arXiv subjects

Kun Ding

Publications and source records attributed to Kun Ding.

At least 73 records · Page 4Linked to original sources

arXiv2022

Non-Hermitian Topology and Exceptional-Point Geometries

Non-Hermitian theory is a theoretical framework that excels at describing open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external environment. The non-Hermitian framework consists of mathematical structures that are fundamentally different from those of Hermitian theories. These structures not only underpin novel approaches for precisely tailoring non-Hermitian systems for applications but also give rise to topologies not found in Hermitian systems. In this paper, we comprehensively review non-Hermitian topology by establishing its relationship with the behaviors of complex eigenvalues and biorthogonal eigenvectors. Special attentions are given to exceptional points - branch-point singularities on the complex eigenvalue manifolds that exhibit non-trivial topological properties. We also discuss recent developments in non-Hermitian band topology, such as the non-Hermitian skin effect and non-Hermitian topological classifications

quant-ph↗

arXiv2022

Non-Hermitian eigenvalue knots and their isotopic equivalence

The spectrum of a non-Hermitian system generically forms a two-dimensional complex Riemannian manifold with distinct topology from the underlying parameter space. Spectral topology permits parametric loops to map the affiliated eigenvalue trajectories into knots. In this work, through analyzing exceptional points and their topology, we uncover the necessary considerations for constructing eigenvalue knots and establish their relation to spectral topology. Using an acoustic system with two periodic synthetic dimensions, we experimentally realize several knots with braid index 3. In addition, by highlighting the role of branch cuts on the eigenvalue manifolds, we show that eigenvalue knots produced by homotopic parametric loops are isotopic such that they can deform into one another by type-II or type-III Reidemeister moves. Our results not only provide a general recipe for constructing eigenvalue knots but also expand the current understanding of eigenvalue knots by showing that they contain information beyond that of the spectral topology.

physics.gen-ph↗

arXiv2022

Geometry-dependent skin effects in reciprocal photonic crystals

Skin effect that all eigenmodes within a frequency range become edge states is dictated by the topological properties of complex eigenvalues unique in non-Hermitian systems. The prevailing attempts to realize such a fascinating effect are confined to either one-dimensional or nonreciprocal systems exhibiting asymmetric couplings. Here, inspired by a recent model Hamiltonian theory, we propose a realistic reciprocal two-dimensional (2D) photonic crystal (PhC) system that shows the desired skin effect. Specifically, we establish a routine for designing such non-Hermitian systems via revealing the inherent connections between the non-trivial eigenvalue topology of order-2 exceptional points (EPs) and the skin effects. Guided by the proposed strategy, we successfully design a 2D PhC that possesses the EPs with nonzero eigenvalue winding numbers. The spectral area along a specific wavevector direction is then formed by leveraging the symmetry of the macroscopic geometry and the unit cell. The projected-band-structure calculations are performed to demonstrate that the desired skin effect exists at the specific crystalline interfaces. We finally employ time-domain simulations to vividly illustrate this phenomenon by exciting a pulse at the center of a finite-sized PhC. Our results form a solid basis for further experimental confirmations and applications of the skin effect.

physics.optics↗

arXiv2021

Experimental Realization of Non-Abelian Permutations in a Three-State Non-Hermitian System

Eigenstates of a non-Hermitian system exist on complex Riemannian manifolds, with multiple sheets connecting at branch cuts and exceptional points (EPs). These eigenstates can evolve across different sheets, a process that naturally corresponds to state permutation. Here, we report the first experimental realization of non-Abelian permutations in a three-state non- Hermitian system. Our approach relies on the stroboscopic encircling of two different exceptional arcs (EAs), which are smooth trajectories of order-2 EPs appearing from the coalescence of two adjacent states. The non-Abelian characteristics are confirmed by encircling the EAs in opposite sequences. A total of five non-trivial permutations are experimentally realized, which together comprise a non-Abelian group. Our approach provides a reliable way of investigating non-Abelian state permutations and the related exotic winding effects in non- Hermitian systems.

quant-ph↗

arXiv2021

Direct Measurement of Topological Properties of an Exceptional Parabola

Non-Hermitian systems can produce branch singularities known as exceptional points (EPs). Different from singularities in Hermitian systems, the topological properties of an EP can involve either the winding of eigenvalues that produces a discriminant number (DN) or the eigenvector holonomy that generates a Berry phase. The multiplicity of topological invariants also makes non-Hermitian topology richer than its Hermitian counterpart. Here, we study a parabola-shaped trajectory formed by EPs with both theory and acoustic experiments. By obtaining both the DNs and Berry phases through the measurement of eigenvalues and eigenfunctions, we show that the EP trajectory endows the parameter space with a non-trivial fundamental group consisting of two non-homotopic classes of loops. Our findings not only shed light on exotic non-Hermitian topology but also provide a route for the experimental characterization of non-Hermitian topological invariants.

quant-ph↗

arXiv2021

Čerenkov radiation in vacuum from a superluminal grating

Nothing can physically travel faster than light in vacuum. This is why it has been considered that there is no Čerenkov radiation (ČR) without an effective refractive index due to some background field. In this Letter, we theoretically predict ČR in vacuum from a spatiotemporally modulated boundary. We consider the modulation of traveling wave type and apply a uniform electrostatic field on the boundary to generate electric dipoles. Since the induced dipoles stick to the interface, they travel at the modulation speed. When the grating travels faster than light, it emits ČR. In order to quantitatively examine this argument, we need to calculate the field scattered at the boundary. We utilise a dynamical differential method, which we developed in the previous paper, to quantitatively evaluate the field distribution in such a situation. We can confirm that all scattered fields are evanescent if the modulation speed is slower than light while some become propagating if the modulation is faster than light.

physics.optics↗

arXiv2021

Calculating spatiotemporally modulated surfaces: a dynamical differential formalism

Electromagnetic waves in a system with a space and time dependent boundary experience both diffraction and Doppler-like frequency conversion. In order to analyse such situations, conventional methods call for either the eigenmodes or the dyadic Green's function in space and time dependent media. Here, we propose a dynamical differential method which does not require either of them. Our method utilises a dynamical coordinate transformation in order to simplify the calculation of the optical response of the space and time dependent system. We reveal that the diffraction symmetry is broken in the presence of traveling-wave type spatiotemporal modulation.

physics.optics↗

arXiv2021

Analysis of Emission Dynamics of a Long Lifetime in Single InAs/GaAs Quantum Dots

A very long lifetime emission with non-single exponential decay characteristic has been reported for single InAs/GaAs quantum dot (QD) samples, in which there exists a long-lived metastable state in the wetting layer (WL) [ACS Photonics 2020,7,3228-3235]. In this article we have proposed a new three-level model to simulate the emission decay curve. In this model, assuming that the excitons in metastable state will diffuse and be trapped by QDs, and then emit fluorescence in QDs, a stretched-like exponential decay formula is derived as I(t)=At^(β-1)e^(-(rt)^β), which can well describe the long lifetime decay curve with an analytical expression of average lifetime <τ>=1/rΓ(1/β+1), where Γ is the Gamma function. Furthermore, based on the proposed three-level model, an expression of the second-order auto-correlation function g^2 (t) which can well fit the measured g^2 (t) curve is also obtained.

quant-ph↗

arXiv2020

Exceptional points make an astroid in non-Hermitian Lieb lattice: evolution and topological protection

An astroid-shaped loop of exceptional points (EPs), comprising four cusps, is found to spawn from the triple degeneracy point in the Brillouin zone (BZ) of a Lieb lattice with nearest-neighbor hoppings when non-Hermiticity is introduced. The occurrence of the EP loop is due to the realness of the discriminant which is guaranteed by the non-Hermitian chiral symmetry. The EPs at the four cusps involve the coalescence of three eigenstates, which is the combined result of the non-Hermitian chiral symmetry and mirror-T symmetry. The EP loop is exactly an astroid in the limit of an infinitesimal non-Hermiticity. The EP loop expands from the $M$ point with increasing non-Hermiticity and splits into two EP loops at a critical non-Hermiticity. The further increase of non-Hermiticity contracts the two EP loops towards and finally to two EPs at the $X$ and $Y$ points in the BZ, accompanied by the emergence of Dirac-like cones. The two EPs vanish at a larger non-Hermiticity. The EP loop disappears and several discrete EPs are found to survive when next-nearest hoppings are introduced to break the non-Hermitian chiral symmetry. A topological invariant called the discriminant number is used to characterize their robustness against perturbations. Both discrete EPs and those on the EP loop(s) are found to show anisotropic asymptotic behaviors. Finally, the experimental realization of the Lieb lattice using a coupled waveguide array is discussed.

cond-mat.mes-hall↗

arXiv2020

Plasmon-field-induced Metastable States in the Wetting Layer: Detected by the Fluorescence Decay Time of InAs/GaAs Single Quantum Dots

We report a new way to slow down the spontaneous emission rate of excitons in the wetting layer (WL) through radiative field coupling between the exciton emissions and the dipole field of metal islands. As a result, a long-lifetime decay process is detected in the emission of InAs/GaAs single quantum dots (QDs). It is found that when the separation distance from WL layer (QD layer) to the metal islands is around 20 nm and the islands have an average size of approximately 50 nm, QD lifetime may change from approximately 1 to 160 ns. The corresponding second-order autocorrelation function g(2) (τ) changes from antibunching into a bunching and antibunching characteristics due to the existence of long-lived metastable states in the WL. This phenomenon can be understood by treating the metal islands as many dipole oscillators in the dipole approximation, which may cause destructive interference between the exciton dipole field and the induced dipole field of metal islands.

physics.optics↗

arXiv2020

Angle-Resolved Thermal Emission Spectroscopy Characterization of Non-Hermitian Meta-Crystals

We establish the angle-resolved thermal emission spectroscopy (ARTES) as a new platform to characterize the intrinsic eigenmode properties of non-Hermitian systems. This method can directly map the dispersion of meta-crystals within the light cone with a high angular resolution. To illustrate its usefulness, we demonstrate the existence of bound states in the continuum (BICs) and non-Hermitian Fermi arcs in a planar corrugated meta-crystal by measuring its angle-resolved thermal emission spectra. We show that change in the thickness of the meta-crystal can induce a band inversion between a BIC and a radiative state, and a pair of exceptional points emerge when the band inversion occurs. With this approach, the band mapping of non-Hermitian photonic systems can become a relatively straightforward task.

physics.app-ph↗

arXiv2020

Casimir induced instabilities at metallic surfaces and interfaces

Surface plasmons subject to a surface distortion split asymmetrically in energy resulting in a net lowering of zero-point energy. This is because surface plasmon eigenvalues are the square of frequencies, a statement generally true for electromagnetic excitations. We utilize the method based on conformal mapping to demonstrate asymmetric splitting under surface corrugations leading to a decrease in zero-point energy of a single corrugated metallic surface contributing to surface reconstructions but too small on its own to drive the reconstruction. However, by introducing a second metallic surface more significant lowering of energy is seen sufficient to drive the instability of a mercury thin film.

cond-mat.mes-hall↗

arXiv2019

Exceptional Cones in 4D Parameter Space

The notion of synthetic dimensions has expanded the realm of topological physics to four dimensional (4D) space lately. In this work, non-Hermiticity is used as a synthetic parameter in PT-symmetric photonic crystals to study the topological physics in 4D non-Hermitian synthetic parameter space. We realize a 3D exceptional hypersurface (EHS) in such 4D parameter space, and the degeneracy points emerge due to the symmetry of synthetic parameters. We further demonstrate the existence of exceptional degenerate points (EDPs) on the EHS that originates from the chirality of exceptional points (EPs), and the exceptional surface near EDPs behaves like a Dirac cone. We further show that a very narrow reflection plateau can be found near these EDPs, and their sensitivity towards the PT-symmetry breaking environmental perturbation can make these degeneracy points useful in optical sensing and many other nonlinear and quantum optical applications.

physics.optics↗

arXiv2019

Realization of complex conjugate media using non-PT-symmetric photonic crystals

While parity-time (PT)-symmetric systems can exhibit real spectra in the exact PT-symmetry regime, the PT-symmetry is actually not a necessary condition for the real spectra. Here we show that non-PT-symmetric photonic crystals carrying Dirac-like cone dispersions can always exhibit real spectra as long as the average non-Hermiticity strength within the unit cell for the eigenstates is zero. By building a non-Hermitian Hamiltonian model, we find that the real spectra of the non-PT-symmetric system can be explained using the concept of pseudo-Hermiticity. We demonstrate using effective medium theories that in the long-wavelength limit, such non-PT-symmetric photonic crystals behave like the so-called complex conjugate medium (CCM) whose refractive index is real but whose permittivity and permeability are complex numbers. The real refractive index for this effective CCM is guaranteed by the real spectrum of the photonic crystals and the complex permittivity and permeability comes from the non-PT-symmetric loss-gain distributions. We show some interesting phenomena associated with the CCM, such as the lasing effect.

physics.optics↗

arXiv2019

Realization of Photonic Charge-2 Dirac Point by Engineering Super-modes in Topological Superlattices

Quite recently a novel variety of unconventional fourfold linear band degeneracy points has been discovered in certain condensed-matter systems. Contrary to the standard 3-D Dirac monopoles, these quadruple points referred to as the charge-2 Dirac points are characterized by nonzero net topological charges, which can be exploited to delve into hitherto unknown realms of topological physics. Here, we report on the experimental realization of the charge-2 Dirac point by deliberately engineering hybrid topological states called super-modes in a 1-D optical superlattice system with two additional synthetic dimensions. Utilizing direct reflection and transmission measurements, we exhibit the existence of super-modes attributed to the synthetic charge-2 Dirac point, which has been achieved in the visible region for the first time. We also show the experimental approach to manipulating two spawned Weyl points that are identically charged in synthetic space. Moreover, topological end modes uniquely resulting from the charge-2 Dirac point can be delicately controlled within truncated superlattice samples, opening a pathway for us to rationally engineer local fields with intense enhancement.

physics.optics↗

arXiv2019

Exceptional points and their coalescence of PT-symmetric interface states in photonic crystals

The existence of surface electromagnetic waves in the dielectric-metal interface is due to the sign change of real parts of permittivity across the interface. In this work, we demonstrate that the interface constructed by two semi-infinite photonic crystals with different signs of the imaginary parts of permittivity also supports surface electromagnetic eigenmodes with real eigenfrequencies, protected by $ PT $ symmetry of such loss-gain interface. Using a multiple scattering method and full wave numerical methods, we show that the dispersion of such interface states exhibit unusual features such as zig-zag trajectories or closed-loops. To quantify the dispersion, we establish a non-Hermitian Hamiltonian model that can account for the zig-zag and closed-loop behaviour for arbitrary Bloch momentums. The properties of the interface states near the Brillouin zone center can also be explained within the framework of effective medium theory. It is shown that turning points of the dispersion are exceptional points (EPs), which are characteristic features of non-Hermitian systems. When the permittivity of photonic crystal changes, these EPs can coalesce into higher order EPs or anisotropic EPs. These interface modes hence exhibit and exemplify many complex phenomena related to exceptional point physics.

physics.optics↗

arXiv2019

Plasmon Localization Assisted by Conformal Symmetry

Plasmonic systems have attracted remarkable interest due to their application to the subwavelength confinement of light and the associated enhancement of light-matter interactions. However, this requires light to dwell at a given spatial location over timescales longer than the coupling rate to any relevant loss mechanism. Here we develop a general strategy for the design of stopped-light plasmonic metasurfaces, by taking advantage of the conformal symmetry which underpins near-field optics. By means of the analytical technique of transformation optics, we propose a class of plasmonic gratings which is able to achieve ultra-slow group velocities, effectively freezing surface plasmon polaritons in space over their whole lifetime. Our method can be universally applied to the localization of polaritons in metallic systems, as well as in highly doped semiconductors and even two-dimensional conductive and polar materials, and may find potential applications in nano-focusing, nano-imaging, spectroscopy and light-harvesting.

physics.optics↗

arXiv2019

Machine prediction of topological transitions in photonic crystals

We train artificial neural networks to distinguish the geometric phases of a set of bands in 1D photonic crystals. We find that the trained network yields remarkably accurate predictions of the topological phases for 1D photonic crystals, even for the geometric and material parameters that are outside of the range of the trained dataset. Another remarkable capability of the trained network is to predict the boundary of topological transition in the parameter space, where a large portion of trained data in the vicinity of that boundary is excluded purposely. The results indicate that the network indeed learns the very essence of the structure of Maxwell's equations, and has the ability of predicting the topological invariants beyond the range of the training dataset.

physics.optics↗