Higher-order Phase Research Articles

Observation of High-Order Quantum Pancharatnam-Berry Phase with Structured Photons

When a quantum system evolves so that it returns to its initial state, it will acquire a geometric phase acting as a memory of the transformation of a physical system, which has been experimentally measured in a variety of physical systems. In optics, the most prominent example is the Pancharatnam-Berry (PB) phase. Recent technological advances in phase and polarization structure have led to the discovery of high-order PB phases with structured light fields. The study on the high-order PB phase is limited in the context of elementary quantum states of light, especially in the case of photon number states. Here, we experimentally investigate the differences of high-order PB phases between single-photon and N00N states. Our results show that the PB phase, like the dynamic phase, can also be doubled under two-photon states, which can greatly improve the phase sensitivity for greater N in N00N states and high-order structured photons. This may show some implications for quantum precision measurement and quantum state engineering based on geometric phase.

Intrinsic second-order topological insulators in two-dimensional polymorphic graphyne with sublattice approximation

In two dimensions, intrinsic second-order topological insulators (SOTIs) are characterized by topological corner states that emerge at the intersections of distinct edges with reversed mass signs, enforced by spatial symmetries. Here, we present a comprehensive investigation within the class BDI to clarify the symmetry conditions ensuring the presence of intrinsic SOTIs in two dimensions. We reveal that the (anti-)commutation relationship between spatial symmetries and chiral symmetry is a reliable indicator of intrinsic corner states. Through first-principles calculations, we identify several ideal candidates within carbon-based polymorphic graphyne structures for realizing intrinsic SOTIs under sublattice approximation. Furthermore, we show that the corner states in these materials persist even in the absence of sublattice approximation. Our findings not only deepen the understanding of higher-order topological phases but also open new pathways for realizing topological corner states that are readily observable.

Network model for magnetic higher-order topological phases

We propose a network-model realization of magnetic higher-order topological phases (HOTPs) in the presence of the combined space-time symmetry C4T—the product of a fourfold rotation and time-reversal symmetry. We show that the system possesses two types of HOTPs. The first type, analogous to Floquet topology, generates a total of eight corner modes at 0 or π eigenphase, while the second type, hidden behind a weak topological phase, yields a unique phase with eight corner modes at ±π/2 eigenphase (after gapping out the counterpropagating edge states), arising from the product of particle-hole and phase-rotation symmetry. By using a bulk Z4 topological index (Q), we found both HOTPs have Q=2, whereas Q=0 for the trivial and the conventional weak topological phase. Together with a Z2 topological index associated with the reflection matrix, we are able to fully distinguish all phases. Our work motivates further studies on magnetic topological phases and symmetry-protected 2π/n boundary modes, as well as suggesting that such phases may find their experimental realization in coupled-ring-resonator networks. Published by the American Physical Society 2024

Aero-optical effects, part I. System-level considerations: tutorial

This paper serves as part I of a two-part tutorial on “aero-optical effects.” We first present background information to assist with our introduction of the topic. Next, we use the aerodynamic environment associated with a hemisphere-on-cylinder beam director to decompose the resulting aberrations (that arise due to aero-optical effects) in terms of piston, tilt, and higher-order phase errors. We also discuss the performance implications that these phase errors have on airborne-laser systems. Recognizing the complexity of these environments, we then discuss how one measures these phase errors using standard wavefront-sensing approaches and the impact these phase errors have on imaging performance. These system-level considerations provide the material needed to survey several sources of aberrations such as boundary layers and shear layers, as well as mechanical contamination, shock waves, and aero-acoustics—all of which we cover in part II of this two-part tutorial.

Rhythmic dynamics of higher-order phase oscillator populations with competitive couplings

Rhythmic dynamics of higher-order phase oscillator populations with competitive couplings

A research of higher-order network emotional phase transitions

This paper explores the law of emotion transmission on the social Internet. By applying higher-order network theory, ER random networks are reconstructed and higher-order network structures with multiple interaction points are generated. The I-state of the SI model is extended to set up the propagation rules of emotions based on higher-order networks. Concepts such as sentiment recession rate are introduced to make sentiment propagate through different simplexes, so as to obtain the propagation rules of higher-order networks. Qualitative analysis of emotional changes during the propagation process verifies the phase transition phenomenon of emotions in the network. By comparing simulated results with actual data, we demonstrate the accuracy of our higher-order network-based emotion propagation model in reflecting real-world trends and outcomes. The study also explores the effects of factors such as the initial proportion of extreme emotions on emotion propagation. This study provides valuable insights into understanding the operation of complex systems and offers important implications for government predictions of opinion development.

High-Resolution Imaging of a Complex Moving Target for Higher-Order Phase Terms Using a Novel Technique

High-Resolution Imaging of a Complex Moving Target for Higher-Order Phase Terms Using a Novel Technique

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.

Improved frequency shift compensation technique and pulse sequence for multi-loop atom interference experiments

With the rapid development of atom interference technology, multi-loop atom interferometers are widely used in the high-precision measurement of various physical constants and testing of various gravity-related effects. However, in ground-based multi-loop atom interference experiments, the systematic error contribution by classical effects is an important factor that affects the experimental measurement accuracy and gravitational effect detection. Based on this, we used the atomic wave-function evolution-phase accumulation method to provide a high-order interference phase of multi-loop atom interferometers in an inhomogeneous gravitational field containing Earth’s rotation. Furthermore, we propose a new scheme that combines optimised frequency-shift compensation technology with an improved pulse sequence to eliminate systematic errors due to the gravity gradient, Earth’s rotation, and their coupling effect with the pulse duration, as well as the coupling effect of laser detuning with the pulse duration. This study lays a theoretical foundation for experiments on multi-loop atom interferometers with higher precision.

Spherical echo-planar time-resolved imaging (sEPTI) for rapid 3D quantitative and susceptibility imaging.

To develop a 3D spherical EPTI (sEPTI) acquisition and a comprehensive reconstruction pipeline for rapid high-quality whole-brain submillimeter and QSM quantification. For the sEPTI acquisition, spherical k-space coverage is utilized with variable echo-spacing and maximum kx ramp-sampling to improve efficiency and signal incoherency compared to existing EPTI approaches. For reconstruction, an iterative rank-shrinking B0 estimation and odd-even high-order phase correction algorithms were incorporated into the reconstruction to better mitigate artifacts from field imperfections. A physics-informed unrolled network was utilized to boost the SNR, where 1-mm and 0.75-mm isotropic whole-brain imaging were performed in 45 and 90 s at 3 T, respectively. These protocols were validated through simulations, phantom, and in vivo experiments. Ten healthy subjects were recruited to provide sufficient data for the unrolled network. The entire pipeline was validated on additional five healthy subjects where different EPTI sampling approaches were compared. Two additional pediatric patients with epilepsy were recruited to demonstrate the generalizability of the unrolled reconstruction. sEPTI achieved 1.4 faster imaging with improved image quality and quantitative map precision compared to existing EPTI approaches. The B0 update and the phase correction provide improved reconstruction performance with lower artifacts. The unrolled network boosted the SNR, achieving high-quality and QSM quantification with single average data. High-quality reconstruction was also obtained in the pediatric patients using this network. sEPTI achieved whole-brain distortion-free multi-echo imaging and and QSM quantification at 0.75 mm in 90 s which has the potential to be useful for wide clinical applications.

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.

High-efficiency and broadband asymmetric spin-orbit interaction based on high-order composite phase modulation.

Asymmetric spin-orbit interaction (ASOI) breaks the limitations in conjugate symmetry of traditional geometric phase metasurfaces, bringing new opportunities for various applications such as spin-decoupled holography, imaging, and complex light field manipulation. Since anisotropy is a requirement for spin-orbit interactions, existing ASOI mainly relies on meta-atom with C1 and C2 symmetries, which usually suffer from an efficiency decrease caused by the propagation phase control through the structural size. Here, we demonstrate for the first time that ASOI can be realized in meta-atoms with rotational symmetry ≥3 by combining the generalized geometric phase with the propagation phase. Utilizing an all-metallic configuration, the average diffraction efficiency of the spin-decoupled beam deflector based on C3 meta-atoms reaches ∼84 % in the wavelength range of 9.3-10.6 μm, which is much higher than that of the commonly used C2 meta-atoms with the same period and height. This is because the anisotropy of the C3 metasurface originates from the lattice coupling effect, which is relatively insensitive to the propagation phase control through the meta-atom size. A spin-decoupled beam deflector and hologram meta-device were experimentally demonstrated and performed well over a broadband wavelength range. This work opens a new route for ASOI, which is significant for realizing high-efficiency and broadband spin-decoupled meta-devices.

Atomic Layer Engineering of Ferroelectricity in Dion-Jacobson Perovskites.

Recent advances in "hybrid-improper" ferroelectricity in Dion-Jacobson (DJ)-type layered perovskites have caused renewed interest in the search for new ferroelectrics. Here, we present an approach for the tailored synthesis of a new homologous series of DJ-type layered perovskites Cs(Bi2Srn-3)(Tin-1Nb)O3n+1. Starting from CsBi2Ti2NbO10 (n = 3), higher-order homologous phases with n = 4 and 5 were successfully synthesized by repeated solid-state calcination with SrTiO3. Characterizations by X-ray diffraction, electron diffraction, transmission electron microscopy, Raman scattering, and second harmonic generation showed the detailed structural features in Cs(Bi2Srn-3)(Tin-1Nb)O3n+1, and the polar structures could be stabilized by proper or hybrid-improper ferroelectricity, depending on the odd or even number of the perovskite layers. Our results provide important insights into the competition between the different mechanisms and the consequences of the ferroelectric properties in homologous layered perovskites.

Phase reduction explains chimera shape: When multibody interaction matters.

We present an extension of the Kuramoto-Sakaguchi model for networks, deriving the second-order phase approximation for a paradigmatic model of oscillatory networks-an ensemble of nonidentical Stuart-Landau oscillators coupled pairwisely via an arbitrary coupling matrix. We explicitly demonstrate how this matrix translates into the coupling structure in the phase equations. To illustrate the power of our approach and the crucial importance of high-order phase reduction, we tackle a trendy setup of nonlocally coupled oscillators exhibiting a chimera state. We reveal that our second-order phase model reproduces the dependence of the chimera shape on the coupling strength that is not captured by the typically used first-order Kuramoto-like model. Our derivation contributes to a better understanding of complex networks' dynamics, establishing a relation between the coupling matrix and multibody interaction terms in the high-order phase model.

Dynamics of Airyprime beams with higher-order spectral phase modulation in the fractional Schrödinger equation

In this paper, the effects of spectral phase modulation on propagation characteristics of Airyprime beams modeled by fractional Schrödinger equation are studied, and the propagation dynamics of Airyprime beams are analyzed. It is found that the second and third-order spectral phase modulation significantly affect the beams dynamics. For the second-order spectral phase modulation, an increase in the Lévy index leads to a forward shift of the peak position, and the peak intensity increases for the positive spectral modulation coefficient, while the opposite tendency of the peak intensity is found for the negative spectral modulation coefficient. In addition, the appearance of multiple peaks depends on the positive modulation coefficient. For the third-order spectral phase modulation, the peak intensity increases under the larger spectral phase modulation coefficient with the backward shift of the maximum peak position, and an increase of the Lévy index results in the forward shift of the focusing position. The results show potential applications of Airyprime beams in various fields such as optical controlling and manipulation.

Twisted hyperbolic-sine-correlated beams.

In this study, a novel class of spatially non-uniformly correlated beams called twisted hyperbolic-sine-correlated (THSC) beams is introduced. The coherence structure of such beam sources is characterized by a hyperbolic sine function with a high-order twist phase embedded in its argument. The propagation properties of the THSC beams are numerically examined in detail. Our results reveal that the order numbers and twist factor of the twist phase has a significant effect on the spectral density and orbital angular momentum (OAM) flux density upon propagation, and they can be used to control the formation of certain specific far-field intensity profiles such as doughnut shape, rectangular window shape, and dumbbell-like shape, as well as the OAM flux distributions such as windmill-like shape. In addition, the THSC beams under certain order numbers may possess peculiar propagation characteristics such as diffraction-effect suppression, lateral shift of intensity maxima and beam spot rotation. Further, we have established a flexible yet compact experimental system to synthesize such kind of beam sources. The evolution properties of the intensity distribution are investigated and analyzed in the experiment.

Talbot-like pattern evolution in complex structured light from a unitary transformation.

Astigmatic unitary transformations allow for the adiabatic connections of all feasible states of paraxial Gaussian beams on the same modal sphere, i.e., Hermite-Laguerre-Gaussian (HLG) modes. Here, we present a comprehensive investigation into the unitary modal evolution of complex structured Gaussian beams, comprised of HLG modes from disparate modal spheres, via astigmatic transformation. The non-synchronized higher-order geometric phases in cyclic transformations originate a Talbot-effect-like modal evolution in the superposition state of these HLG modes, resulting in pattern variations and revivals in transformations with specific geodesic loops. Using Ince-Gaussian modes as an illustrative example, we systematically analyze and experimentally corroborate the beamforming mechanism behind the pattern evolution. Our results outline a generic modal conversion theory of structured Gaussian beams via astigmatic unitary transformation, offering a new approach for shaping spatial modal structure. These findings may inspire a wide variety of applications based on structured light.

Ultracold-molecule higher-order topological phases induced by long-range dipolar interactions in optical-tweezer lattices

Ultracold-molecule higher-order topological phases induced by long-range dipolar interactions in optical-tweezer lattices

Tunable hybrid-order Weyl semimetal via staggered magnetic flux

We investigate a hybrid-order Weyl semimetal (HOWS) constructed by stacking the two-dimensional kagome lattice with staggered magnetic flux. By adjusting the magnitude of flux, higher-order topological phases are tunably intertwined with the first-order topological Chern insulators, which is governed by the evolution of Weyl points. Meanwhile the surface Fermi arcs undergo topological Lifshitz transition. Notably, due to the breaking of time-reversal symmetry (TRS), a novel split of a quadratic double Weyl point occurs, giving rise to additional three type-II Weyl points hybridizing with one type-I node. This phenomenon plays a crucial role in realizing high-Chern-number phases with C=±2 and reveals a new mechanism for the emergence of type-II Weyl fermions in topological kagome semimetals. We anticipate that this study will stimulate further investigation into the unique physics of kagome materials and Weyl semimetals.

Phase-locking-free all-optical matching system for 100 Gbaud QPSK optical signal.

Photonic firewall is a monitoring protection device that will directly detect and locate optical network attacks at the optical layer, which can effectively ensure the security of optical networks. An all-optical matching system is the core part of photonic firewall, which determines the performance of a photonic firewall, so it is of great significance to research and develop all-optical matching system for high-speed and high-order modulation formats signals. At present, an all-optical matching system for binary modulation formats is relatively mature, but the all-optical matching system for high-order phase modulation format signals is still limited by how to solve the problem of phase synchronization. In this paper, a new all-optical matching system based on self-interference matching is proposed for quadrature phase shift keying (QPSK) optical signal, which avoids the introduction of local target sequence optical signals and phase-locking circuits. The theoretical analysis and simulation verification are conducted for the designed system. The results demonstrate that the system can accurately identify and locate 4-symbol or 8-symbol target sequences in the input QPSK optical signals with 16-symbol and 32-symbol data sequences at a data rate of 100 Gbaud.