changing the potential parameters and strength of the cubic nonlinearity are also discussed. These results will have the implication for understanding the relevant quantum droplet phenomena and designing the related experiments.