Topological Charge Research Articles

Circle packing on spherical caps

We have studied the packing of congruent disks on a spherical cap, for caps of different size and number of disks, N. This problem has been considered before only in the limit cases of circle packing inside a circle and on a sphere (Tammes problem), whereas all intermediate cases are unexplored. Finding the preferred packing configurations for a domain with both curvature and border could be useful in the description of physical and biological systems (for example, colloidal suspensions or the compound eye of an insect), with potential applications in engineering and architecture (e.g., geodesic domes). We have carried out an extensive search for the densest packing configurations of congruent disks on spherical caps of selected angular widths (θmax=π/6, π/4, π/2, 3π/4, and 5π/6) and for several values of N. The numerical results obtained in the present work have been used to establish (at least qualitatively) some general features for these configurations, in particular the behavior of the packing fraction as function of the number of disks and of the angular width of the cap, or the nature of the topological defects in these configurations (it was found that as the curvature increases, the overall topological charge on the border tends to become more negative). Finally, we have studied the packing configurations for N=19, 37, 61, and 91 (hexagonal numbers) for caps ranging from the flat disk to the whole sphere, to observe the evolution (and eventual disappearance) of the curved hexagonal packing configurations while increasing the curvature.

Spin-Locked WS2 Vortex Emission via Photonic Crystal Bound States in the Continuum.

Owing to their strong exciton effects and valley polarization properties, monolayer transition-metal dichalcogenides (1L TMDs) have unfolded the prospects of spin-polarized light-emitting devices. However, the wavefront control of exciton emission, which is critical to generate structured optical fields, remains elusive. In this work, the experimental demonstration of spin-locked vortex emission from monolayer Tungsten Disulfide (1L WS2) integrated with Silicon Nitride (SiNx) PhC slabs is presented. The symmetry-protected bound states in the continuum (BIC) in the SiNx PhC slabs engender azimuthal polarization field distribution in the momentum space with a topological singularity in the center of the Brillouin zone, which imposes the resonantly enhanced WS2 exciton emission with a spin-correlated spiral phase front by taking advantage of the winding topologies of resonances with the assistance of geometric phase scheme. As a result, exciton emission from 1L WS2 exhibits helical wavefront and doughnut-shaped intensity beam profile in the momentum space with topological charges locked to the spins of light. This strategy on spin-dependent excitonic vortex emission may offer the unparalleled capability of valley-polarized structured light generation for 1L TMDs.

Single pair of charge-2 Dirac and charge-2Weyl phonons in GeO2

Abstract The presence of a pair of Weyl and Dirac points (WP–DP) in topological semimetal states is intriguing and sought after due to the effects associated with chiral topological charges. However, identifying these states in real materials poses a significant challenge. In this study, by means of first-principles calculations we predict the coexistence of charge-2 Dirac and charge-2 Weyl phonons at high-symmetry points within a noncentrosymmetric P41212 space group. Furthermore, we propose GeO2 as an ideal candidate for realizing these states. Notably, we observe two distinct surface arcs that connect the Dirac and Weyl points across the entire Brillouin zone, which could facilitate their detection in future experimental investigations. This study not only presents a tangible material for experimentalists to explore the topological properties of WP–DP states but also opens up new avenues in the quest for ideal platforms to study chiral particles.

Full QCD with milder topological freezing

We simulate Nf = 2 + 1 QCD at the physical point combining open and periodic boundary conditions in a parallel tempering framework, following the original proposal by M. Hasenbusch for 2d CPN−1 models, which has been recently implemented and widely employed in 4d SU(N) pure Yang-Mills theories too. We show that using this algorithm it is possible to achieve a sizable reduction of the auto-correlation time of the topological charge in dynamical fermions simulations both at zero and finite temperature, allowing to avoid topology freezing down to lattice spacings as fine as a ∼ 0.02 fm. Therefore, this implementation of the Parallel Tempering on Boundary Conditions algorithm has the potential to substantially push forward the investigation of the QCD vacuum properties by means of lattice simulations.

Eliminating Skyrmion Hall Effect in Ferromagnetic Skyrmions.

Skyrmion Hall effect (SkHE) remains an obstacle for the application of magnetic skyrmions. While methods have been established to cancel or compensate SkHE in artificial antiferromagnets and ferrimagnets, eliminating intrinsic SkHE in ferromagnets is still a big challenge. Here, we propose a strategy to eliminate SkHE by intercalating nonmagnetic elements into van der Waals bilayer ferromagnets featuring in-plane ferromagnetism. The in-plane magnetism, along with a delicate balance among exchange interactions, Dzyaloshinskii-Moriya interactions (DMI), and magnetocrystalline anisotropy, creates interlayer bimerons/quadmerons, whose polarity can be controlled by DMI. Opposite DMI in the upper and lower layers results in opposite polarity and topological charge number Q-locking of topological spin texture, therefore, eliminating the SkHE. By intercalating Sr (Ba) in bilayer VSe2, we identify ten topological magnetic structures with zero topological charge number. Furthermore, we present a phase diagram illustrating diverse magnetic configurations achievable within the bimagnetic atomic layer, offering valuable guidance for future investigations.

Holographic encryption with power-exponent helicon-conical optical vortices

We present a holographic encryption technique that combines the orbital angular momentum (OAM) multiplexing method with power-exponent helico-conical (PEHC) optical vortices. By incorporating the power exponent and normalization factor of the PEHC beam's phase into the selective modulation of OAM modes, we unlock their potential as encoding degrees of freedom in holographic multiplexing. Through the integration of these parameters with the topological charge, we develop an approach to OAM multiplexing for encryption, increasing both the storage capacity of holographic information and data security. To validate our proposed method, we conducted numerical simulations and optical experiments, which confirmed the promising potential of utilizing the adopted noncanonical vortices as an efficient and reliable strategy for achieving holographic encryption.

High-topological-number skyrmions with tunable diameters in two-dimensional frustrated J1−J2 magnets

Skyrmions are intriguing quasiparticles in the field of condensed matter due to their unique physics and promising applications in spintronic devices. However, despite abundant studies on skyrmions with a topological charge of Q = 1, there have been only few on those with higher Q (≥2) due to their intrinsic instability in Dzyaloshinskii–Moriya interaction (DMI) systems. In this work, applying the frustrated J1−J2 Heisenberg spin model, we investigate the stability of high-Q skyrmions and the manipulation of their diameters in a hexagonal close-packed lattice through atomistic simulations and first-principles calculations. First, three spin textures, called spiral, skyrmion, and ferromagnetic, are identified by varying (J1, J2), and it is shown that skyrmions with higher Q can occupy a wider range of (J1, J2) values. The diameter of the skyrmions can then be finely tuned using the frustration strength (|J2/J1|), the single-ion anisotropy (K), and an external magnetic field (B). As B increases, the high-Q skyrmions split into skyrmions with smaller Q and can be annihilated by a larger B. Furthermore, we find that the CoCl2 monolayer satisfies the criteria for a frustrated J1−J2 magnet, and its magnetic behaviors align with the aforementioned conclusions. In addition, high-Q skyrmions are identified in the CoCl2 monolayer, and the corresponding energy barriers for skyrmion collapse are investigated. Our findings pave the way for prospective spintronic applications based on high-Q and nanoscale skyrmionic textures.

ExSitu Production and Storage of Exciton-Polariton Vortices in Higher-Order Topological Corner Modes.

We propose a scheme for producing and manipulating quantized exciton-polariton vortices in the higher-order topological corner modes of a two-dimensional array of micropillars. By nonresonantly exciting p-orbital condensates with different orientations at two input corners, polariton vortices carrying the required topological charges can be controllably created at output corners away from the pumping spots. Besides, polariton vortices formed at input corners can be copied to the output corners through the topological edge states. Our scheme provides topological double insurance for intrinsic binary information memory and holds potential applications in remote information processing.

Improving the Stationary Entanglement of a Laguerre-Gaussian Cavity Mode with a Rotating Mirror via Nonlinear Cross-Kerr Interactions and Parametric Interactions.

Quantum entanglement is essential in performing many quantum information tasks. Here, we theoretically investigate the stationary entanglement between a Laguerre-Gaussian (LG) cavity field and a rotating end mirror in an LG-cavity optorotational system with a nonlinear cross-Kerr (CK) interaction and a degenerate optical parametric amplifier (OPA). We calculate the logarithmic negativity of the system to quantify the stationary entanglement. We examine the influence of various system parameters such as the cavity detuning, the strength of the nonlinear CK interaction, the parametric gain and phase of the OPA, the power of the input Gaussian laser, the topological charge of the LG-cavity field, the mass of the rotating end mirror, and the ambient temperature on the stationary entanglement. Under the combined effect of the nonlinear CK interaction and the OPA, we find that the stationary entanglement can be substantially enhanced at lower Gaussian laser powers, smaller topological charges of the LG-cavity field, and larger masses of the rotating end mirror. We show that the combination of the nonlinear CK interaction and the OPA can make the stationary entanglement more robust against the ambient temperature.

Toroidal phase topologies within paraxial laser beams

Control of topologies in structured light fields with multi-degrees of freedom integrates fundamental optical physics and topological invariance. Beyond the simple phase vortex, three-dimensional (3D) topological singularities and related nonsingular textures have recently gained significant interest. Here, we experimentally demonstrate the creation of a family of toroidal phase topologies within paraxial laser beams. By employing single two-dimensional (2D) phase control, we generate propagating 3D topological textures, effectively embodying the topological configuration of a four-dimensional (4D) parameter space. The resulting light fields exhibit amplitude isosurfaces of toroidal vortices and hopfionic phase textures, both controlled by topological charges. The ability to prepare scalar phase textures of light offers new insights into the high-dimensional control of complex structured textures and may find significant applications in light-matter interactions, optical manipulation, and optical information encoding.

Bessel–Bessel–Gaussian vortex laser beams

Abstract We obtain and investigate Bessel–Bessel–Gaussian vortex beams (BBG beams) with the complex amplitude being equal to a product of the Gaussian function with two Bessel functions, whose arguments are expressed as complicated radicals including the cylindrical coordinates and a free parameter that defines the shape of the intensity distribution. If this parameter is small, the intensity has the shape of an inhomogeneous ring. For larger values of this parameter, the intensity has the shape of two arcs or ‘crescents’, oriented by their concave sides to each other. The complex amplitude of such beams is derived in explicit form for an arbitrary distance from the waist. We demonstrate that the BBG beams rotate upon propagation anomalously fast: at a distance much shorter than the Rayleigh length, the intensity distribution is already rotated by almost 45°, whereas typically, the rotation angle of vortex Gaussian beams is equal to the Gouy phase. It is also shown that the parameter of the BBG beam allows controlling its topological charge (TC): when the parameter value is positive and increases, the beam TC also increases stepwise by an even number. Besides, we study two other similar vortex BBG beams: either with four local intensity maxima, lying on the Cartesian coordinates axes, or with one intensity maximum with a crescent shape, whose center is on the horizontal axis. The derived three new families of asymmetric vortex laser beams, whose complex amplitude is described by explicit analytical expressions at an arbitrary distance from the waist, extend the variety of laser beams that can be used for manipulating and rotating microparticles, free space data transmission, and in quantum informatics.

Perfect vortex beams generation based on reflective geometric phase metasurfaces

Perfect vortex beam (PVB) is a propagating light field with radial intensity distribution independent of topological charge and carrying orbital angular momentum (OAM). PVBs can be generated through the Fourier transformation of a Bessel-Gaussian (BG) beam, which traditionally requires a precisely aligned optical setup consisting of a spiral phase plate, a conical lens, and a Fourier lens. However, such traditional schemes are usually bulky and unstable. Here, we have utilized a method that differs from conventional approaches, employing metasurfaces designed as planar Pancharatnam-Berry (PB) phase elements to substitute for all the required components. Unlike traditional methods based on reflective or refractive elements, metasurface elements can significantly reduce the system's footprint. Because the use of metallic metasurfaces allows for a more flattened design plane, in this paper, we have demonstrated the generation of PVB within the 8 GHz microwave frequency band based on a single-layer metallic metasurface. The metasurface is composed of a square ring metal structure, which can serve as a half wave plate to provide the required geometric phase distribution for incident circularly polarized light to generate PVB. By rigorously optimizing the parameters of the square-ring structures, we have generated vortex beams carrying OAM with different topological charges. These vortex beams exhibit a constant radial intensity distribution, which validates their "perfect" characteristics. In addition, we also extracted the mode purity of different vortex beams, so that the mode states of different vortex beams can be distinguished. These results provide broader value for the application of perfect vortex beams in communication.

A novel multiple-image encryption with multi-petals structured light

The study proposed a novel multiple-image encryption scheme using spatial multiplexing under the illumination of a multi-petals structured light. The security is enhanced through the multi-petals structured light with coherent superposition of several vortex beams with different topological charges. Through the system, an image array is formed behind the sub-petals of the complex structured light. Using Fresnel diffraction, each image is encrypted into the ciphertext by the Fibonacci Lucas transform. The multi-petals structured light with different orbital angular momentum can integrate more system parameters as the additional keys resulting in rich key space with improved security level of the cryptosystem. The feasibility and security of the proposed methods are validated through both numerical simulation and experiments. The research has strong and practical applications for three-dimensional information encryption system.

Micro-displacement measurement of optical interference with two-ring conjugated vortices

In this paper, we propose a two-ring conjugated vortex beam interferometer. The inner ring and outer ring of the vortex beams has different signs and topological charges. When combined, they produce an intricate pattern of interference fringes that resemble a flower petal, featuring both concentric inner and outer rings which rotates with different directions. We use the scale-invariant feature transformation algorithm to find the feature points. Then we use these points to measure the rotation angle of the outer ring relative to the inner ring and calculate the displacement based on it. We realize the measurement of sub-nanometer displacement. The displacement resolution is 0.38° nm−1. It is improved by about 12.55% compared with only the inner ring. The displacement corresponding to the minimum detectable angle of CCD is reduced from 0.080 nm to 0.060 nm. It will be a promising method in precision machining micro-vibration sensing, surface unevenness sensing, and microbial movement sensing and high-precision measurement of micro-displacement.

Lattice generation utilizing fractional Talbot effect and high-order orbital angular momentum optical vortices

The concept of orbital angular momentum (OAM) has garnered significant attention from researchers since its discovery, with a steady uncovering of its properties over the past three decades. Initially overlooked, the role of OAM in the optical vortex lattice (OVL) has gained prominence due to recent scholarly efforts. This study delves into the modification of OAM by employing controlled topological charge to generate high-order OVL. Furthermore, it explores the Talbot effect within the context of multi-beam interference. The findings indicate that the interference of three beams of light results in the formation of both Kagome and Super-honeycomb lattices, whereas the interference of four beams leads to the emergence of the Lieb lattice. This research offers novel insights into light interference and light field regulation and its application.

Reconfigurable directional selective tunneling of p-type phonons in polarized elastic wave systems

There have been many studies on the ground state of phononic crystals, but few studies on the nature of the excited state. In this paper, we introduce the asymmetric Klein tunneling method in phononic systems, which enables selective direction and control of elastic waves by inducing polarization through an external field in an artificial barrier. Using tight-binding theory, we systematically studied phononics in a super-honeycomb structure, demonstrating the anisotropic transition properties of excited state phonons through a matrix model involving the ground state’s s-type and the first excited state’s p-type wave functions. Additionally, we exploit the thermal sensitivity of epoxy to achieve localized thermal field-induced distortion of the bottom flat band, forming a tiled Dirac cone, and thereby creating a reconfigurable polarized artificial barrier in the elastic wave system. Elastic waves propagate in these systems with topological charge conservation. Combining this with the theoretical of excited-state phonons, we demonstrate asymmetric Klein tunneling with directional selectivity in the elastic wave carriers, and systematically investigate the performance of this tunneling. Furthermore, we design a four-port elastic waveguide based on the principle of asymmetric tunneling, which achieves exceptional directional selectivity of elastic wave signals by adjusting the polarization direction of barriers at the junctions. These studies not only extend the application of Klein tunneling in elastic wave systems but also open new research avenues for the study of elastic wave devices controlled by various external fields, showing direct application potential in elastic wave signal processing.

Thermodynamic topology of quantum corrected AdS-Reissner-Nordstrom black holes in Kiselev spacetime

In this paper, we consider the intricate thermodynamic topology of quantum-corrected Anti-de Sitter-Reissner-Nordstrm (AdS-RN) black holes within the framework of Kiselev spacetime. By employing the generalized off-shell Helmholtz free energy approach, we meticulously compute the thermodynamic topology of these selected black holes. Furthermore, we establish their topological classifications. Our findings reveal that quantum correction terms influence the topological charges of black holes in Kiselev spacetime, leading to novel insights into topological classifications. Our research findings elucidate that, in contrast to the scenario in which ω = 0 and a = 0.7 with total topological charge W = 0 and ω = –4/3 with total topological charge W = –1, in other cases, the total topological charge for the black hole under consideration predominantly stabilizes at +1. This stabilization occurs with the significant influence of the parameters a, c, and ω on the number of topological charges. Specifically, when ω assumes the values of ω = –1/3, ω = –2/3, and ω = –1, the total topological charge will consistently be W = +1.

Topological charge and spin Hall effects due to skyrmions in canted antiferromagnets

Topological charge and spin Hall effects due to skyrmions in canted antiferromagnets

Synthetic non-Abelian topological charges in ultracold atomic gases

Synthetic non-Abelian topological charges in ultracold atomic gases

On the stability of vortex quantum droplets

We discuss the stability of topological quantum droplets with the shape of two-dimensional soliton rings endowed with angular momentum that stem from a symmetric binary mixture in a Bose–Einstein condensate, with a strong trapping in one of the three spatial dimensions. We show that, in the lossless symmetric case, modeled by a Schrödinger equation with a Shannon-type nonlinear potential function, stable eigenstates can exist for arbitrarily large values of their topological charge l, provided the number of atoms is above a certain threshold. By comprehensive numerical computations, we analyze in detail cases up to l=50. We have found the perturbation modes and their eigenvalues, determining in each case which one dominates and destabilizes the solutions that lie below the stability threshold. We compare these results to the fate of the eigenstates that evolve in time. We also study the stability of the droplets under dynamical conditions by simulating collisions with potential barriers.