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The response of a ternary, parity–time-symmetric system that exhibits a third-order exceptional point increases as a function of the cube-root of induced perturbations. Exceptional points, exceptional optics Recent insights into open (non-Hermitian) physical systems have led to a new range of optical systems in which, counter-intuitively, loss is introduced. By careful tuning of loss and gain, certain degeneracies called 'exceptional points' emerge, which have intriguing properties that can be harnessed, for example, in new types of lasers, one-way optical waveguides and topological effects. Two papers in this issue demonstrate the high sensitivity of such non-Hermitian degeneracies to external perturbations, which can be used for precision sensing and detection. Weijian Chen et al . report sensing of nanoparticles with exceptional points generated in a silicon dioxide micro-toroid resonator. Hossein Hodaei et al . generated a higher-order exceptional point by coupling three micro-rings made from a semiconductor laser material. This third-order exceptional point has an even higher, cube-root (rather than square-root) dependence on perturbations. The two papers together provide a new route to ultraprecise chip-based sensing systems. Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the environment. They correspond to points in parameter space at which the eigenvalues of the underlying system and the corresponding eigenvectors simultaneously coalesce 1 , 2 , 3 . In optics, the abrupt nature of the phase transitions that are encountered around exceptional points has been shown to lead to many intriguing phenomena, such as loss-induced transparency 4 , unidirectional invisibility 5 , 6 , band merging 7 , 8 , topological chirality 9 , 10 and laser mode selectivity 11 , 12 . Recently, it has been shown that the bifurcation properties of second-order non-Hermitian degeneracies can provide a means of enhancing the sensitivity (frequency shifts) of resonant optical structures to external perturbations 13 . Of particular interest is the use of even higher-order exceptional points (greater than second order), which in principle could further amplify the effect of perturbations, leading to even greater sensitivity. Although a growing number of theoretical studies have been devoted to such higher-order degeneracies 14 , 15 , 16 , their experimental demonstration in the optical domain has so far remained elusive. Here we report the observation of higher-order exceptional points in a coupled cavity arrangement—specifically, a ternary, parity–time-symmetric photonic laser molecule—with a carefully tailored gain–loss distribution. We study the system in the spectral domain and find that the frequency response associated with this system follows a cube-root dependence on induced perturbations in the refractive index. Our work paves the way for utilizing non-Hermitian degeneracies in fields including photonics, optomechanics 10 , microwaves 9 and atomic physics 17 , 18 .

Non-Hermitian (NH) photonic systems leverage gain and loss to open new directions for nanophotonic technologies. However, the quantum and thermal noise intrinsically associated with gain/loss affects the eigenvalue/eigenvector structure of NH systems, and thus the existence of exceptional points, as well as the practical noise performance of these systems. Here, we present a comparative analysis of the impact of different gain and loss mechanisms on the noise generated in gain–loss compensated NH waveguide systems. Our results highlight important differences in the eigenvalue/eigenvector structure, noise power, photon statistics and squeezing. At the same time, we identify some universal properties such as the occurrence of phase-transition points in parameter space and intriguing phenomena related to them, including coalescence of pairs of eigenvectors, gain–loss compensation, and linear scaling of the noise with the length of the waveguide. We believe that these results contribute to a better understanding of the impact of the gain/loss mechanism on the noise generated in NH systems.

Manipulating topological invariants is possible by modifying the global properties of optical devices to alter their band structures. This could be achieved by statically altering devices or dynamically reconfiguring devices with considerably different geometric parameters, even though it inhibits switching speed. Recently, optical nonlinearity has emerged as a tool for tailoring topological and non-Hermitian (NH) properties, promising fast manipulation of topological phases. In this work, we observe topologically protected NH phase transitions driven by optical nonlinearity in a silicon nanophotonic Floquet topological insulator. The phase transition occurs from forbidden bandgaps to NH conducting edge modes, which emerge at a nonlinearity-induced gain–loss junction along the boundaries of a topological insulator. We find static NH edge modes and dynamic phase transitions involving exceptional points at a speed of hundreds of picoseconds, which inherently retain topological protections against fabrication imperfections. This work shows an interplay between topology and non-Hermiticity by means of nonlinear optics, and it provides a way of manipulating multiple phase transitions at high speeds that is applicable to many other materials with strong nonlinearities, which could promote the development of unconventionally robust light-controlled devices for classical and quantum applications. The phase transition from a topologically trivial state to non-Hermitian conducting edge modes can be controlled by optical nonlinearities, achieving picosecond switching speeds.

Parity-time (PT) symmetry has been unveiling new photonic regimes in non-Hermitian systems, with opportunities for lasing, sensing and enhanced light-matter interactions. The most exotic responses emerge at the exceptional point (EP) and in the broken PT-symmetry phase, yet in conventional PT-symmetric systems these regimes require large levels of gain and loss, posing remarkable challenges in practical settings. Floquet PT-symmetry, which may be realized by periodically flipping the effective gain/loss distribution in time, can relax these requirements and tailor the EP and PT-symmetry phases through the modulation period. Here, we explore Floquet PT-symmetry in an integrated photonic waveguide platform, in which the role of time is replaced by the propagation direction. We experimentally demonstrate spontaneous PT-symmetry breaking at small gain/loss levels and efficient control of amplification and suppression through the excitation ports. Our work introduces the advantages of Floquet PT-symmetry in a practical integrated photonic setting, enabling a powerful platform to observe PT-symmetric phenomena and leverage their extreme features, with applications in nanophotonics, coherent control of nanoscale light amplification and routing. Here the authors unveil an approach rooted in non-Hermitian physics to precisely control light amplification in an integrated photonic platform, paving the way for innovative on-chip functionalities, like coherent control of light amplification and routing.

Recent studies on exceptional points (EPs) in non-Hermitian optical systems have revealed unique traits, including unidirectional invisibility, chiral mode switching and laser self-termination. In systems featuring gain/loss components, EPs are commonly accessed below the lasing threshold, i.e., in the linear regime. In this work, we experimentally demonstrate that EP singularities in coupled semiconductor nanolasers can be accessed above the lasing threshold, where they become branch points of a nonlinear dynamical system. Contrary to the common belief that unavoidable cavity detuning impedes the formation of EPs, here we demonstrate that such detuning is necessary for compensating the carrier-induced frequency shift, hence restoring the EP. Furthermore, we find that the pump imbalance at lasing EPs varies with the total pump power, enabling their continuous tracking. This work uncovers the unstable nature of EPs above laser threshold in coupled semiconductor lasers, offering promising opportunities for the realization of self-pulsing nanolaser devices and frequency combs. The authors report on the experimental observation and characterization of exceptional points above the lasing threshold in photonic crystal nanocavities.

In this paper, a generalized nonlinear Schrödinger equation with variable coefficients is investigated. According to the analytic soliton solutions, the dromion-like structures between soliton interactions are revealed, and interaction properties are discussed. By changing the values of gain/loss, group velocity dispersion and self-phase modulation parameters, influences of them on interaction intensity and phase of solitons are presented. Besides, methods of controlling the path and spacing of solitons are suggested. Results of this paper may be potential valuable to the study of soliton interactions in inhomogeneous optical fibers and have applications in all-optical switches.

In this work, we investigated the temporal evolution of optical power in the Ikeda Map with Balanced Gain and Loss. The system comprises two feedback loops which interact with each other via a 50:50 directional coupler. The attenuation and amplification are distributed equally in the feedback loops in the configuration. From the bifurcation diagram, it could be inferred that the system exhibits the period-doubling cascade to chaos as a function of the gain/loss parameter. In the chaotic regime, we have found that a static input signal leads to the emergence of chaotic dynamics in the system. But if the input signal is superimposed with Gaussian noise, then the temporal dynamics in the system could be transformed from chaotic to noisy periodic. Furthermore, considering a total of 25 instances, we evaluated the probability of chaos control in the system.

ContextsTo quantify ecosystem service (ES) changes caused by the dynamic of green vegetation (GV) during rapid urbanization, it is necessary to fully understand the ‘real’ conversion pattern of GV, yet key and ‘real’ conversion patterns within specific periods and contributions to GV quality remain poorly understood.ObjectivesWe use normalized difference vegetation index (NDVI) as a mediator to represent GV quality. Land cover transfer matrix (LCTM) and urban greenspace dynamic index (UGDI) were employed to fully understand GV dynamic from quantity-quality and gain-loss perspectives. The Pearl River Delta Metropolitan Region (PRDMR), one of the fastest urbanizing regions in the world, was selected as a case.ResultsFrom 1990 to 2015, built-up land, forests and grasslands has the most dynamic conversion, and also has the most significant impact on NDVI. The NDVI value of the newly-built forest (0.29) was much lower than that of the lost forest (0.5), which demonstrate the value and importance of existing natural forest ecosystem, as newly-built forest does not provide the same ESs (although newly-built forest generally has stronger carbon sequestration ability). Hence, we reconfirm and suggest that in regional ecological planning and management, in addition to creating new, higher quality GV, it is essential to protect existing natural forest ecosystems.ConclusionThe study proposed new and full perspectives, including quantity-quality and gain-loss angle of view, enhance the understanding of GV dynamic and can be used in other related analyses. Results also provide important theoretical bases for regional ecological planning and natural forest ecosystem protection.

Recent evidence have indicated that ferroptosis, a novel iron-dependent form of non-apoptotic cell death, plays a critical role in human cancers. Besides, emerging literatures have revealed the ovel function of N6-methyladenosine (m6A) in bladder cancer physiological. However, the underlying mechanism of m6A on bladder cancer is still unclear. Here, present work revealed that m6A methyltransferase (‘writer’) WTAP up-regulated in bladder cancer tissue and cells, indicating the poor prognosis of bladder cancer patients. Functionally, gain/loss-of-functional experiments illustrated that WTAP promoted the viability of bladder cancer cells and inhibited the erastin-induced ferroptosis. Mechanistically, there was a remarkable m6A modification site on 3’-UTR of endogenous antioxidant factor NRF2 RNA and WTAP could install its methylation. Moreover, m6A reader YTHDF1 recognized the m6A site on NRF2 mRNA and enhanced its mRNA stability. Therefore, these findings demonstrated potential therapeutic strategyies for bladder cancer via m6A-dependent manner.