Exceptional spectrum and dynamic magnetization

A macroscopic effect can be induced by a local non-Hermitian term in a many-body system, when it manifests simultaneously level coalescence of a full real degeneracy spectrum, leading to exceptional spectrum. In this paper, we propose a family of systems that support such an intriguing property. It is generally consisted of two arbitrary identical Hermitian sub-lattices in association with unidirectional couplings between them. We show exactly that all single-particle eigenstates coalesce in pairs even only single unidirectional coupling appears. It means that all possible initial states obey the exceptional dynamics, resulting in some macroscopic phenomena, which never appears in a Hermitian system. As an application, we study the dynamic magnetization induced by complex fields in an itinerant electron system. It shows that an initial saturated ferromagnetic state at half-filling can be driven into its opposite state according to the dynamics of high-order exceptional point. Any Hermitian quench term cannot realize a steady opposite saturated ferromagnetic state. Numerical simulations for the dynamical processes of magnetization are performed for several representative situations, including lattice dimensions, global random and local impurity distributions. It shows that the dynamic magnetization processes exhibit universal behavior.

Generalized temporal coupled-mode theory for a P T-symmetric optical resonator and Fano resonance in a P T-symmetric photonic heterostructure

We have proposed generalized temporal coupled-mode theory for P T-symmetric optical resonator, and on this basis we have explained the Fano resonance in P T-symmetric photonic heterostructure. Our theoretical predictions agree very well with the simulated results obtained by transfer matrix method, which confirms the correctness of our theory. Compared with conventional Fano resonance in optical resonator with time-reversal symmetry, in this Fano resonance the amplitudes of scattering coefficients can be tuned in much larger range, which can be much larger than one, and tend to infinity at singular scattering point, where the rates of dissipation and accumulation are equal to each other and the difference of the phases of the coupling coefficients between output fields and resonant mode is equal to ±π/2. Not only that, the quality factor Q here can be negative out of accumulation, and approaches infinity at this singular scattering point. The phases of reflections jump π in the vicinity of the minima of corresponding amplitudes. We believe that we open a new door to study Fano resonance in non-Hermitian optics and inspire relevant study in other non-Hermitian wave systems.

Band structures and scattering properties of the simplest one-dimensional [Formula: see text]-symmetric photonic crystal

We elucidate the band structures and scattering properties of the simplest one-dimensional parity-time ([Formula: see text])-symmetric photonic crystal. Its unit cell comprises one gain layer and one balanced loss layer. Herein, the analytic expressions of the band structures and scattering properties are derived, and based on these relations, we reveal and explain the following phenomena: Exceptional point pairs appear from Brillouin boundaries at a nonzero non-Hermiticity. With an increase in non-Hermiticity, each of these pairs moves toward the Brillouin center, finally coalescing into a single point at the Brillouin center at a critical non-Hermiticity value. Near the exceptional point, singular scattering is observed and explained. This refers to the phenomenon whereby transmittances and reflectances for left and right incidences reach exceptionally large values simultaneously. Moreover, these are infinite at some discrete points at which poles and zeros of the scattering matrix are attained. In forbidden gaps, unidirectional weak visibility, where transmittances are zero, is disclosed and analyzed: specifically, the reflectance for incidence from one side is very large, whereas that for incidence from the other side is very small. In this phenomenon, the eigenstates of the scattering matrix are the incident waves from the left and right sides, and their eigenvalues are the corresponding reflectances. Our results are important as new functional optical devices can potentially be developed by utilizing these novel phenomena.

Polarization eigenstates analysis of helically structured thin films

The optical properties of thin films are generally determined by direct photometric quantities. We show that additional insight into the properties of anisotropic thin films can be obtained by computing the polarization eigenstates and eigenvalues of their Jones matrices. We consider helically structured thin films, which display intriguing optical response, such as the circular Bragg resonance. Using numerical simulations and actual measurements, we show that the eigenvectors are mutually orthogonal in most regions of the wavevector space, except near the circular Bragg and the oblique resonances. Special wavevector values, called exceptional points, are found where the Jones matrix becomes defective and its eigenvectors coalesce. Exceptional points are also found in pairs of wavevector values differing only by a sample rotation by π around the direction normal to the sample; this property is shown to arise from Saxton - de Hoop's reciprocity principle, which applies to lossy materials and contains time reversal symmetry, which only applies to lossless materials, as a special case.

Overcoming the Diffraction Limit on the Size of Dielectric Resonators Using an Amplifying Medium

Existing methods for the creation of subwavelength resonators use either structures with negative permittivity, by exploiting subwavelength plasmonic resonances, or dielectric structures with a high refractive index, which reduce the wavelength. Here, we provide an alternative to these two methods based on a modification of the modes of dielectric resonators by means of an active medium. On the example of the dielectric active layer of size substantially smaller than a half-wavelength of light, we demonstrate that there is a gain at exceeding of which the change in phase due to the reflection at the layer boundaries compensates the change in phase due to propagation over the layer. Above this value of the gain, an unconventional mode forms, in which the phase shift after a round-trip of the light is zero. We show that this mode can be exploited to create a laser, the size of which is much smaller than the wavelength of the generated light and scales inversely with the square of absolute value of the refractive index in the active medium. Our results pave the way to creation of dielectric lasers of subwavelength size.

Directly modulated azimuthally polarized vector beam laser design

Directly modulated vector beam lasers are increasingly desirable for wide applications ranging from optical manipulation to optical communications. We report the first, to our knowledge, high-speed directly modulated vector beam laser with azimuthally polarized emission. It is a microcylinder cavity interacted with a proper second-order grating on top, which enables single mode lasing and efficient surface emission. Through theoretical and numerical analysis, the laser is designed in detail. With an optimized top grating, the emission of the laser is an azimuthally polarized vector beam. With high-differential-gain material and a small active region, the laser can be directly modulated with a high 3 dB bandwidth reach of 40 GHz in simulation. The proposed high-speed directly modulated semiconductor laser with an azimuthally polarized vector beam is promising for applications in fiber space communications or quantum information.

Unveiling the Enhancement of Spontaneous Emission at Exceptional Points

Exceptional points (EPs), singularities of non-Hermitian physics where complex spectral resonances degenerate, are one of the most exotic features of nonequilibrium open systems with unique properties. For instance, the emission rate of quantum emitters placed near resonators with EPs is enhanced (compared to the free-space emission rate) by a factor that scales quadratically with the resonance quality factor. Here, we verify the theory of spontaneous emission at EPs by measuring photoluminescence from photonic-crystal slabs that are embedded with a high-quantum-yield active material. While our experimental results verify the theoretically predicted enhancement, they also highlight the practical limitations on the enhancement due to material loss. Our designed structures can be used in applications that require enhanced and controlled emission, such as quantum sensing and imaging.

Far-Field Correlations Verifying Non-Hermitian Degeneracy of Optical Modes

An experimental verification of an exceptional point (EP) in a stand-alone chaotic microcavity is a tough issue because as deformation parameters are fixed the traditional frequency analysis methods cannot be applied any more. Through numerical investigations with an asymmetric Reuleaux triangle microcavity (ARTM), we find that the eigenvalue difference of paired modes can approach near-zero regardless of nonorthogonality of the modes. In this case, for a definite verification of EPs in experiments, wave function coalescence should be confirmed. For this, we suggest the method of exploiting correlation of far-field patterns (FFPs), which is directly related to spatial mode patterns. In an ARTM, we demonstrate that the FFP correlation of paired modes can be used to confirm wave function coalescence when an eigenvalue difference approaches near zero.

Coherent full polarization control based on bound states in the continuum

Bound states in the continuum (BICs) are resonant modes of open structures that do not suffer damping, despite being compatible with radiation in terms of their momentum. They have been raising significant attention for their intriguing topological features, and their opportunities in photonics to enhance light-matter interactions. In parallel, the coherent excitation of optical devices through the tailored interference of multiple beams has been explored as a way to enhance the degree of real-time control over their response. Here, we leverage the combination of these phenomena, and exploit the topological features of BICs in the presence of multiple input beams to enable full polarization control on the entire Poincaré sphere in a photonic crystal slab only supporting a symmetry-protected BIC, experimentally demonstrating highly efficient polarization conversion controlled in real time through the superposition of coherent excitations. Our findings open exciting opportunities for a variety of photonic and quantum optics applications, benefitting from extreme wave interactions and topological features around BICs combined with optical control through coherent interference of multiple excitations.

Dynamic manipulation of WGM lasing by tailoring the coupling strength

Miniaturized lasing with dynamic manipulation is critical to the performance of compact and versatile photonic devices. However, it is still a challenge to manipulate the whispering gallery mode lasing modes dynamically. Here, we design the quasi-three-dimensional coupled cavity by a micromanipulation technique. The coupled cavity consists of two intersection polymer microfibers. The mode selection mechanism is demonstrated experimentally and theoretically in the coupled microfiber cavity. Dynamic manipulation from multiple modes to single-mode lasing is achieved by controlling the coupling strength, which can be quantitatively controlled by changing the coupling angle or the coupling distance. Our work provides a flexible alternative for the lasing mode modulation in the on-chip photonic integration.

Single-mode lasing in an AlGaInAs/InP dual-port square microresonator

Mode selection is crucial to achieving stable single-mode lasing in microlasers. Here, we demonstrate experimentally a dual-port square microresonator for single-mode lasing with a side-mode-suppression ratio (SMSR) exceeding 40 dB. By connecting waveguides at two opposite vertices, the quality factor for the antisymmetric mode (ASM) is much higher than that of the symmetric mode (SM), enabling single-mode lasing. Furthermore, far-field interference patterns similar to Young's two-slit interference are observed. This microlaser is capable of providing two optical sources simultaneously for optical signal processing in high-density integrated photonic circuits.

Design and optimization of a passive PT-symmetric grating with asymmetric reflection and diffraction

In recent years, notions drawn from non-Hermitian physics and parity-time (PT) symmetry have raised considerable attention in photonics, enabling various novel structures with entirely new and unexpected features. Here we propose, design, and optimize a compact passive PT-symmetric grating to achieve asymmetric reflection and diffraction based on a silicon-on-insulator (SOI) platform. The structure is composed of two sets of interleaved tailored gratings, which are all well-defined on the top of a silicon waveguide. Without additional loss or gain materials, the effective index and the scattering loss of the waveguide mode are modulated by the structure design. To our knowledge, it is the first time that the scattering loss arising from grating elements is regarded as an efficient way to realize PT-symmetric structure. The complicated multi-parameter optimization process of the proposed PT-symmetric grating is completed by using the particle swarm optimization (PSO) algorithm. In the simulation, asymmetric reflection with high contrast ratio is realized. We also find that the waveguide-to-free-space diffraction from one side of the structure is significantly suppressed, leading to asymmetric diffraction. Moreover, we investigate the fabrication tolerance of the proposed PT-symmetric grating. Our work provides a new perspective for exploring and creating complicated on-chip PT-symmetric devices.

Reconfigurable chiral exceptional point and tunable non-reciprocity in a non-Hermitian system with phase-change material

Non-Hermitian optics has emerged as a feasible and versatile platform to explore many extraordinary wave phenomena and novel applications. However, owing to ineluctable systematic errors, the constructed non-Hermitian phenomena could be easily broken, thus leading to a compromising performance in practice. Here we theoretically proposed a dynamically tunable mechanism through GST-based phase-change material (PCM) to achieve a reconfigurable non-Hermitian system, which is robust to access the chiral exceptional point (EP). Assisted by PCM that provides tunable coupling efficiency, the effective Hamiltonian of the studied doubly-coupled-ring-based non-Hermitian system can be effectively modulated to resist the external perturbations, thus enabling the reconfigurable chiral EP and a tunable non-reciprocal transmission. Moreover, such tunable properties are nonvolatile and require no static power consumption. With these superior performances, our findings pave a promising way for reconfigurable non-Hermitian photonic devices, which may find applications in tunable on-chip sensors, isolators and so on.

Non-Hermitian mode-locking synthesized by parity-time and anti-parity-time symmetric modulations

We study the pulse characteristics in a laser mode-locked by active modulators with non-Hermitian driven signals. The signal assembles a parity-time (P T) symmetric and an anti-parity-time (A P T) symmetric function with fundamental and harmonic frequencies, respectively, inducing the complex coupling between modes in the frequency domain. A one-dimensional synthetic lattice is used to analyze the spectral mode coupling. By enlarging the weight and harmonic order of the A P T part of the signal, the optical spectrum can be adjusted from redshift to blueshift. Simultaneously, the pulse duration and spectral width are shortened and broadened, respectively. The work explores the role of non-Hermitian modulation in the mode-locked laser area.

Anomalous Single-Mode Lasing Induced by Nonlinearity and the Non-Hermitian Skin Effect

Single-mode operation is a desirable but elusive property for lasers operating at high pump powers. Typically, single-mode lasing is attainable close to threshold, but increasing the pump power gives rise to multiple lasing peaks due to inter-modal gain competition. We propose a laser with the opposite behavior: multimode lasing occurs at low output powers, but pumping beyond a certain value produces a single lasing mode, with all other candidate modes experiencing negative effective gain. This phenomenon arises in a lattice of coupled optical resonators with non-fine-tuned asymmetric couplings, and is caused by an interaction between nonlinear gain saturation and the non-Hermitian skin effect. The single-mode lasing is observed in both frequency domain and time domain simulations. It is robust against on-site disorder, and scales up to large lattice sizes. This finding might be useful for implementing high-power laser arrays.

Wide-range robust wireless power transfer using heterogeneously coupled and flippable neutrals in parity-time symmetry

Recently, stationary wireless power transfer (WPT) has been widely adopted in commercial devices. However, the current WPT configuration is limited in its operational area and susceptible to operating condition changes, impeding its applications for dynamic environments. To overcome the limitations, we propose a WPT system with laterally aligned neutral elements in parity-time (PT) symmetry, which can widen the operational area with the number of neutrals N. Compared to the conventional multiple-input-single-output WPT, the dimension of system complexity is substantially reduced from R × C^N to R^N+1 because the neutral amplitudes are simply controlled by coupling capacitors. The operational frequency is automatically adjusted to a real eigenvalue of the PT-symmetric system to achieve high voltage gain and efficiency, making the system robust. The performance of the system calculated by the coupled-mode theory was experimentally verified with rigid and flexible types of receivers, confirming its potential in both industrial and biomedical electronics.

Linear response theory of open systems with exceptional points

Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order M_s with M_s = 2, 3, …, M, depending on the choice of input and output channels.

The authors develop a closed-form expansion of the linear response associated with resonant non-Hermitian systems having exceptional points and demonstrate that the spectral response may involve different super Lorentzian lineshapes depending on the input/output channel configuration.

Single-mode narrow-linewidth fiber ring laser with SBS-assisted parity-time symmetry for mode selection

A single-longitudinal-mode narrow-linewidth fiber ring laser with stimulated Brillouin scattering (SBS) assisted parity-time (PT) symmetry for mode selection in a single fiber loop is proposed and experimentally demonstrated. When an optical pump is launched into the fiber loop along one direction, an SBS gain for the Stokes light along the opposite direction is produced. For two light waves at the Stokes frequency propagating along the two opposite directions, one will have a net gain and the other will have a net loss. By incorporating a fiber Bragg grating (FBG) with partial reflection in the loop, mutual coupling between the two counterpropagating Stokes light waves is achieved. The SBS gain can be controlled by tuning the angle between the polarization directions of the pump and the Stokes light waves through a polarization controller (PC). Once the gain and loss coefficients between the two counterpropagating light waves are controlled to be identical in magnitude, and that the gain coefficient is greater than the coupling coefficient caused by the FBG, PT symmetry breaking is achieved, making the mainmode to sidemode ratio highly enhanced, single mode lasing is thus achieved. The approach is evaluated experimentally. For a fiber ring laser with a cavity length of 8.02 km, single-mode lasing with a narrow 3-dB linewidth of 368 Hz and a sidemode suppression ratio of around 33 dB is demonstrated. The wavelength tunable range from 1550.02 to 1550.18 nm is also demonstrated.

Anyonic-parity-time symmetry in complex-coupled lasers

Non-Hermitian Hamiltonians, and particularly parity-time (PT) and anti-PT symmetric Hamiltonians, play an important role in many branches of physics, from quantum mechanics to optical systems and acoustics. Both the PT and anti-PT symmetries are specific instances of a broader class known as anyonic-PT symmetry, where the Hamiltonian and the PT operator satisfy a generalized commutation relation. Here, we study theoretically these novel symmetries and demonstrate them experimentally in coupled lasers systems. We resort to complex coupling of mixed dispersive and dissipative nature, which allows unprecedented control on the location in parameter space where the symmetry and symmetry breaking occur. Moreover, tuning the coupling in the same physical system allows us to realize the special cases of PT and anti-PT symmetries. In a more general perspective, we present and experimentally validate a new relation between laser synchronization and the symmetry of the underlying non-Hermitian Hamiltonian.

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.

Nonlinear Optical Potential with Parity-Time Symmetry in a Coherent Atomic Gas

We propose a scheme to realize a parity-time (PT) symmetric nonlinear system in a coherent atomic gas via electromagnetically induced transparency. We show that it is possible to construct an optical potential with PT symmetry due to the interplay among the Kerr nonlinearity stemmed from the atom-photon interaction, the linear potential induced by a far-detuned Stark laser field, and the optical gain originated from an incoherent pumping. Since the real part of the PT-symmetric potential depends only on the intensity of the probe field, the potential is nonlinear and its PT-symmetric properties are determined by the input laser intensity of the probe field. Moreover, we obtain the fundamental soliton solutions of the system and attain their stability region in the system parameter space. The dependence of the exceptional point (EP) location on the soliton maximum amplitude is also illustrated. The research results reported here open a new avenue for understanding the unique properties of PT symmetry of a nonlinear system. They are also promising for designing novel optical devices applicable in optical information processing and transmission.

Parity-Time Symmetry Enabled Band-Pass Filter Featuring High Bandwidth-Tunable Contrast Ratio

Integrated optical filters based on microring resonators play a critical role in many applications, ranging from wavelength division multiplexing and switching to channel routing. Bandwidth tunable filters are capable of meeting the on-demand flexible operations in complex situations, due to their advantages of scalability, multi-functionality, and being energy-saving. Recent studies have investigated how parity-time (PT) symmetry coupled-resonant systems can be applied to the bandwidth-tunable filters. However, due to the trade-off between the bandwidth-tunable contrast ratio and insertion loss of the system, the bandwidth-tunable contrast ratio of this method is severely limited. Here, the bandwidth-tunable contrast ratio is defined as the maximum bandwidth divided by the minimum bandwidth. In this work, we show that a high bandwidth-tunable contrast ratio and low insertion loss of the system can be achieved simultaneously by increasing the coupling strength between the input port and the resonant. Theoretical analysis under different coupling states reveals that the low insertion loss can be obtained when the system initially operates at the over-coupling condition. A high bandwidth-tunable contrast ratio PT-symmetry band-pass filter with moderate insertion loss is shown on the Silicon platform. Our scheme provides an effective method to reduce the insertion loss of on-chip tunable filters, which is also applicable to the high-order cascaded microring systems.

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.

Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos

The dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level spacing distribution. While decoherence generally suppresses these dynamical signatures, the nonlinear non-Hermitian evolution with balanced gain and loss (BGL) in an energy-dephasing scenario can enhance manifestations of quantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians, BGL increases the span of the ramp, lowering the dip as well as the value of the plateau, providing an experimentally realizable physical mechanism for spectral filtering. The chaos enhancement due to BGL is optimal over a family of filter functions that can be engineered with fluctuating Hamiltonians.

Transforming Space with Non-Hermitian Dielectrics

Coordinate transformations are a versatile tool to mold the flow of light, enabling a host of astonishing phenomena such as optical cloaking with metamaterials. Moving away from the usual restriction that links isotropic materials with conformal transformations, we show how nonconformal distortions of optical space are intimately connected to the complex refractive index distribution of an isotropic non-Hermitian medium. Remarkably, this insight can be used to circumvent the material requirement of working with refractive indices below unity, which limits the applications of transformation optics. We apply our approach to design a broadband unidirectional dielectric cloak, which relies on nonconformal coordinate transformations to tailor the non-Hermitian refractive index profile around a cloaked object. Our insights bridge the fields of two-dimensional transformation optics and non-Hermitian photonics.

Single longitudinal mode lasing near the exceptional point in a fiber laser using a tunable isolator

Parity time symmetry breaking was obtained in a specially designed fiber ring laser with a homemade tunable isolator in the cavity. The dynamic evolution of the cavity eigenmodes around the exceptional point (EP) was further experimentally studied. We showed that operating the laser near the EP can facilitate single longitudinal mode lasing. A single-frequency fiber laser with a linewidth of 163 Hz was first, to the best of our knowledge, demonstrated near the EP of the cavity without using any filter with a narrow bandwidth.

Quantum Squeezing and Sensing with Pseudo-Anti-Parity-Time Symmetry

The emergence of parity-time (PT) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum PT symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-PT (pseudo-APT) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the spontaneous pseudo-APT symmetry breaking leads to an exceptional point, across which there is a transition between different types of quantum squeezing dynamics; i.e., the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-APT-symmetric (broken) region. Such dramatic changes of squeezing factors and quantum dynamics near the exceptional point are utilized for ultraprecision quantum sensing. These exotic quantum phenomena and sensing applications can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates. Our Letter offers a physical platform for investigating exciting APT symmetry physics in the quantum realm, paving the way for exploring fundamental quantum non-Hermitian effects and their quantum technological applications.

Curving the space by non-Hermiticity

Quantum systems are often classified into Hermitian and non-Hermitian ones. Extraordinary non-Hermitian phenomena, ranging from the non-Hermitian skin effect to the supersensitivity to boundary conditions, have been widely explored. Whereas these intriguing phenomena have been considered peculiar to non-Hermitian systems, we show that they can be naturally explained by a duality between non-Hermitian models in flat spaces and their counterparts, which could be Hermitian, in curved spaces. For instance, prototypical one-dimensional (1D) chains with uniform chiral tunnelings are equivalent to their duals in two-dimensional (2D) hyperbolic spaces with or without magnetic fields, and non-uniform tunnelings could further tailor local curvatures. Such a duality unfolds deep geometric roots of non-Hermitian phenomena, delivers an unprecedented routine connecting Hermitian and non-Hermitian physics, and gives rise to a theoretical perspective reformulating our understandings of curvatures and distance. In practice, it provides experimentalists with a powerful two-fold application, using non-Hermiticity to engineer curvatures or implementing synthetic curved spaces to explore non-Hermitian quantum physics.

Fast encirclement of an exceptional point for highly efficient and compact chiral mode converters

Exceptional points (EPs) are degeneracies at which two or more eigenvalues and eigenstates of a physical system coalesce. Dynamically encircling EPs by varying the parameters of a non-Hermitian system enables chiral mode switching, that is, the final state of the system upon a closed loop in parameter space depends on the encircling handedness. In conventional schemes, the parametric evolution during the encircling process has to be sufficiently slow to ensure adiabaticity. Here, we show that fast parametric evolution along the parameter space boundary of the system Hamiltonian can relax this constraint. The proposed scheme enables highly efficient transmission and more compact footprint for asymmetric mode converters. We experimentally demonstrate these principles in a 57 μm-long double-coupled silicon waveguide system, enabling chiral mode switching with near-unity transmission efficiency at 1550 nm. This demonstration paves the way towards high-efficiency and highly integrated chiral mode switching for a wide range of practical applications.

Observation of Weyl exceptional rings in thermal diffusion

Thermal diffusion is dissipative and strongly related to non-Hermitian physics. At the same time, non-Hermitian Weyl systems have spurred tremendous interest across photonics and acoustics. This correlation has been long ignored and hence shed little light upon the question of whether the Weyl exceptional ring (WER) in thermal diffusion could exist. Intuitively, thermal diffusion provides no real parameter dimensions, thus prohibiting a topological nature and WER. This work breaks this perception by imitating synthetic dimensions via two spatiotemporal advection pairs. The WER is achieved in thermal diffusive systems. Both surface-like and bulk states are demonstrated by coupling two WERs with opposite topological charges. These findings extend topological notions to diffusions and motivate investigation of non-Hermitian diffusive and dissipative control.

A non-Hermitian Weyl equation indispensably requires a three-dimensional (3D) real/synthetic space, and it is thereby perceived that a Weyl exceptional ring (WER) will not be present in thermal diffusion given its purely dissipative nature. Here, we report a recipe for establishing a 3D parameter space to imitate thermal spinor field. Two orthogonal pairs of spatiotemporally modulated advections are employed to serve as two synthetic parameter dimensions, in addition to the inherent dimension corresponding to heat exchanges. We first predict the existence of WER in our hybrid conduction–advection system and experimentally observe the WER thermal signatures verifying our theoretical prediction. When coupling two WERs of opposite topological charges, the system further exhibits surface-like and bulk topological states, manifested as stationary and continuously changing thermal processes, respectively, with good robustness. Our findings reveal the long-ignored topological nature in thermal diffusion and may empower distinct paradigms for general diffusion and dissipation controls.

Can Weak Chirality Induce Strong Coupling between Resonant States?

Strong coupling between resonant states is usually achieved by modulating intrinsic parameters of optical systems, e.g., the refractive index of constituent materials or structural geometries. Externally introduced chiral enantiomers may couple resonances, but the extremely weak chirality of natural enantiomers largely prevents the system from reaching strong coupling regimes. Whether weak chirality could induce strong coupling between resonant states remains an open question. Here, we realize strong coupling between quasibound states in the continuum of a high-Q metasurface, assisted with externally introduced enantiomers of weak chirality. We establish a chirality-involved Hamiltonian to quantitatively describe the correlation between the coupling strength and the chirality of such systems, which provides an insightful recipe for enhancing the coupling of resonant states further in the presence of quite weak chirality. Consequently, high-sensitivity chiral sensing is demonstrated, in which the circular dichroism signal is enhanced 3 orders higher than the case without strong coupling. Our findings present a distinct strategy for manipulating optical coupling between resonances, revealing opportunities in chiral sensing, topological photonics, and quantum optics.

Correlations at PT-Symmetric Quantum Critical Point

We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a Hermitian Fermi gas. The fermionic Green's function decays in a power law fashion for large distances, as expected from gapless excitations, although the exponent is reduced from -1 due to the quantum Zeno effect. In spite of the gapless nature of the excitations, the ground state entanglement entropy saturates to a finite value, independent of the subsystem size due to the non-Hermitian correlation length intrinsic to the system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or opens up a gap and protects PT symmetry, respectively. Our results challenge the concept of universality in non-Hermitian systems, where quantum criticality can be masked due to non-Hermiticity.

A large-scale single-mode array laser based on a topological edge mode

Topological lasers have been intensively investigated as a strong candidate for robust single-mode lasers. A typical topological laser employs a single-mode topological edge state, which appears deterministically in a designed topological bandgap and exhibits robustness to disorder. These properties seem to be highly attractive in pursuit of high-power lasers capable of single mode operation. In this paper, we theoretically analyze a large-scale single-mode laser based on a topological edge state. We consider a sizable array laser consisting of a few hundreds of site resonators, which support a single topological edge mode broadly distributed among the resonators. We build a basic model describing the laser using the tight binding approximation and evaluate the stability of single mode lasing based on the threshold gain difference Δα between the first-lasing edge mode and the second-lasing competing bulk mode. Our calculations demonstrate that stronger couplings between the cavities and lower losses are advantageous for achieving stable operation of the device. When assuming an average coupling of 100 cm-1 between site resonators and other realistic parameters, the threshold gain difference Δα can reach about 2 cm-1, which would be sufficient for stable single mode lasing using a conventional semiconductor laser architecture. We also consider the effects of possible disorders and long-range interactions to assess the robustness of the laser under non-ideal situations. These results lay the groundwork for developing single-mode high-power topological lasers.

Ultralow-Threshold and High-Quality Whispering-Gallery-Mode Lasing from Colloidal Core/Hybrid-Shell Quantum Wells

The realization of efficient on-chip microlasers with scalable fabrication, ultralow threshold, and stable single-frequency operation is always desired for a wide range of miniaturized photonic systems. Herein, an effective way to fabricate nanostructures- whispering-gallery-mode (WGM) lasers by drop-casting CdSe/CdS@Cd_{1- x} Zn_x S core/buffer-shell@graded-shell nanoplatelets (NPLs) dispersion onto silica microspheres is presented. Benefiting from the excellent gain properties from the interface engineered core/hybrid shell NPLs and high-quality factor WGM resonator from excellent optical field confinement, the proposed room-temperature NPLs-WGM microlasers show a record-low lasing threshold of 3.26 µJ cm^-2 under nanosecond laser pumping among all colloidal NPLs-based lasing demonstrations. The presence of sharp discrete transverse electric- and magnetic-mode spikes, the inversely proportional dependence of the free spectra range on microsphere sizes and the polarization anisotropy of laser output represent the first direct experimental evidence for NPLs-WGM lasing nature, which is verified theoretically by the computed electric-field distribution inside the microcavity. Remarkably, a stable single-mode lasing output with an ultralow lasing threshold of 3.84 µJ cm^-2 is achieved by the Vernier effect through evanescent field coupling. The results highlight the significance of interface engineering on the optimization of gain properties of heterostructured nanomaterials and shed light on developing future miniaturized tunable coherent light sources.

Dual-wavelength switchable single-mode lasing from a lanthanide-doped resonator

The development of multi-wavelength lasing, particularly with the wavelength tuning in a wide spectral range, is challenging but highly desirable for integrated photonic devices due to its dynamic switching functionality, high spectral purity and contrast. Here, we propose a general strategy, that relies on the simultaneous design on the electronic states and the optical states, to demonstrate dynamically switchable single-mode lasing spanning beyond the record range (300 nm). This is achieved through integrating the reversely designed nanocrystals with two size-mismatched coupled microcavities. We show an experimental validation of a crosstalk-free violet-to-red single-mode behavior through collective control of asymmetric excitation and excitation wavelength. The single-mode action persists for a wide power range, and presents significant enhancement when compared with that in the microdisk laser. These findings enlighten the reverse design of luminescent materials. Given the remarkable doping flexibility, our results may create new opportunities in a variety of frontier applications.

Vortex radiation from a single emitter in a chiral plasmonic nanocavity

Manipulating single emitter radiation is essential for quantum information science. Significant progress has been made in enhancing the radiation efficiency and directivity by coupling quantum emitters with microcavities and plasmonic antennas. However, there has been a great challenge to generate complex radiation patterns such as vortex beam from a single emitter. Here, we report a chiral plasmonic nanocavity, which provides a strong local chiral vacuum field at an exceptional point. We show that a single linear dipole emitter embedded in the nanocavity will radiate to vortex beam via anomalous spontaneous emission with a Purcell enhancement factor up to ∼1000. Our scheme provides a new field manipulation method for chiral quantum optics and vortex lasers at the nanoscale.

Mode selection in InGaAs/InGaAsP quantum well photonic crystal lasers based on coupled double-heterostructure cavities

Photonic crystal lasers with a high-Q factor and small mode volume are ideal light sources for on-chip nano-photonic integration. Due to the submicron size of their active region, it is usually difficult to achieve high output power and single-mode lasing at the same time. In this work, we demonstrate well-selected single-mode lasing in a line-defect photonic crystal cavity by coupling it to the high-Q modes of a short double-heterostructure photonic crystal cavity. One of the FP-like modes of the line-defect cavity can be selected to lase by thermo-optically tuning the high-Q mode of the short cavity into resonance. Six FP-like modes are successively tuned into lasing with side mode suppression ratios all exceeding 15 dB. Furthermore, we show a continuous wavelength tunability of about 10 nm from all the selected modes. The coupled cavity system provides a remarkable platform to explore the rich laser physics through the spatial modulation of vacuum electromagnetic field at submicron scale.

Metasurface-empowered spectral and spatial light modulation for disruptive holographic displays

The holographic display, one of the most realistic ways to reconstruct optical images in three-dimensional (3D) space, has gained a lot of attention as a next-generation display platform for providing deeper immersive experiences to users. So far, diffractive optical elements (DOEs) and spatial light modulators (SLMs) have been used to generate holographic images by modulating electromagnetic waves at each pixel. However, such architectures suffer from limitations in terms of having a resolution of only a few microns and the bulkiness of the entire optical system. In this review, we describe novel metasurfaces-based nanophotonic platforms that have shown exceptional control of electromagnetic waves at the subwavelength scale as promising candidates to overcome existing restrictions, while realizing flat optical devices. After introducing the fundamentals of metasurfaces in terms of spatial and spectral wavefront modulation, we present a variety of multiplexing approaches for high-capacity and full-color metaholograms exploiting the multiple properties of light as an information carrier. We then review tunable metaholograms using active materials modulated by several external stimuli. Afterward, we discuss the integration of metasurfaces with other optical elements required for future 3D display platforms in augmented/virtual reality (AR/VR) displays such as lenses, beam splitters, diffusers, and eye-tracking sensors. Finally, we address the challenges of conventional nanofabrication methods and introduce scalable preparation techniques that can be applied to metasurface-based nanophotonic technologies towards commercially and ergonomically viable future holographic displays.

A tale of two kinds of exceptional point in a hydrogen molecule

We study the parity and time-reversal(PT)symmetric quantum physics in a non-Hermitian non-relativistic hydrogen molecule with local (Hubbard type) Coulomb interaction. We consider non-Hermiticity generated from both kinetic and orbital energies of the atoms and encounter the existence of two different types of exceptional points (EPs) in pairs. These two kinds of EP are characteristically different and depend differently on the interaction strength. Our discovery may open the gates of a rich physics emerging out of a simple Hamiltonian resembling a two-site Hubbard model.

Fully integrated parity-time-symmetric electronics

Harnessing parity-time symmetry with balanced gain and loss profiles has created a variety of opportunities in electronics from wireless energy transfer to telemetry sensing and topological defect engineering. However, existing implementations often employ ad hoc approaches at low operating frequencies and are unable to accommodate large-scale integration. Here we report a fully integrated realization of parity-time symmetry in a standard complementary metal-oxide-semiconductor process technology. Our work demonstrates salient parity-time symmetry features such as phase transition as well as the ability to manipulate broadband microwave generation and propagation beyond the limitations encountered by existing schemes. The system shows 2.1 times the bandwidth and 30% noise reduction compared to conventional microwave generation in the oscillatory mode, and displays large non-reciprocal microwave transport from 2.75 to 3.10 GHz in the non-oscillatory mode due to enhanced nonlinearities. This approach could enrich integrated circuit design methodology beyond well-established performance limits and enable the use of scalable integrated circuit technology to study topological effects in high-dimensional non-Hermitian systems.

Superhybrid Mode-Enhanced Optical Torques on Mie-Resonant Particles

Circularly polarized light carries spin angular momentum, so it can exert an optical torque on the polarization-anisotropic particle by the spin momentum transfer. Here, we show that giant positive and negative optical torques on Mie-resonant (gain) particles arise from the emergence of superhybrid modes with magnetic multipoles and electric toroidal moments, excited by linearly polarized beams. Anomalous positive and negative torques on particles (doped with judicious amount of dye molecules) are over 800 and 200 times larger than the ordinary lossy counterparts, respectively. Meanwhile, a rotational motor can be configured by switching the s- and p-polarized beams, exhibiting opposite optical torques. These giant and reversed optical torques are unveiled for the first time in the scattering spectrum, paving another avenue toward exploring unprecedented physics of hybrid and superhybrid multipoles in metaoptics and optical manipulations.

Directional coupling with parity-time symmetric Bragg gratings

Parity-time symmetric Bragg gratings produce unidirectional reflection around the exceptional point. We propose and explore directional coupling of gain and loss modulated waveguide Bragg gratings operating at around 880 nm with long-range surface plasmon polaritons. Step-in-width modulation of a Ag stripe supporting long-range plasmons combined with a periodic modulation of the cladding were used to balance the real and imaginary index perturbation of the gratings. IR140 dye molecules in solvent forms a portion of the uppercladding, providing gain under optical pumping. We investigate directional coupling between a pair of parity-time symmetric waveguide Bragg gratings operating near their exceptional point, arranged in various configurations - duplicate, duplicate-shifted and duplicate-flipped. We also investigate coupling to a bus waveguide and to a conventional waveguide Bragg grating. Unidirectional multi-wavelength reflection and coupled supermode conversion are predicted.

Observation of Transient Parity-Time Symmetry in Electronic Systems

We demonstrate the transient parity-time (PT) symmetry in electronics. It is revealed by equivalent circuit transformation according to the switching states of electronic systems. With the phasor method and Laplace transformation, we derive the hidden PT-symmetric Hamiltonian in the switching oscillation, which are characterized by free oscillation modes. Both spectral and dynamic properties of the PT electronic structure demonstrate the phase transition with eigenmode orthogonality. Importantly, the observed transient PT symmetry enables exceptional-point-induced optimal switching oscillation suppression, which shows the significance of PT symmetry in electronic systems with temporary responses. Our work paves the way for breakthroughs in the PT symmetry theory and has essential applications such as anti-interference in switch-mode electronics.

Unidirectional single-mode lasing realization and temperature-induced mode switching in asymmetric GaN coupled cavities

Effective lasing mode control and unidirectional coupling of semiconductor microlasers are vital to boost their applications in optical interconnects, on-chip communication, and bio-sensors. In this study, symmetric and asymmetric GaN floating microdisks and coupled cavities are designed based on the Vernier effect and then fabricated via electron beam lithography, dry-etching of GaN, and isotropic wet-etching of silicon (Si) support. The lasing properties, including model number, threshold, radiation direction, and mode switching method, are studied. Compared to its symmetrical structure, both experimental and simulated optical field distributions indicate that the lasing outgoing direction can be controlled with a vertebral angle on the disk. The whispering gallery mode (WGM) lasing of the structures, with a quasi-single-mode lasing at 374.36 nm, a dual-mode lasing at 372.36 nm, and 373.64 nm at coupled cavities, are obtained statically. More interestingly, a switching between dual-mode and single-mode can be achieved dynamically via a thermal-induced mode shifting.

Topological optomechanical amplifier in synthetic PT -symmetry

We propose how to achieve synthetic PT symmetry in optomechanics without using any active medium. We find that harnessing the Stokes process in such a system can lead to the emergence of exceptional point (EP), i.e., the coalescing of both the eigenvalues and the eigenvectors of the system. By encircling the EP, both nonreciprocal optical amplification and chiral mode switching can be achieved. As a result, our synthetic PT -symmetric optomechanics works as a topological optomechanical amplifier. This provides a surprisingly simplified route to realize PT -symmetric optomechanics, indicating that a wide range of EP devices can be created and utilized for various applications such as topological optical engineering and nanomechanical processing or sensing.

Non-Hermitian metasurface with non-trivial topology

The synergy between topology and non-Hermiticity in photonics holds immense potential for next-generation optical devices that are robust against defects. However, most demonstrations of non-Hermitian and topological photonics have been limited to super-wavelength scales due to increased radiative losses at the deep-subwavelength scale. By carefully designing radiative losses at the nanoscale, we demonstrate a non-Hermitian plasmonic-dielectric metasurface in the visible with non-trivial topology. The metasurface is based on a fourth order passive parity-time symmetric system. The designed device exhibits an exceptional concentric ring in its momentum space and is described by a Hamiltonian with a non-HermitianZ 3 topological invariant of V = -1. Fabricated devices are characterized using Fourier-space imaging for single-shot k-space measurements. Our results demonstrate a way to combine topology and non-Hermitian nanophotonics for designing robust devices with novel functionalities.

Parity-time symmetry in monolithically integrated graphene-assisted microresonators

Recently, optical systems with parity-time (PT) symmetry have attracted considerable attention due to its remarkable properties and promising applications. However, these systems usually require separate photonic devices or active semiconductor materials. Here, we investigate PT symmetry and exceptional points (EPs) in monolithically integrated graphene-assisted coupled microresonators. Raman effect and graphene cladding are utilized to introduce the balanced gain and loss. We show that PT-symmetry breaking and EPs can be achieved by changing the pump power and the chemical potential. In addition, the intracavity field intensities experience suppression and revival as the graphene-induced loss increases. Due to the unique distribution of optical field, tunable nonreciprocal light transmission is theoretically demonstrated when introducing the gain saturation nonlinearity. The maximum isolation ratio can reach 26 dB through optimizing the relevant parameters. Our proposed scheme is monolithically integrated, CMOS compatible, and exhibits remarkable properties for microscale light field manipulation. These superior features make our scheme has promising applications in optical communication, computing and sensing.

Transient growth and dissipative exceptional points

In the context of non-Hermitian photonics, we study the physics of transient growth in coupled waveguide systems that exhibit higher-order exceptional points. We demonstrate the counterintuitive effect of transient growth despite the decaying spectrum, which is a direct consequence of the underlying modal nonorthogonality. Eigenvalue analysis fails to capture the power dynamics and thus we have to rely on methods of nonmodal stability theory, namely singular value decomposition and pseudospectra. The relation between the order of the exceptional point and transient growth is also examined. Our work provides a general methodology that can be applied to any non-Hermitian system that contains complex elements with more loss than gain, and exploits the boundaries of transient amplification in dissipative environments.

A new type of non-Hermitian phase transition in open systems far from thermal equilibrium

We demonstrate a new type of non-Hermitian phase transition in open systems far from thermal equilibrium, which can have place in the absence of an exceptional point. This transition takes place in coupled systems interacting with reservoirs at different temperatures. We show that the spectrum of energy flow through the system caused by the temperature gradient is determined by the [Formula: see text]-potential. Meanwhile, the frequency of the maximum in the spectrum plays the role of the order parameter. The phase transition manifests itself in the frequency splitting of the spectrum of energy flow at a critical point, the value of which is determined by the relaxation rates and the coupling strength. Near the critical point, fluctuations of the order parameter diverge according to a power law with the critical exponent that depends only on the ratio of reservoirs temperatures. The phase transition at the critical point has the non-equilibrium nature and leads to the change in the energy flow between the reservoirs. Our results pave the way to manipulate the heat energy transfer in the coupled out-of-equilibrium systems.

Complex energies of the coherent longitudinal optical phonon-plasmon coupled mode according to dynamic mode decomposition analysis

In a dissipative quantum system, we report the dynamic mode decomposition (DMD) analysis of damped oscillation signals. We used a reflection-type pump-probe method to observe time-domain signals, including the coupled modes of long-lived longitudinal optical phonons and quickly damped plasmons (LOPC) at various pump powers. The Fourier transformed spectra of the observed damped oscillation signals show broad and asymmetric modes, making it difficult to evaluate their frequencies and damping rates. We then used DMD to analyze the damped oscillation signals by precisely determining their frequencies and damping rates. We successfully identified the LOPC modes. The obtained frequencies and damping rates were shown to depend on the pump power, which implies photoexcited carrier density. We compared the pump-power dependence of the frequencies and damping rates of the LOPC modes with the carrier density dependence of the complex eigen-energies of the coupled modes by using the non-Hermitian phenomenological effective Hamiltonian. Good agreement was obtained between the observed and calculated dependences, demonstrating that DMD is an effective alternative to Fourier analysis which often fails to estimate effective damping rates.