Physics Of Exceptional Points Research Articles

Electrically tunable topological phase transition in non-Hermitian optical MEMS metasurfaces.

Exceptional points (EPs), unique junctures in non-Hermitian open systems where eigenvalues and eigenstates simultaneously coalesce, have gained notable attention in photonics because of their enthralling physical principles and unique properties. Nonetheless, the experimental observation of EPs, particularly within the optical domain, has proven rather challenging because of the grueling demand for precise and comprehensive control over the parameter space, further compounded by the necessity for dynamic tunability. Here, we demonstrate the occurrence of optical EPs when operating with an electrically tunable non-Hermitian metasurface platform that synergizes chiral metasurfaces with piezoelectric MEMS mirrors. Moreover, we show that, with a carefully constructed metasurface, a voltage-controlled spectral space can be finely tuned to access not only the chiral EP but also the diabolic point characterized by degenerate eigenvalues and orthogonal eigenstates, thereby allowing for dynamic topological phase transition. Our work paves the way for developing cutting-edge optical devices rooted in EP physics and opening uncharted vistas in dynamic topological photonics.

Non-hermiticity in spintronics: oscillation death in coupled spintronic nano-oscillators through emerging exceptional points

The emergence of exceptional points (EPs) in the parameter space of a non-hermitian (2D) eigenvalue problem has long been interest in mathematical physics, however, only in the last decade entered the scope of experiments. In coupled systems, EPs give rise to unique physical phenomena, and enable the development of highly sensitive sensors. Here, we demonstrate at room temperature the emergence of EPs in coupled spintronic nanoscale oscillators and exploit the system’s non-hermiticity. We observe amplitude death of self-oscillations and other complex dynamics, and develop a linearized non-hermitian model of the coupled spintronic system, which describes the main experimental features. The room temperature operation, and CMOS compatibility of our spintronic nanoscale oscillators means that they are ready to be employed in a variety of applications, such as field, current or rotation sensors, radiofrequeny and wireless devices, and in dedicated neuromorphic computing hardware. Furthermore, their unique and versatile properties, notably their large nonlinear behavior, open up unprecedented perspectives in experiments as well as in theory on the physics of exceptional points expanding to strongly nonlinear systems.

Transient Loss-Induced Non-Hermitian Degeneracies for Ultrafast Terahertz Metadevices.

Non-Hermitian degeneracies, also known as exceptional points (EPs), have attracted considerable attention due to their unique physical properties. In particular, metasurfaces related to EPs can open the way to unprecedented devices with functionalities such as unidirectional transmission and ultra-sensitive sensing. Herein, an active non-Hermitian metasurface with a loss-induced parity-time symmetry phase transition for ultrafast terahertz metadevices is demonstrated. Specifically, the eigenvalues of the non-Hermitian transmission matrix undergo a phase transition under optical excitation and are degenerate at EPs in parameter space, which is accompanied by the collapse of chiral transmission. Ultrafast EP modulation on a picosecond time scale can be realized through variations in the transient loss at a non-Hermitian metasurface pumped by pulsed excitation. Furthermore, by exploiting the physical characteristics of chiral transmission EPs, a switchable quarter-wave plate based on the photoactive metasurface is designed and experimentally verified and realized the corresponding function of polarization manipulation. This work opens promising possibilities for designing functional terahertz metadevices and fuses EP physics with active metasurfaces.

Scattering exceptional point in the visible

Exceptional point (EP) is a special degeneracy of non-Hermitian systems. One-dimensional transmission systems operating at EPs are widely studied and applied to chiral conversion and sensing. Lately, two-dimensional systems at EPs have been exploited for their exotic scattering features, yet so far been limited to only the non-visible waveband. Here, we report a universal paradigm for achieving a high-efficiency EP in the visible by leveraging interlayer loss to accurately control the interplay between the lossy structure and scattering lightwaves. A bilayer framework is demonstrated to reflect back the incident light from the left side ( | r−1 | >0.999) and absorb the incident light from the right side ( | r+1 | < 10–4). As a proof of concept, a bilayer metasurface is demonstrated to reflect and absorb the incident light with experimental efficiencies of 88% and 85%, respectively, at 532 nm. Our results open the way for a new class of nanoscale devices and power up new opportunities for EP physics.

Chiral exceptional point and coherent suppression of backscattering in silicon microring with low loss Mie scatterer

Non-Hermitian systems with their spectral degeneracies known as exceptional points (EPs) have been explored for lasing, controlling light transport, and enhancing a sensor’s response. A ring resonator can be brought to an EP by controlling the coupling between its frequency degenerate clockwise and counterclockwise traveling modes. This has been typically achieved by introducing two or more nanotips into the resonator’s mode volume. While this method provides a route to study EP physics, the basic understanding of how the nanotips’ shape and size symmetry impact the system’s non-Hermicity is missing, along with additional loss from both in-plane and out-of-plane scattering. The limited resonance stability poses a challenge for leveraging EP effects for switches or modulators, which requires stable cavity resonance and fixed laser-cavity detuning. Here we use lithographically defined asymmetric and symmetric Mie scatterers, which enable subwavelength control of wave transmission and reflections without deflecting to additional radiation channels. We show that those pre-defined Mie scatterers can bring the system to an EP without post tuning, as well as enable chiral light transport within the resonator. Counterintuitively, the Mie scatterer results in enhanced quality factor measured on the transmission port, through coherently suppressing the backscattering from the waveguide surface roughness. The proposed device platform enables pre-defined chiral light propagation and backscattering-free resonances, needed for various applications such as frequency combs, solitons, sensing, and other nonlinear optical processes such as photon blockade, and regenerative oscillators.Graphical

On-chip single-photon chirality encircling exceptional points

Exceptional points (EPs), typically defined as the degeneracy points of a non-Hermitian Hamiltonian, have been investigated in various physical systems such as photonic systems. In particular, the intriguing topological structures around EPs have given rise to novel strategies for manipulating photons and the underlying mechanism is especially useful for on-chip photonic applications. Although some on-chip experiments using lasers have been reported, EP-based photonic chips working in the quantum regime have been largely elusive. Here, we propose a single-photon experiment to dynamically encircle an EP in on-chip photonic waveguides possessing passive anti-parity-time symmetry. Photon coincidences measurement reveals a chiral feature of transporting single photons, which can act as a building block for on-chip quantum devices that require asymmetric transmissions. Our findings pave the way for on-chip experimental study on the physics of EPs as well as inspiring applications for on-chip non-Hermitian quantum devices.

Precise Control of Single-Crystal Perovskite Nanolasers.

Efficient control of integrated light sources is crucial to advancing practical applications of nanophotonics. Despite the success of microlasers, their sophisticated nanostructures are not applicable in nanolasers. The situation for bottom-up-synthesized nanolasers becomes more challenging due to the constraints of fixed cavity shapes and fragile material stability. Here, the physics of exceptional points (EPs) is employed, and a strategy is demonstrated to precisely tune the lasing actions in lead halide perovskite nanorods. By placing a nanoparticle to the boundary of a square nanocavity, it is shown that EPs regularly and controllably emerge as a function of the nanoparticle position. Consequently, both the internal lasing actions and their far-field radiation can be completely reversed with a tiny displacement of <100nm. The new strategy for controlling lasing actions in nanocavities is confirmed with numerical simulations and lasing experiments. This research can also bring new avenues for ultrasensitive position sensing.

Non-Hermitian Sensing in Photonics and Electronics: A Review.

Recently, non-Hermitian Hamiltonians have gained a lot of interest, especially in optics and electronics. In particular, the existence of real eigenvalues of non-Hermitian systems has opened a wide set of possibilities, especially, but not only, for sensing applications, exploiting the physics of exceptional points. In particular, the square root dependence of the eigenvalue splitting on different design parameters, exhibited by 2 × 2 non-Hermitian Hamiltonian matrices at the exceptional point, paved the way to the integration of high-performance sensors. The square root dependence of the eigenfrequencies on the design parameters is the reason for a theoretically infinite sensitivity in the proximity of the exceptional point. Recently, higher-order exceptional points have demonstrated the possibility of achieving the nth root dependence of the eigenfrequency splitting on perturbations. However, the exceptional sensitivity to external parameters is, at the same time, the major drawback of non-Hermitian configurations, leading to the high influence of noise. In this review, the basic principles of PT-symmetric and anti-PT-symmetric Hamiltonians will be shown, both in photonics and in electronics. The influence of noise on non-Hermitian configurations will be investigated and the newest solutions to overcome these problems will be illustrated. Finally, an overview of the newest outstanding results in sensing applications of non-Hermitian photonics and electronics will be provided.

Response strengths of open systems at exceptional points

Open quantum and wave systems exhibit exotic degeneracies at exceptional points in parameter space that have attracted considerable attention in various fields of physics, including optics and photonics. One reason is the strong response of open systems at such degeneracies to external perturbations and excitations. We introduce two characteristics of exceptional points that quantify the response in terms of energy eigenvalues and eigenstates, intensity, and dynamics. The concept is verified for several physically relevant examples. This work provides a new perspective on the physics of exceptional points.

Exceptional points in lossy media lead to deep polynomial wave penetration with spatially uniform power loss.

Waves entering a spatially uniform lossy medium typically undergo exponential intensity decay, arising from either the energy loss of the Beer-Lambert-Bouguer transmission law or the evanescent penetration during reflection. Recently, exceptional point singularities in non-Hermitian systems have been linked to unconventional wave propagation. Here, we theoretically propose and experimentally demonstrate exponential decay free wave propagation in a purely lossy medium. We observe up to 400-wave deep polynomial wave propagation accompanied by a uniformly distributed energy loss across a nanostructured photonic slab waveguide with exceptional points. We use coupled-mode theory and fully vectorial electromagnetic simulations to predict deep wave penetration manifesting spatially constant radiation losses through the entire structured waveguide region regardless of its length. The uncovered exponential decay free wave phenomenon is universal and holds true across all domains supporting physical waves, finding immediate applications for generating large, uniform and surface-normal free-space plane waves directly from dispersion-engineered photonic chip surfaces.

Topological engineering of terahertz light using electrically tunable exceptional point singularities.

The topological structure associated with the branch point singularity around an exceptional point (EP) can provide tools for controlling the propagation of light. Through use of graphene-based devices, we demonstrate the emergence of EPs in an electrically controlled interaction between light and a collection of organic molecules in the terahertz regime at room temperature. We show that the intensity and phase of terahertz pulses can be controlled by a gate voltage, which drives the device across the EP. Our electrically tunable system allows reconstruction of the Riemann surface associated with the complex energy landscape and provides topological control of light by tuning the loss imbalance and frequency detuning of interacting modes. Our approach provides a platform for developing topological optoelectronics and studying the manifestations of EP physics in light-matter interactions.

Reverse-chiral response of two T -symmetric optical systems hosting conjugate exceptional points

Exceptional points (EPs) are a special kind of singularity that appear as topological defects in parameter-dependent open systems. Here we propose the concept of conjugate EPs, where a level-repulsion phenomenon between two coupled complex states can occur in the vicinity of a square-root branch point, which is analytically associated with the presence of two complex conjugate EPs. Depending on the iteration parameter, two corresponding levels are analytically connected via one of two conjugate EPs. Here, we report the hosting of two conjugate EPs in two complementary equivalent systems connected with time-reversal ($\mathcal{T}$) symmetry by using the framework of a gain-loss assisted dual-mode planar optical waveguide. We establish that if the complex potential of any system hosts an EP, then the $\mathcal{T}$-symmetric potential of the same system can host the associated conjugate EP. Owing to the EP-aided nonadiabatic population transfer based on device chirality, the reverse-chiral responses of two $\mathcal{T}$-symmetric devices have been explored in the context of an asymmetric-mode-conversion process. The proposed scheme has the potential to open up a credible platform to study the physics of EPs in $\mathcal{T}$-symmetric systems.

Exceptional points of all-dielectric nanoresonators

In the recent years, all-dielectric nanophotonics has been showing promising potential for biotechnology, with important progress in the development of efficient all-optical, all-dielectric nanosensing devices overcoming the ohmic losses inherently present in their plasmonic counterparts. In the quest to achieve single molecule sensitivities, a judicious design of the optical response of the nanoantennas is required. Here, we approach this problem from the perspective of non-Hermitian physics and investigate the interaction of two finite nanorods supporting Mie resonances, with the aim of maximizing the frequency detuning induced by a perturbation of the structure. We develop a simple semi-analytical technique to efficiently investigate the coupled system, and we find that Coulomb interactions, together with mutual interference induced by breaking the dimer symmetry, can effectively bring the structure towards a non-Hermitian singularity, an exceptional point, that can potentially increase the sensitivity. The results of this work are expected to lead to novel developments in all-optical single molecule detection, and merge for the first time all-dielectric nanophotonics with exceptional point physics.

Accessing the Exceptional Points in a Graphene Plasmon–Vibrational Mode Coupled System

The coupling of plasmons and vibrational modes has been routinely observed in graphene and other 2D systems in both near-field and far-field spectroscopy. However, the relation between coupling strength and modal losses, and exceptional point physics has not been discussed. Here we apply a non-Hermitian framework to a model system of molecular layers on graphene and show that the transition point between strong and weak coupling regimes coincides with the exceptional point of non-Hermitian physics. We further show that the exceptional point can be conveniently located by changing the incident angle of the light and the graphene Fermi energy. Finally, we show that enhanced spectral sensitivity is obtained from small changes in molecular film thickness when the system is tuned to the exceptional point.

Light Absorption in Nanowire Photonic Crystal Slabs and the Physics of Exceptional Points: The Shape Shifter Modes.

Semiconductor nanowire arrays have been demonstrated as promising candidates for nanoscale optoelectronics applications due to their high detectivity as well as tunable photoresponse and bandgap over a wide spectral range. In the infrared (IR), where these attributes are more difficult to obtain, nanowires will play a major role in developing practical devices for detection, imaging and energy harvesting. Due to their geometry and periodic nature, vertical nanowire and nanopillar devices naturally lend themselves to waveguide and photonic crystal mode engineering leading to multifunctional materials and devices. In this paper, we computationally develop theoretical basis to enable better understanding of the fundamental electromagnetics, modes and couplings that govern these structures. Tuning the photonic response of a nanowire array is contingent on manipulating electromagnetic power flow through the lossy nanowires, which requires an intimate knowledge of the photonic crystal modes responsible for the power flow. Prior published work on establishing the fundamental physical modes involved has been based either on the modes of individual nanowires or numerically computed modes of 2D photonic crystals. We show that a unified description of the array key electromagnetic modes and their behavior is obtainable by taking into account modal interactions that are governed by the physics of exceptional points. Such models that describe the underlying physics of the photoresponse of nanowire arrays will facilitate the design and optimization of ensembles with requisite performance. Since nanowire arrays represent photonic crystal slabs, the essence of our results is applicable to arbitrary lossy photonic crystals in any frequency range.

Exceptional Points in Flat Optics: A Non-Hermitian Line-Wave Scenario

Line waves are recently discovered wave entities that are localized along two directions, and therefore can be viewed as the one-dimensional counterpart of surface waves. These waves can be supported at discontinuities of the surface reactance and/or resistance of low-dimensional materials such as metasurfaces or graphene. Here, a broader class of non-Hermitian surface-impedance junctions is studied that can support coupled line waves, and allows investigating different one-dimensional waveguiding mechanisms in a unified framework. It is theoretically demonstrated that, under parity-time-symmetry conditions, exceptional points can occur in a truly flat-optics scenario, hence endowing these waveguiding systems with the attractive features of both line-wave and exceptional-point physics, and shedding further light on the phase transitions existing in these systems. It is also shown that the required surface-impedance parameters are compatible with those attainable with typical models of photoexcited graphene metasurfaces at terahertz frequencies. Besides providing additional understanding in the physics of line waves, which is still in its infancy, these results pave the way to intriguing developments in the largely unexplored field of non-Hermitian flat optics, with possible applications ranging from sensing to lasing and on-chip optical signal processing.

Non-Hermitian Kibble-Zurek Mechanism with Tunable Complexity in Single-Photon Interferometry

Non-Hermitian descriptions of quantum matter have seen impressive progress recently, with major advances in understanding central aspects such as their topological properties or the physics of exceptional points, the non-Hermitian counterpart of critical points. Here, we use single-photon interferometry to reconstruct the non-Hermitian Kibble-Zurek mechanism and its distinct scaling behavior for exceptional points, by simulating the defect production upon performing slow parameter ramps. Importantly, we are able to realise also higher-order exceptional points, providing experimental access to their theoretically predicted characteristic Kibble-Zurek scaling behaviour. Our work represents a crucial step in increasing the experimental complexity of non-Hermitian quantum time-evolution. It thus also furthers the quest to move the frontier from purely single-particle physics towards increasingly complex settings in the many-body realm.

Observation of topological bound states in a double Su-Schrieffer-Heeger chain composed of split ring resonators

The observation of abundant topological properties in optical platforms has attracted people's attention due to their great advantages in fundamental topological research and practical applications. Here, we use a double Su-Schrieffer-Heeger (SSH) chain structure composed of split ring resonators (SRRs) to mimic a Kitaev model. By properly tuning the orientation angles of the slits of the SRRs, we can ingeniously design the complex coupling distribution. We experimentally measure the topological phase transition of the double SSH model by adjusting the distance between the two chains and observe the topological bound states in the topological nontrivial phase. Importantly, inserting a trivial structure into the topological chain, we show the coupling of two topological bound states. By increasing the length of the inserted trivial chain, we observe that two topological bound states gradually approach each other and degenerate in the critical state. In addition, we theoretically study the controllable topological bound states and exceptional point physics formed by topological bound states. Our findings not only clearly show the establishing process of the photonic bound states in a double SSH chain, but also may facilitate some applications such as sensors, energy transfer, and switch with topological protection.5 MoreReceived 2 September 2020Revised 20 January 2021Accepted 25 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013122Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMetamaterialsTopological effects in photonic systemsTopological phases of matterAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Subharmonic Entrainment Breather Solitons in Ultrafast Lasers

We study theoretically and experimentally the subharmonic entrainment (SHE) breather soliton in mode-locked lasers for the first time, in which the ratio of the breather period to the round-trip time is an integer. We build a non-Hermitian degeneracy map of breather soliton, and illustrate that SHE arises between the two exceptional points (EPs). We obtain SHE at the ratio of 20, observe the evolution of breather soliton when tuning the gain and/or cavity loss, and prove that this phenomenon can improve the stability of breather soliton. Our research brings insight into the EP physics of ultrafast lasers and makes the mode-locked laser a powerful test bed for non-Hermitian degeneracy, which may open a new course in ultrafast laser research.

Chiral State Conversion in a Levitated Micromechanical Oscillator with In Situ Control of Parameter Loops*Supported by the Fundamental Research Funds for the Central Universities (Grant No. WK2030000032), the National Key R&D Program of China (Grant No. 2018YFA0306600), the CAS (Grant Nos. GJJSTD20170001 and QYZDY-SSW-SLH004), and Anhui Initiative in Quantum Information Technologies (Grant No. AHY050000).

Physical systems with gain and loss can be described by a non-Hermitian Hamiltonian, which is degenerated at the exceptional points (EPs). Many new and unexpected features have been explored in the non-Hermitian systems with a great deal of recent interest. One of the most fascinating features is that chiral state conversion appears when one EP is encircled dynamically. Here, we propose an easy-controllable levitated microparticle system that carries a pair of EPs and realize slow evolution of the Hamiltonian along loops in the parameter plane. Utilizing the controllable rotation angle, gain and loss coefficients, we can control the structure, size and location of the loops in situ. We demonstrate that, under the joint action of topological structure of energy surfaces and nonadiabatic transitions, the chiral behavior emerges both along a loop encircling an EP and even along a straight path away from the EP. This work broadens the range of parameter space for the chiral state conversion, and proposes a useful platform to explore the interesting properties of exceptional points physics.