PT-symmetric Systems Research Articles

Parity–Time Symmetry in Bidirectionally Coupled Semiconductor Lasers

We report on the numerical analysis of intensity dynamics of a pair of mutually coupled, single-mode semiconductor lasers that are operated in a configuration that leads to features reminiscent of parity–time symmetry. Starting from the rate equations for the intracavity electric fields of the two lasers and the rate equations for carrier inversions, we show how these equations reduce to a simple 2 × 2 effective Hamiltonian that is identical to that of a typical parity–time (PT)-symmetric dimer. After establishing that a pair of coupled semiconductor lasers could be PT-symmetric, we solve the full set of rate equations and show that despite complicating factors like gain saturation and nonlinearities, the rate equation model predicts intensity dynamics that are akin to those in a PT-symmetric system. The article describes some of the advantages of using semiconductor lasers to realize a PT-symmetric system and concludes with some possible directions for future work on this system.

Photonic spin Hall effect in PT symmetric metamaterials

We proposed and demonstrated that PT symmetric metamaterials could be used to achieve enhanced spin Hall effect (SHE) of light. We find that when laser mode is excited in PT symmetric system, the enhanced SHE could be obtained in both transmitted and reflected beams. In addition, as exceptional points (EPs) of PT symmetric system can happen for both p- and s-polarizations, the enhanced SHE of reflected light can function for both horizontally and vertically polarized incident beams. Particularly, these EPs can lead to unidirectional reflectionlessness, asymmetric SHE with maximum contrast ratio of 48 is obtained by launching light beams near EPs. Our work opens up a new path to obtain enhanced transverse displacement for both reflected and transmitted light and enables more opportunities in manipulating photonic SHE.

Parity-time-symmetry-breaking gyroscopes: lasing without gain and subthreshold regimes.

We show that the lasing threshold for two coupled resonators (CRs) corresponds to lasing without gain (LWG), a phenomenon analogous to lasing without inversion in atomic systems, when parity-time (PT) symmetry is broken. The use of LWG for gyroscopes may resolve some of the difficulties associated with PT-symmetric gyroscopes. In particular, we find that PT-symmetric systems suffer from undamped Rabi oscillations, whereas LWG systems are overdamped. In addition, observation of enhanced sensitivity should be more straightforward in LWG gyros because the enhancement remains above unity even at couplings far from the exceptional point (EP). Finally, LWG gyros operate more like conventional laser gyroscopes with one frequency for each output direction, and therefore there is no ambiguity in the direction of rotation. Gain saturation in CR systems is found to dramatically boost the size of the sensitivity enhancement, eliminate the Rabi oscillations, and enlarge the parameter space around the EP over which the enhancement is expected to occur. A second situation with broken symmetry is also examined: CR systems below threshold. Whereas the pole in sensitivity coincides with the EP at threshold, the pole can occur far away from the EP for subthreshold systems. Our analysis also puts previous results on passive and active fast-light cavities using atomic vapor cells into the context of EP-enhanced sensing with non-Hermitian Hamiltonians.

Broadband and wide-angle invisibility with PT-symmetric 2D-Weyl semimetal

Inspired by the magnificent features of two-dimensional (2D) materials that aroused much of the interest in recent materials science research, we study PT-symmetric 2D-Weyl semimetal (WSM) to reveal the broadband and wide-angle invisible configurations in a PT-symmetric optical slab system. Desired unidirectional reflectionlessness and invisibility phenomena are obtained by the optimal control of system parameters. We unravel the mystery of broadband and wide-angle invisibility in regular slab materials with finite refractive indices by means of the plenary expressions. We show that materials whose refractive indices are relatively small (usually around η=1) give rise to quite a lot of broadband and wide-angle (almost all incidence angles) invisible configurations. This is not observed with any 2D material other than 2D WSMs. Our findings suggest concrete expedience to experimental realizations in this direction.

Noise figure of electromagnetic systems with parity and time-reversal symmetry.

The primary bottlenecks in designing and implementing PT-symmetric systems at microwave frequency ranges are noise and instability which can weakly break PT-symmetry resulting in system performance degradation. Practical implementation of such systems and devices require significant level of control and stability and it is crucial to analyze the noise performance of such systems in terms of noise figure and signal-to-noise ratio. We describe and develop a simulation model to calculate noise figure of PT-symmetric system and evaluate the performance degradation. We also discuss application design and circuit configurations that could reduce the noise figure resulting in better performance.

Dynamically encircling an exceptional point in anti-parity-time symmetric systems: asymmetric mode switching for symmetry-broken modes

Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes. The counterpart symmetry-broken modes (i.e., each eigenmode is localized in one waveguide only), which are more useful for applications such as on-chip optical signal processing, exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching. Here, we solve this problem by resorting to anti-parity-time (anti-PT) symmetric systems and utilizing their unique topological structure, which is very different from that of PT-symmetric systems. We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting point in the PT-broken phase results in chiral dynamics. As a result, symmetry-broken modes can be used for asymmetric mode switching, which is a phenomenon and application unique to anti-PT-symmetric systems. We perform experiments to demonstrate the new wave-manipulation scheme, which may pave the way towards designing on-chip optical systems with novel functionalities.

Observation of PT-symmetric quantum interference

Parity-Time (PT) symmetric quantum mechanics is a complex extension of conventional Hermitian quantum mechanics in which physical observables possess a real eigenvalue spectrum. However, an experimental demonstration of the true quantum nature of PT symmetry has been elusive thus far, as only single-particle physics has been exploited to date. In our work, we demonstrate two-particle quantum interference in a PT-symmetric system. We employ integrated photonic waveguides to reveal that PT-symmetric bunching of indistinguishable photons shows strongly counterintuitive features. We substantiate our experimental results by modelling the system by a quantum master equation, which we analytically solve using Lie algebra methods. Our work paves the way for nonlocal PT-symmetric quantum mechanics as a novel building block for future quantum devices.

Brief Review: Simulation of Novel Systems Using Duality Quantum Algorithm

In this article, we review the recent works of quantum simulation of novel systems briefly, the parity-time-reversal-symmetric (PT-symmetric) quantum system and the Yang-Baxter-equation (YBE) system, using duality quantum algorithm. Duality quantum algorithm studies the linear combinations of unitary operators, making it possible to simulate non-unitary evolutions of novel quantum systems. A PT-symmetric quantum system is a typical non-Hermitian system of which the evolution is not unitary and cannot be simulated directly by a conventional quantum computer. A recent work by C. Zheng has established a theory to simulate a general PT-symmetric two level system by duality quantum computing. The other typical example is the YBE quantum systems, of which the evolutions can be both unitary and non-unitary. C. Zheng and S. J. Wei described a theory that the two hand sides of the YBE can be simulated efficiently by the duality quantum algorithm in their recent research. Perspectives of future applications are expected at last. Copyright © VBRI Press.

Simulating Broken PT-Symmetric Hamiltonian Systems by Weak Measurement.

By embedding a PT-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between PT-symmetric quantum theory and weak measurement theory. We show that the weak measurement can give rise to the inner product structure of PT-symmetric systems, with the preselected state and its postselected state resident in the dilated conventional system. Typically in quantum information theory, by projecting out the irrelevant degrees and projecting onto the subspace, even local broken PT-symmetric Hamiltonian systems can be effectively simulated by this weak measurement paradigm.

Spectral singularity enhances transverse spin

We study the transverse spin and the Belinfante spin momentum in a gain–loss balanced waveguide, known to be one of the first and most studied examples of PT-symmetric systems. Such a guide supports the spectral singularities leading to infinite scattering amplitudes for both reflection and transmission. We show that near the spectral singularity there can be dramatic enhancement of the transverse spin and the transverse spin momentum. Note that these exotic spin and spin momentum have recently been observed experimentally despite having tiny magnitudes, making it worthy to explore ways and means to enhance these fundamentally important elusive quantities.

Quantum Behavior of a PT -Symmetric Two-Mode System with Cross-Kerr Nonlinearity

Quantum behavior of two oscillator modes, with mutually balanced gain and loss and coupled via linear coupling (including energy conserving as well as energy non-conserving terms) and nonlinear cross-Kerr effect, is investigated. Stationary states are found and their stability analysis is given. Exceptional points for PT -symmetric cases are identified. Quantum dynamics treated by the model of linear operator corrections to a classical solution reveals nonclassical properties of individual modes (squeezing) as well as their entanglement.

Eternal life of entropy in non-Hermitian quantum systems

We find a new effect for the behaviour of Von Neumann entropy. For this we derive the framework for describing Von Neumann entropy in non-Hermitian quantum systems and then apply it to a simple interacting PT symmetric bosonic system. We show that our model is well defined even in the PT broken regime with the introduction of a time-dependent metric and that it displays three distinct behaviours relating to the PT symmetry of the original time-independent Hamiltonian. When the symmetry is unbroken, the entropy undergoes rapid decay to zero (so-called "sudden death") with a subsequent revival. At the exceptional point it decays asymptotically to zero and when the symmetry is spontaneously broken it decays asymptotically to a finite constant value ("eternal life").

Nonlocal homogenization of PT -symmetric multilayered structures

Unique and highly tunable optical properties of PT-symmetric systems and metamaterials enable a plenty of entirely new linear and nonlinear optical phenomena with numerous applications, e.g., for designing subdiffraction lenses, nonreciprocal devices, etc. Therefore, the artificial media with the PT symmetry attract ever-increasing attention and are now a subject for intensive investigations. One of the commonly used methods providing information about the optical response of artificial nanostructural media is a so-called effective medium theory. Here we examine the possibility of utilizing the effective medium theory for a comprehensive analysis of PT-symmetric multilayered systems composed of alternating loss and gain slabs. We show that applicability of local effective material parameters (or Maxwell Garnett approximation) is very limited and cannot be exploited for a prediction of exceptional points marking a PT symmetry breaking. On the other hand, nonlocal bianisotropic effective medium parameters can be reliably used, if the thickness of a unit cell is much smaller than the radiation wavelength. In the case of obliquely incident plane waves, we reveal the limitation on the loss-gain coefficient, which should not be too large compared with the real part of the permittivity. We believe that our findings can improve the fundamental understanding of physics behind PT-symmetric systems and advance the development of auxiliary tools for analyzing their peculiar optical response.

Parity-time symmetry and exceptional points in photonics.

Exploiting the interplay between gain, loss and the coupling strength between different optical components creates a variety of new opportunities in photonics to generate, control and transmit light. Inspired by the discovery of real eigenfrequencies for non-Hermitian Hamiltonians obeying parity–time (PT) symmetry, many counterintuitive aspects are being explored, particularly close to the associated degeneracies also known as ‘exceptional points’. This Review explains the underlying physical principles and discusses the progress in the experimental investigation of PT-symmetric photonic systems. We highlight the role of PT symmetry and non-Hermitian dynamics for synthesizing and controlling the flow of light in optical structures and provide a roadmap for future studies and potential applications. This Review discusses recent developments in the area of non-Hermitian physics, and more specifically the special case of non-Hermitian optical systems with parity–time symmetry.

The broken condition and regulation of a non-conjugated PT symmetric waveguide system

In this paper, a modified method to analyze and regulate the broken condition of a general parity-time symmetric waveguide system with non-conjugated refractive index profile ( nr1-jni1 and nr2+jni2) is proposed. The broken condition can be regulated by altering the width of waveguide. For the general PT symmetric waveguide system, this method provides a simple design to reduce the requirement of gain medium. This finally makes it easier to design a waveguide system on the basis of a now available material and to achieve broken condition. The analysis of a non-conjugate refractive index double channel waveguides is carried out as an example, and the calculation error is less than 4% compared with the result of FDTD simulation.

Mechanical exceptional-point-induced transparency and slow light.

Recently, the conception of PT symmetry has attracted considerable attention in various fields such as optics, acoustics, and atomic physics because of the existence of exceptional point (EP) and its importance in understanding non-Hermitian physics. Here, we propose a new scheme of investigating the mechanical-EP-induced transparency and tunable fast-to-slow light phenomena in PT-symmetric mechanical systems. We find that (i) the transmission of the probe field changes from singleto double transparency windows via the transition from a broken mechanical PT-symmetric phase to an unbroken mechanical PT-symmetric phase; (ii) the efficiency of transparency can be significantly enhanced about three orders of magnitude in the vicinity of the mechanical EP, compared to passive mechanical resonators system; and (iii) the mechanical EP can not only amplify the group delay, but also manipulate the switch from slow light to fast light, which may offer an approach to achieve the practical application of slow light and relevant to the optical switcher and communication network. Our results reveal that the exotic properties of the mechanical EP can result in enormous enhancement of the transmitted probe power and novel steering of fast and slow light.

Restriction of the Fermion Mass Spectrum in PT-Symmetric Systems and its Implications For Studying Dark Matter

We formulate principal positions of a non-Hermitian model with a γ5-extension of the fermion mass, which are often neglected in investigating this subject. A consistent approach to this problem requires the constraint m ≤ M, where M bounds the entire fermion mass spectrum. An analogous approach was proposed in the geometric model, which can be regarded as the first PT-symmetric non-Hermitian fermion model with a γ5-extension of mass. Exotic particles appear in both these theories. A detailed consideration of the properties of these particles allows conjecturing that they are possible candidates in the structure of dark matter. We also discuss a simple estimate for determining the maximum admissible value of the fermion mass M.

Exceptional surfaces in PT-symmetric non-Hermitian photonic systems

Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional points or one-dimensional lines of exceptional points. Here, we substantially expand the space of exceptional systems by designing two-dimensional surfaces of exceptional points, and find that symmetries are a key element to protect such exceptional surfaces. We construct them using symmetry-preserving non-Hermitian deformations of topological nodal lines, and analyze the associated symmetry, topology, and physical consequences. As a potential realization, we simulate a parity-time-symmetric 3D photonic crystal and indeed find the emergence of exceptional surfaces. Our work paves the way for future explorations of systems of exceptional points in higher dimensions.

Microwave Tunneling and Robust Information Transfer Based on Parity-Time-Symmetric Absorber-Emitter Pairs.

Robust signal transfer in the form of electromagnetic waves is of fundamental importance in modern technology, yet its operation is often challenged by unwanted modifications of the channel connecting transmitter and receiver. Parity-time- (PT-) symmetric systems, combining active and passive elements in a balanced form, provide an interesting route in this context. Here, we demonstrate a PT-symmetric microwave system operating in the extreme case in which the channel is shorted through a small reactance, which acts as a nearly impenetrable obstacle, and it is therefore expected to induce large reflections and poor transmission. After placing a gain element behind the obstacle, and a balanced lossy element in front of it, we observe full restoration of information and overall transparency to an external observer, despite the presence of the obstacle. Our theory, simulations, and experiments unambiguously demonstrate stable and robust wave tunneling and information transfer supported by PT symmetry, opening opportunities for efficient communication through channels with dynamic changes, active filtering, and active metamaterial technology.

Research progress of hybrid cavity-magnon systems

近年来腔自旋波混合系统引起人们的研究兴趣. 基于自旋波体系的优点, 有望建立一个以自旋波量子为核心的、实现不同物理系统之间信息传递的平台. 本文简要介绍了腔自旋波混合系统的发展进程, 阐明自旋波量子与微波腔光子的耦合机制; 着重介绍了近期在腔自旋波混合系统中关于非线性和赝厄米性方面的研究进展, 其中包括非线性效应引起的腔自旋波量子极化激元的双稳, 宇称-时间(PT)对称哈密顿量的实现和PT对称自发破缺相变二阶奇点的观测, 以及如何构造非PT对称的赝厄米哈密顿量来实现三阶奇点等.