Fractional Topological Charge Research Articles

Skyrmion and meron ordering in quasi-two-dimensional chiral magnets

We revisit the well-known theoretical phase diagram for a two-dimensional chiral magnet with an easy-axis uniaxial anisotropy and an applied magnetic field. A particular emphasis is given to merons---quanta of the phase transition between the cycloid and the hexagonal skyrmion lattice, which possess fractional topological charges $\ifmmode\pm\else\textpm\fi{}1/2$. A localized state of two coupled merons with opposite topological charges exhibits the nonreciprocal current-driven dynamics: it experiences no skyrmion Hall effect, but due to the asymmetry of the attracting intermeron potential gives rise to asymmetric current-velocity characteristics. We also address the problem of skyrmion ordering into hexagonal and square skyrmion crystals. In an entire field range, the square lattice turns out a saddle point state between differently oriented hexagonal lattices. Merons separating elongated skyrmions were also shown to form a local energy minimum by forming a hexagonal lattice shadowing the ordinary lattice of skyrmions. In addition, we focus on the anisotropy-driven transformations of modulated phases and their isolated counterparts, which exist as detached branches of solutions on both sides from the critical anisotropy value. Moreover, a family of isolated skyrmions with both rotational senses can be found near this anisotropy value. Our results are useful from both the fundamental point of view, since they complement previous findings, and from the point of view of applications, since they provide guidelines for developing meron-based spintronic devices.

Generating elliptic perfect optical vortex beams with efficient dielectric metasurface in the ultraviolet spectrum

Due to the helical phase profile as well as the topological charge-independent doughnut spatial structure, perfect vortex beams have attract attentions in fiber communications and particle manipulations. However, for some advanced applications such as optical cage and optical microfluidic sorting and acceleration, it is more meaningful to generate asymmetric optical vortex fields such as elliptic perfect optical vortex (EPOV) beams. Herein we utilize silicon nitride nanopillars, functioning as half-wave plates, to construct high-efficiency geometric phase metasurfaces for the generation of EPOV beams with the integer and fractional topological charges in the ultraviolet range. By adjusting scaling factor, the shape of beams can be freely changed from circle to ellipse. In addition, multi-channel EPOV beams with arbitrary shape and different topological charges are produced with the help of the superposition principle of phase in Fourier space. We envision that this ultraviolet metasurface-based generator of EPOV beams can be used for manipulation of microscopic particle along an ellipse with acceleration and for the generation OAM-entangled photons.

SU(N) fractional instantons and the Fibonacci sequence

We study, by means of numerical methods, new SU(N) self-dual instanton solutions on R × T3 with fractional topological charge Q = 1/N. They are obtained on a box with twisted boundary conditions with a very particular choice of twist: both the number of colours and the ’t Hooft ZN fluxes piercing the box are taken within the Fibonacci sequence, i.e. N = Fn (the nth number in the series) and left|overrightarrow{m}right| = left|overrightarrow{k}right| = Fn−2. Various arguments based on previous works and in particular on ref. [1], indicate that this choice of twist avoids the breakdown of volume independence in the large N limit. These solutions become relevant on a Hamiltonian formulation of the gauge theory, where they represent vacuum-to-vacuum tunneling events lifting the degeneracy between electric flux sectors present in perturbation theory. We discuss the large N scaling properties of the solutions and evaluate various gauge invariant quantities like the action density or Wilson and Polyakov loop operators.

From concept to reality: computing visual vortex beam interferometer for displacement measurement.

In addition to the concept of picometer resolution, we discuss macro displacement measurement with a vortex beam interferometer. Three factors limiting large displacement measurement are resolved. Small topological charge numbers promise both high sensitivity and large displacement measurements. With a computing visual method, a virtual moiré pointer image immune to beam misalignment is proposed to calculate displacements. Interestingly, the absolute benchmark is found for cycle counting in the moiré pointer image of fractional topological charge. The vortex beam interferometer would not stop at the tiny displacement measurement in simulations. We report experimental measurements of nanoscale to hundred millimeter displacement in a vortex beam displacement measurement interferometer (DMI) for the first time, to the best of our knowledge.

Multiple-image encryption using phase jump gradient factors -based OAM multiplexing holography

Orbital angular momentum (OAM) has been widely implemented in information encryption as an independent degree of freedom. In this paper, we propose using phase gradient factor of vortex phase structure as an independent degree of freedom for further boosting OAM information carrying capacity. The orthogonality of different phase gradient factors is firstly demonstrated. Multiple images encoded in different phase gradients even with the same integral or fractional topological charge (TC) can be simultaneously encrypted free of crosstalk. Herein, the safety and the multiplexing capacity are greatly enhanced while keeping the fractional topological charge interval as small as 0.1. In the decryption process, the encoded information can only be reconstructed under the incident vortex beam illumination with inverse TC at correct focus distances and accurate phase jump gradient factors. The feasibility and the security of proposed method are both verified in the experiments and the numerical simulations. This opens up a new avenue for high security and practical information encryption systems.

Quantum anomalous semimetals

The topological states of matter and topological materials have been attracting extensive interests as one of the frontier topics in condensed matter physics and materials science since the discovery of quantum Hall effect in 1980s. So far all the topological phases such as integer quantum Hall effect and topological insulators are characterized by integer topological invariants. None is a half integer or fractional. Here we propose a type of semimetals which hosts a single cone of Wilson fermions. The Wilson fermions possess linear dispersion near the Dirac point, but break the chiral or parity symmetry such that an unpaired Dirac cone can be realized on a lattice. In order to avoid the fermion doubling problem, the chiral symmetry or parity symmetry must be broken explicitly if the hermiticity, locality and translational invariance all hold. We find that the system can be classified by the relative homotopy group, and a half-integer topological invariant. We term the nontrivial quantum phase as quantum anomalous semimetal. The work opens the door towards exploring novel states of matter with fractional topological charge.

Generation of terahertz radiation with fractional or integer OAMs from a fractional-order vortex two-color field

This paper investigates the generation of the ultra-broadwidth (0.1–30 THz) terahertz (THz) radiation carrying fractional/integer orbital angular momentums (OAMs) via the interaction of the two-color (ω 0 and 2ω 0) laser field carrying initial fractional topological charges (TCs) with air in a moderate pump intensity regime (20 TW cm−2 < I pump < 50 TW cm−2). The two four-wave mixing (FWM) processes (i.e., ω 0 + ω′0 − 2ω 0 → ω THz and 2ω 0 − ω 0 − ω′0 → ω THz) are responsible for THz generation. The two processes can produce two THz pulses. They interfere with each other and THz interference vortex beams are obtained. More importantly, the generation probability from the first FWM process grows while that of the second process declines in the positive frequency region over distance. This is largely due to the combined action of phase mismatch and the blue shift of the THz center frequency. For a longer distance, THz fractional vortex beams (FVBs)/integer vortex beams (IVBs) are produced by the dominant FWM process (ω 0 + ω′0 − 2ω 0 → ω THz). Therefore, via employing different combinations of the initial TCs of the ω 0 and 2ω 0 pulses, one can manipulate the generation of the THz vortex beams with arbitrary fractional-order or integer-order TCs at some specific propagation distances. What is even more interesting is that, when employing half-integer TCs, THz FVBs with varying TC over distance can be produced, companied with birth and annihilation of the alternative vortex pair. This is principally due to diffraction-related effects and the unstable nature of the fractional vortex structures. This simple manipulation for THz waves carrying arbitrary fractional or integer TCs in this scheme encourages the applications for optically rotation, manipulation of molecular or cell assays and image edge enhancement in the field of biomedicine.

Parallel creation of propagable integer- and fractional-order vector vortex beams using mode extraction principle.

Propagable fractional-order vector vortex beams with fractional topological charge provide new possibilities in optics. However, their complicated polarizations give rise to a big challenge in creating multiple vector vortex beam channels. Here, we solve this scientific problem by generating fractional- and integer-order vector vortex beams in parallel using the mode extraction principle along with an optical pen. Based on the principle of mode extraction, integer- and fractional-order vector vortex beams can be extracted in the focal region of an objective lens directly from a single m = 30-order vector vortex beam. Their number, position, amplitude, and phase are further controlled by the parameters of an optical pen. This work not only presents an example of how to manipulate the polarization and phase of a light beam simultaneously using the principle of mode extraction, but also may open new avenues for the applications of integer- and fractional-order vector vortex beams.

Generation of integer and fractional perfect vortex beams using all-dielectric geometrical phase metasurfaces

Perfect vortex (PV) beams possess a radial intensity profile independent of their topological charges, overcoming the defects of the regular vortex beams. However, the bulky optical elements used in conventional methods for generation of PV beams limit their potential applications. Metasurfaces are ultra-thin version of metamaterials with the flexible ability of controlling electromagnetic waves, promising great potential applications in many optical fields. Here, an all-dielectric metasurface based on a geometrical phase is demonstrated, featuring broadband and high efficiency in manipulation of circularly polarized light. We numerically simulate the performance of the unit-cell and metasurface for generating PV beams carrying integer and fractional topological charges. We hope the designed metasurface will provide an ultra-compact way for generation of high-quality PV beams.

Distributed Edge-Enhanced Imaging With a Fractional Spiral Phase Filter Using Random Light

A gradual edge-enhanced ghost imaging method with pseudo-thermal light is proposed in both the theory and experiment. In the experiment, a phase object and fractional spiral phase filter are placed symmetrically in the imaging plane of the pseudo-thermal light source in the distributed test and reference beams of the lensless ghost imaging system. The procedure of gradual edge-enhanced ghost imaging is carried out by modulating the fractional topological charge from 0 to 1. We observe that the brightness of the object edge increases with the increase of the fractional topological charge. It is also found that the intensity distribution is uniform and isotropic when the topological charge is an integer; otherwise, the intensity distribution is not uniform. Theoretical analysis is also provided. The proposed gradual edge-enhanced ghost imaging scenario releases the position limitation in the Fourier plane for the filter of the traditional phase filtering imaging process. The method is believed to have prospective applications in microscopic imaging and biomedical detection.

A Theoretical Description of Integrated OAM Beam Emitters Using Conical Wave Model

A theoretical model, suitable for multiple structures of integrated vortex beam emitters, is proposed, developed and verified. Using the interference superposition of multiple plane waves in the far-field plane, which have the same wavevector in the z-direction, the expressions of the orbital angular momentum (OAM) beam field emitted from integrated devices are obtained. The results are applicable to OAM beams with larger or fractional topological charges, and consider different initial polarization states, which means different structures. Especially, when ϑ = 0, p = 0, the result is the same as those derived from the dipole model and is consistent with the previous experimental results. The calculated results show that it can obtain more accurate far-field light field with topological charge l increasing gradually and gain the same Ex and Ey with different initial polarization states. By constructing this model, the generation mechanism of the integrated OAM beam emitters can be easily understood and the beam vortex can be generated naturally and flexibly.

Spin-current instability at a magnetic domain wall in a ferromagnetic superfluid: A generation mechanism of eccentric fractional skyrmions

Spinful superfluids of ultracold atoms are ideal for investigating the intrinsic properties of spin current and texture because they are realized in an isolated, nondissipative system free from impurities, dislocations, and thermal fluctuations. This study theoretically reveals the impact of spin current on a magnetic domain wall in spinful superfluids. An exact wall solution is obtained in the ferromagnetic phase of a spin-1 Bose-Einstein condensate with easy-axis anisotropy at zero temperature. The bosonic-quasiparticle mechanics analytically show that the spin current along the wall becomes unstable if the velocity exceeds the critical spin-current velocities, leading to complicated situations because of the competition between transverse magnons and ripplons. Our direct numerical simulation reveals that this system has a mechanism to generate an eccentric fractional skyrmion, which has a fractional topological charge, but its texture is not similar to that of a meron. This mechanism is in contrast to the generation of conventional skyrmions in easy-axis magnets. The theoretical findings can be examined in the same situation as in a recent experiment on ultracold atoms. In terms of the universality of spontaneous symmetry breaking, unexplored similar phenomena are expected in different physical systems with the same broken symmetry.

Zoology of Multiple-Q Spin Textures in a Centrosymmetric Tetragonal Magnet with Itinerant Electrons.

Magnetic skyrmion is a topologically stable particle‐like swirling spin texture potentially suitable for high‐density information bit, which was first observed in noncentrosymmetric magnets with Dzyaloshinskii–Moriya interaction. Recently, nanometric skyrmion has also been discovered in centrosymmetric rare‐earth compounds, and the identification of their skyrmion formation mechanism and further search of nontrivial spin textures are highly demanded. Here, magnetic structures in a prototypical skyrmion‐hosting centrosymmetric tetragonal magnet GdRu2Si2 is exhaustively studied by performing the resonant X‐ray scattering experiments. A rich variety of double‐Q magnetic structures, including the antiferroic order of meron(half‐skyrmion)/anti‐meron‐like textures with fractional local topological charges are identified. The observed intricate magnetic phase diagram is successfully reproduced by the theoretical framework considering the four‐spin interaction mediated by itinerant electrons and magnetic anisotropy. The present results will contribute to the better understanding of the novel skyrmion formation mechanism in this centrosymmetric rare‐earth compound, and suggest that itinerant electrons can ubiquitously host a variety of unique multiple‐Q spin orders in a simple crystal lattice system.

Conversions of linear-circular polarizations and spin-orbital angular momentums in a focused vector vortex beam with fractional topological charges

We perform theoretical and experimental studies on the tight focusing properties of a vector vortex beam with fractional order topology charges. The fractional-order vector vortex optical fields (FO-VVOF) are experimentally generated by using the 4f system and the hologram technology. In comparison to the integral-order vortex, the 3-dimensional (3D) field distributions of FO-VVOF in the focal volume exhibit unique vectorial structure characteristics. The conversions between the linear and the circular polarizations (spin angular momentum) occur in a tight focusing fractional vortex. Furthermore, the hybrid spin-orbital angular momentum conversions in the longitudinal component in a tight focusing FO-VVOF lead to the interesting distributions of the orbital angular momentum. The dynamic conversions closely depend on the initial topology charge numbers and polarization distributions. The underlying physics of this unique phenomenon is discussed in detail. These results may have potential applications in particle micro-manipulation, quantum information processing and optical field manipulation.

Nonperturbative effects in the Standard Model with gauged 1-form symmetry

We study the Standard Model with gauged {mathrm{mathbb{Z}}}_{N=2,3,6}^{(1)} subgroups of its {mathrm{mathbb{Z}}}_6^{(1)} 1-form global symmetry, making the gauge group frac{mathrm{SU}(3)times mathrm{SU}(2)times mathrm{U}(1)}{{mathrm{mathbb{Z}}}_N} . We show that, on a finite {mathbbm{T}}^3 , there are self-dual instantons of fractional topological charge. They mediate baryon- and lepton-number violating processes. We compare their amplitudes to the ones due to the usual BPST-instantons. We find that the small hypercharge coupling suppresses the fractional-instanton contribution, unless the torus size is taken sub-Planckian, or extra matter is added above the weak scale. We also discuss these results in light of the cosmological bounds on the torus size.

Strongly coupled QFT dynamics via TQFT coupling

We consider a class of quantum field theories and quantum mechanics, which we couple to ℤN topological QFTs, in order to classify non-perturbative effects in the original theory. The ℤN TQFT structure arises naturally from turning on a classical background field for a ℤN 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to ℤN TQFT, the non-perturbative expansion parameter is exp[−SI/N] = exp[−8π2/g2N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T3 × {S}_L^1 can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in mathbbm{CP} 1 model, and mass gap for arbitrary θ in mathbbm{CP} N−1, N ≥ 3 on ℝ2.

Machine learning based accurate recognition of fractional optical vortex modes in atmospheric environment

Optical vortex beam with fractional orbital angular momentum (OAM) has great potential to increase the capacity of optical communication and information processing in classical and quantum regimes. However, atmospheric turbulence (AT) in free space distorts the helical phase-front of vortex beams and causes the mode diffusion, seriously hindering the practical application. Herein, using a convolutional neural network approach with an improved residual neural network architecture, we overcome the hurdle to give the accurate recognition of the fractional OAM in the AT. As demonstrated on the petal interference patterns, a type of hybrid beams carrying double OAM modes is utilized to provide two controllable degrees of freedom for greater recognition of more subtle OAM modes, e.g., the fractional topological charge number l and the angular ratio n. Our studies show that with various l and n, the recognition accuracy of OAM over 20 000 images is as high as 85.30% even under the strong AT parameter (Cn2 = 5 × 10−14 m−2/3) and the long propagation distance (z = 1500 m). Our findings represent a remarkable achievement toward highly accurate recognition of fractional OAM with broad bandwidth in the atmospheric environment, expanding the applications for the general interest of machine learning based OAM optical communication.

Angular momentum of the vortex ultrashort pulsed beam with a smaller beam waist.

The angular momentum (AM) of light has important implications for many fields of optics research, such as optics communication, quantum information and laser-scan microscopy. Thus, in this paper, we intend to investigate the average AM of the vortex ultrashort pulsed beam (VUPB), which is generated and widely applied in the field of high-intensity and ultrafast regimes. According to the vector potential, we firstly derive the electromagnetic field of the VUPB, then analyze the spatial intensity, the phase profile and the polarization state of the beam. We explore that the total AM per photon of VUPB is not n ℏ value when the beam waist w0 is of wavelength or sub-wavelength order, since the polarization of VUPB is changed from linear to circular polarization with the decrease of beam waist, which introduces the conversion of the orbital AM to the spin AM. Moreover, based on the conservation of the total AM, the minimum waist of VUPB can be obtained, which is dependent on the pulse duration time α and topological charge n. Finally, the average AM of the fractional VUPB expressed by the superposition of the integer VUPB with different weights, is analyzed, which is not equal to the AM of fractional CW beam μ - sin (2μπ)/2π (μ is the fractional topological charge), but is associated with the beam waist w0 and α. Therefore, we think that the AM of VUPB can be controlled by adjusting the α and w0.

Quasi-stable fractional vortex solitons in nonlocal nonlinear media

This paper studied the propagations of fractional vortex beams in nonlocal nonlinear media, and found that quasi-stable solitons can form when the nonlocality is strong enough and the initial power is equal to the critical power. The propagation properties, including intensity patterns, phase structures, transverse energy flows, and rotation period, were all investigated. The critical power of solitons with different topological charges is the same, however, the orbital angular momentum (OAM) of that increases with the increase of fractional topological charge. In addition, we revealed that fractional vortex solitons have lateral shifts in the y-direction, and the shift values can be controlled by the fractional topological charge. Obviously, the quasi-stable fractional vortex solitons have important academic value and potential application to optical switches, optical wrenches and optical communications, etc.

Vortex random fiber laser with controllable orbital angular momentum mode

In this paper, we propose and experimentally demonstrate a vortex random fiber laser (RFL) with a controllable orbital angular momentum (OAM) mode. The topological charge of the vortex RFL can range from − 50 t o 50 with nearly watt-level output power. A triangular toroidal interferometer is constructed to verify the spiral phase structure of the generated vortex random laser with a special coherence property. Vortex RFLs with fractional topological charge are also performed in this work. As the first demonstration of a vortex RFL with a controllable OAM mode (to the best of our knowledge), this work may not only offer a valuable reference on temporal modulation of a vortex beam and optical field control of an RFL but also provide a potential vortex laser source for applications in imaging, sensing, and communication.