Higher-order States Research Articles

Rotating nonlinear states in trapped binary Bose–Einstein condensates under the action of the spin–orbit coupling

Abstract We report results of systematic analysis of confined steadily rotating patterns in the two-component BEC including the spin–orbit coupling (SOC) of the Rashba type, which acts in the interplay with the attractive or repulsive intra-component and inter-component nonlinear interactions and confining potential. The analysis is based on the system of the Gross–Pitaevskii equations (GPEs) written in the rotating coordinates. The resulting GPE system includes effective Zeeman splitting. In the case of the attractive nonlinearity, the analysis, performed by means of the imaginary-time simulations, produces deformation of the known two-dimensional SOC solitons (semi-vortices and mixed-modes). Essentially novel findings are reported in the case of the repulsive nonlinearity. They demonstrate patterns arranged as chains of unitary vortices which, at smaller values of the rotation velocity Ω, assume the straight (single-string) form. At larger Ω, the straight chains become unstable, being spontaneously replaced by a trilete star-shaped array of vortices. At still larger values of Ω, the trilete pattern rebuilds itself into a star-shaped one formed of five and, then, seven strings. The transitions between the different patterns are accounted for by comparison of their energy. It is shown that the straight chains of vortices, which form the star-shaped structures, are aligned with boundaries between domains populated by plane waves with different wave vectors. A transition from an axisymmetric higher-order (multiple) vortex state to the trilete pattern is investigated too.

Secure control for uncertain nonlinear cyber–physical systems: A prescribed-time scheme based on temporal scaling

In this paper, the prescribed-time secure control is explored for uncertain nonlinear cyber–physical systems through temporal scaling transformation and gain control technique, where the nonlinearity is more generic than common linear growth conditions due to the presence of large uncertainties and low-order states. Given that security risks exist in open networks, the impact of deception attacks is considered, whereas, this prevents the gain control technique from being applied directly to control design. To lift the restriction, a novel auxiliary system is firstly constructed to cleverly turn the secure control to the boundedness control of the auxiliary system. Next, a crucial bridge, temporal scaling transformation, is employed to transform the control issue in the finite time into infinite time, which opens up more possibilities for solving studied issues. Then, by the gain control technique, a Zeno-free secure control strategy with dynamically adjustable triggering mechanism is devised, which successfully ensures the convergence of system states within the prescribed time meanwhile counteracting deception attacks. Further, an improved nonlinearity, i.e. containing both low-order and high-order states, is discussed. Particularly, the proposed control strategies not only avoid real-time control updates, but also the gains therein handle system nonlinearities efficiently. Eventually, the validity of major results is verified via simulation examples.

High-Energy Neutrino Flavor State Transition Probabilities

We analytically determine neutrino transitional probabilities and abundance ratios at various distances from the source of creation in several astrophysical contexts, including the Sun, supernovae and cosmic rays. In doing so, we determine the probability of a higher-order transition state from ντ→νλ, where νλ represents a more massive generation than Standard Model neutrinos. We first calculate an approximate cross-section for high-energy neutrinos which allows us to formulate comparisons for the oscillation distances of solar, supernova and higher-energy cosmic ray neutrinos. The flavor distributions of the resulting neutrino populations from each source detected on Earth are then compared via fractional density charts.

Multifold Topological Point with Quadratic Order in Binary Skutterudite Rhodium Triarsenide.

The exploration of topological nodal point states has recently evolved, moving beyond traditional linear crossings to include higher-order dispersions and multifold degeneracies. This study utilizes first-principles calculations to uncover an ideal multifold nodal point of quadratic order in the binary skutterudite rhodium triarsenide. The band structures around this nodal point show not only simple configuration but also clean distribution. Notably, a type-III dispersion condition has also been identified. When considering the effects of spin-orbit coupling, the nodal point retains both its multiple degeneracy and quadratic characteristics, although the band degeneracy transitions from 3-fold to quadruple. Detailed symmetry argument and model analysis have been provided, and precise band surface distribution has been obtained. Furthermore, the material is characterized by multiple significant arc surface states, as confirmed by the projected topological surface states. The clear separation of these states from the bulk bands facilitates experimental investigation. In summary, the multifold nodal point state identified in this research, along with the corresponding material candidate, presents an exceptional platform for the further study of higher-order topological point states, potentially catalyzing advancements in this emerging field.

Higher-order topological corner states and origin in monolayer LaBrO

Abstract Intrinsic higher-order topological insulators driven solely by orbital coupling are rare in electronic materials. Here, we propose that monolayer LaBrO is an intrinsic two-dimensional second-order topological insulator. The generalized second-order topological phase arises from the coupling between the 5d orbital of the La atom and the 2p orbital of the O atom. The underlying physics can be thoroughly described by a four-band generalized higher-order topological model. Notably, the edge states and corner states of monolayer LaBrO exhibit different characteristics in terms of morphology, number, and location distribution under different boundary and nanocluster configurations. Furthermore, the higher-order topological corner states of monolayer LaBrO are robust against variations in spin-orbit coupling and different values of Hubbard U. This provides a material platform for studying intrinsic 2D second-order topological insulators.

Driven-dissipative phases and dynamics in non-Markovian nonlinear photonics

Interactions between photons (nonlinearities) enable a powerful form of control over the state of light. This control has enabled technologies such as light sources at new wavelengths, ultra-short optical pulses, frequency-comb metrology systems, even quantum light sources. Common to a wide variety of nonlinear optical technologies is an equilibrium between an energy source, such as an external laser, and dissipation, such as radiation loss or absorption. In the vast majority of these systems, the coupling between the system and the outside world (which leads to loss) is well described as “Markovian,” meaning that the outside world has no memory of its past state. In this work, we introduce a class of driven-dissipative systems in which a nonlinear cavity experiences non-Markovian coupling to the outside world. In the classical regime, we show that these non-Markovian cavities can have extremely low thresholds for nonlinear effects, as well as self-pulsing instabilities at THz rates, and rich phase diagrams with alternating regions of stability and instability. In the quantum regime, we show how these systems, when implemented on state-of-the-art platforms, can enable generation of strongly squeezed cavity states with intensity fluctuations that can be more than 15 dB below the classical limit, in contrast to the Markovian driven-dissipative cavity, in which the limit is 3 dB. In the regime of few-photon nonlinearity, such non-Markovian cavities can enable a deterministic protocol to generate Fock states of high order, which are long-desired, but still elusive at optical frequencies. We expect that exploiting non-Markovian couplings in nonlinear optics should in the future lead to even richer possibilities than those discussed here for both classical and quantum light manipulations.

Dual-band large-area topological edge states and higher-order corner states in a valley Hall photonic crystal

Dual-band large-area topological edge states and higher-order corner states in a valley Hall photonic crystal

Observation of multifunctional robust topological states based on asymmetric C4 photonic crystals

Recent advancements in high-order topological insulators have heralded new opportunities for the innovation and utilization of optical devices. This paper presents a composite asymmetric C4 photonic crystal to achieve multifunctional, robust topological states. Through detailed analysis of the fine changes in the topological bandgap induced by distortion parameters, we facilitate the realization of topological edge states in wavelength division multiplexing applications. We utilize both trivial and nontrivial properties of the topological bandgap to precisely manipulate zero-dimensional angular states, one-dimensional topological boundary states, and two-dimensional body states. Through simulations and experimental results, our advanced asymmetric C4 photonic crystal structure demonstrates superior robustness for the transmission of topological edge states. Our research paves the way for the deployment of more robust topological boundary state transmission systems and advances the application potential of higher-order topological states.

HoLens: A visual analytics design for higher-order movement modeling and visualization

Higher-order patterns reveal sequential multistep state transitions, which are usually superior to origin-destination analyses that depict only firstorder geospatial movement patterns. Conventional methods for higher-order movement modeling first construct a directed acyclic graph (DAG) of movements and then extract higher-order patterns from the DAG. However, DAG-based methods rely heavily on identifying movement keypoints, which are challenging for sparse movements and fail to consider the temporal variants critical for movements in urban environments. To overcome these limitations, we propose HoLens, a novel approach for modeling and visualizing higher-order movement patterns in the context of an urban environment. HoLens mainly makes twofold contributions: First, we designed an auto-adaptive movement aggregation algorithm that self-organizes movements hierarchically by considering spatial proximity, contextual information, and temporal variability. Second, we developed an interactive visual analytics interface comprising well-established visualization techniques, including the H-Flow for visualizing the higher-order patterns on the map and the higher-order state sequence chart for representing the higher-order state transitions. Two real-world case studies demonstrate that the method can adaptively aggregate data and exhibit the process of exploring higher-order patterns using HoLens. We also demonstrate the feasibility, usability, and effectiveness of our approach through expert interviews with three domain experts.

Ideal quadratic nodal point in half-Heusler semimetal LaPtBi

The research focus on topological states in electronic systems has recently expanded from traditional linear dispersions to encompass higher-order dispersions. These higher-order dispersions exhibit unique physical properties, including high topological charge, exotic magnetoresponse, and novel transport behaviors. In this study, we employ first-principles calculations to propose the half-Heusler material LaPtBi as an ideal quadratic nodal point semimetal. Our comprehensive analysis of the band structure reveals an ideal nodal point located precisely at the Fermi level, exhibiting quadratic dispersion in all directions. This finding is supported by symmetry analysis and effective model arguments. Moreover, when the spin-orbit coupling effect is considered, the nodal point transitions from triple to quadruple degeneracy, while maintaining its quadratic dispersion. The material also features multiple prominent arc surface states originating from the nodal point, which are distinctly separated from the bulk bands. This separation facilitates experimental verification. Overall, LaPtBi, with its quadratic nodal point and advantageous properties, serves as an ideal platform for further research. The study of this material is expected to enhance our understanding of higher-order topological states in electronic systems, potentially driving future advancements in the field.

Hierarchical bound states in heat transport

Higher-order topological phases in non-Hermitian photonics revolutionize the understanding of wave propagation and modulation, which lead to hierarchical states in open systems. However, intrinsic insulating properties endorsed by the lattice symmetry of photonic crystals fundamentally confine the robust transport only at explicit system boundaries, letting alone the flexible reconfiguration in hierarchical states at arbitrary positions. Here, we report a dynamic topological platform for creating the reconfigurable hierarchical bound states in heat transport systems and observe the robust and nonlocalized higher-order states in both the real- and imaginary-valued bands. Our experiments showcase that the hierarchical features of zero-dimension corner and nontrivial edge modes occur at tailored positions within the system bulk states instead of the explicit system boundaries. Our findings uncover the mechanism of non-localized hierarchical non-trivial topological states and offer distinct paradigms for diffusive transport field management.

Optimized higher-order photon state classification by machine learning

The classification of higher-order photon emission becomes important with more methods being developed for deterministic multiphoton generation. The widely used second-order correlation g(2) is not sufficient to determine the quantum purity of higher photon Fock states. Traditional characterization methods require a large amount of photon detection events, which leads to increased measurement and computation time. Here, we demonstrate a machine learning model based on a 2D Convolutional Neural Network (CNN) for rapid classification of multiphoton Fock states up to |3⟩ with an overall accuracy of 94%. By fitting the g(3) correlation with simulated photon detection events, the model exhibits an efficient performance particularly with sparse correlation data, with 800 co-detection events to achieve an accuracy of 90%. Using the proposed experimental setup, this CNN classifier opens up the possibility for quasi-real-time classification of higher photon states, which holds broad applications in quantum technologies.

Higher-order topological phase with subsystem symmetries

Abstract A wide variety of higher-order symmetry-protected topological phases (HOSPT) with gapless corners or hinges have been proposed as descendants of topological crystalline insulators protected by spatial symmetry. In this work, we address a new class of higher-order topological states that do not require crystalline symmetries but instead rely on subsystem symmetry for protection. We propose several strongly interacting models with gapless hinges or corners based on a decorated hinge-wall condensate picture. The hinge-wall, which appears as the defect configuration of a Z 2 paramagnet, is decorated with a lower-dimensional SPT state. Such a unique hinge-wall decoration structure leads to gapped surfaces separated by gapless hinges. The non-trivial nature of the hinge modes can be captured by a 1 + 1 D conformal field theory with a Wess–Zumino–Witten term. Moreover, we establish a no-go theorem to demonstrate the ungappable nature of the hinges by making a connection between the generalized Lieb–Schultz–Mattis theorem and the boundary anomaly of the HOSPT state. This universal correspondence engenders a comprehensive criterion to determine the existence of HOSPT under certain symmetries, regardless of the microscopic Hamiltonian.

Vortex superlattice induced second-order topological mid-gap states in first-order topological insulators and superconductors

Topological defects such as vortex and dislocations, support zero-energy localized states as a reflection of the bulk topology, in first-order topological insulators and superconductors. Furthermore, emergent first-order topological mid-gap states have been discovered driven by the magnetic vortex superlattice. However, whether the higher-order topological mid-gap states would emerge from the first-order topological insulators and superconductors with the vortex superlattice remains elusive. In this work, we propose vortex superlattice could induce second-order topological mid-gap states with staggered lattice spacings for vortices in first-order topological insulators and superconductors. These higher-order topological mid-gap states originate from the staggered tunneling between vortex-induced bound states and the emergent π flux on vortex superlattices, as an intrinsic exhibition of the interplay between vortices and bulk topology for the first-order topological states. Our work uncovers higher-topological characteristics of topological-defect superlattice in first-order topological states, and develops a controllable environment for the creation and exploration of higher-order topological states.

Optical edge-to-screw singularity state conversions

Optical singularity states, which significantly affect propagation properties of light in free space or optical medium, can be geometrically classified into screw and edge types. These different types of singularity states do not exhibit direct connection, being decoupled from each other in the absence of external perturbations. Here we demonstrate a novel optical process in which a higher-order edge singularity state initially nested in the propagating Gaussian light field gradually involves into a screw singularity with a new-born topological charge determined by order of the edge state. The considered edge state comprises an equal superposition of oppositely charged vortex and antivortex modes. We theoretically and experimentally realize this edge-to-screw conversion process by introducing intrinsic vortex–antivortex interaction. We also present a geometrical representation for mapping this dynamical process, based on the higher-order orbital Poincaré sphere. Within this framework, the edge-to-screw conversion is explained by a mapping of state evolution from the equator to the north or south pole of the Poincaré sphere. Our demonstration provides a novel approach for manipulating singularity state by the intrinsic vortex–antivortex interactions. The presented phenomenon can be also generalized to other wave systems such as matter wave, water wave, and acoustic wave.

Delocalization of higher-order topological states in higher-dimensional non-Hermitian quasicrystals

Delocalization of higher-order topological states in higher-dimensional non-Hermitian quasicrystals

Uniform design-based self-healing evaluation for active distribution network

With the increase in power demand and system complexity, accurately evaluate the self-healing performance of distribution network has become one of the key factors in ensuring the reliability and stability of power supply. To address the issues of incomplete evaluation scenarios and low evaluation efficiency in current self-healing evaluation, this paper proposes the uniform design-based method for evaluating the self-healing performance of the distribution network. It enables comprehensive and fast evaluation of self-healing under multiple fault scenarios. Firstly, three indicators are proposed to evaluate the self-healing performance: self-healing rate, self-healing speed, and self-healing operation complexity. Then, the calculation of three self-healing indicators is carried out under the self-healing strategy that coordinates both network reconstruction and island partition. By uniformly sampling the enumerated k-order system states, the computational time cost is greatly decreased, avoiding the problem of high computational complexity under high-order states and improving the efficiency of evaluation process. Finally, case study shows that the uniform design method greatly decreases the computational time (nearly 20 times faster than the state enumeration) on the IEEE 33-node distribution network.

Coherent transfer of higher-order polarization state of photons to spin structure state of electrons in a semiconductor

Coherent transfer of higher-order polarization state of photons to spin structure state of electrons in a semiconductor

Higher-order topological Dirac phase in Y3InC: a first-principles study

Higher-order topological insulators hosting intriguing topologically protected hinge or corner states are of significant research interest. However, materials that possess higher-order topological hinge states associated with gapless bulk Dirac phases still need to be explored. Using first-principles calculations with hybrid exchange functional, we explore the electronic structure and topological properties of Y3InC and a few of its sister compounds, totaling 16 bulk materials. A symmetry-protected triple point phase, with dominated d-t 2g character, is observed in Y3InC without spin–orbit coupling (SOC). Interestingly, the SOC induces a twin Dirac node phase in the bulk Y3InC. Furthermore, the computed Z 4 topological invariant reveals the higher-order topological nature of investigated materials. To demonstrate the gapless hinge states, we conduct edge state calculations using a rod-shaped geometry of Y3InC. Remarkably, Y3InC is identified to host multi-Dirac nodes in the bulk and surface phases together with the higher-order hinge states. These results lay the groundwork for further experimental and theoretical investigations into cubic antiperovskite materials for higher-order topological phases.

Higher-order topological states in acoustic two-dimensional Penrose quasicrystals

Higher-order topological states in acoustic two-dimensional Penrose quasicrystals