Topological Modes Research Articles

Effect of electromechanical coupling on locally resonant quasiperiodic metamaterials

Electromechanical metamaterials have been the focus of many recent studies for use in simultaneous energy harvesting and vibration control. Metamaterials with quasiperiodic patterns possess many useful topological properties that make them a good candidate for study. However, it is currently unknown what effect electromechanical coupling may have on the topological bandgaps and localized edge modes of a quasiperiodic metamaterial. In this paper, we study a quasiperiodic metamaterial with electromechanical resonators to investigate the effect on its bandgaps and localized vibration modes. We derive here the analytical dispersion surfaces of the proposed metamaterial. A semi-infinite system is also simulated numerically to validate the analytical results and show the band structure for different quasiperiodic patterns, load resistors, and electromechanical coupling coefficients. The topological nature of the bandgaps is detailed through an estimation of the integrated density of states. Furthermore, the presence of topological edge modes is determined through numerical simulation of the energy harvested from the system. The results indicate that quasiperiodic metamaterials with electromechanical resonators can be used for effective energy harvesting without changes in the bandgap topology for weak electromechanical coupling.

AC-DC Fuzzy Linear Active Disturbance Rejection Control Strategy of Front Stage of Bidirectional Converter Based on V2G

Aiming at the problems of output voltage fluctuation and current total harmonic distortion (THD) in the front stage totem-pole bridgeless PFC of two-stage V2G (Vehicle to Grid) vehicle-mounted bi-directional converter, a fuzzy linear active disturbance rejection control strategy for V2G front-stage AC-DC power conversion system is proposed. Firstly, the topological working mode of the totem-pole bridgeless PFC is analyzed, and the mathematical model is established. Combined with the system model and the linear active disturbance rejection theory, a double closed-loop controller is designed with the second-order linear active disturbance rejection control as the voltage outer loop and PI control as the current inner loop. The controller can realize self-adaptive tuning of the proportional gain coefficient of the active disturbance rejection controller through fuzzy reasoning and realize self-adaptive control. Simulation and experimental results show that this method can better solve the problems of slow system response and high total harmonic distortion rate of input current and effectively improve the system’s robustness.

Topological Edge Modes in One-dimensional Photonic Artificial Structures (Invited)

Topological Edge Modes in One-dimensional Photonic Artificial Structures (Invited)

Quasiperiodic photonic crystal fiber [Invited

In the fields of light manipulation and localization, quasiperiodic photonic crystals, or photonic quasicrystals (PQs), are causing an upsurge in research because of their rotational symmetry and long-range orientation of transverse lattice arrays, as they lack translational symmetry. It allows for the optimization of well-established light propagation properties and has introduced new guiding features. Therefore, as a class, quasiperiodic photonic crystal fibers, or photonic quasicrystal fibers (PQFs), are considered to add flexibility and richness to the optical properties of fibers and are expected to offer significant potential applications to optical fiber fields. In this review, the fundamental concept, working mechanisms, and invention history of PQFs are explained. Recent progress in optical property improvement and its novel applications in fields such as dispersion control, polarization-maintenance, supercontinuum generation, orbital angular momentum transmission, plasmon-based sensors and filters, and high nonlinearity and topological mode transmission, are then reviewed in detail. Bandgap-type air-guiding PQFs supporting low attenuation propagation and regulation of photonic density states of quasiperiodic cladding and in which light guidance is achieved by coherent Bragg scattering are also summarized. Finally, current challenges encountered in the guiding mechanisms and practical preparation techniques, as well as the prospects and research trends of PQFs, are also presented.

Phase-Dislocation-Mediated High-Dimensional Fractional Acoustic-Vortex Communication.

With unlimited topological modes in mathematics, the fractional orbital angular momentum (FOAM) demonstrates the potential to infinitely increase the channel capacity in acoustic-vortex (AV) communications. However, the accuracy and stability of FOAM recognition are still limited by the nonorthogonality and poor anti-interference of fractional AV beams. The popular machine learning, widely used in optics based on large datasets of images, does not work in acoustics because of the huge engineering of the 2-dimensional point-by-point measurement. Here, we report a strategy of phase-dislocation-mediated high-dimensional fractional AV communication based on pair-FOAM multiplexing, circular sparse sampling, and machine learning. The unique phase dislocation corresponding to the topological charge provides important physical guidance to recognize FOAMs and reduce sampling points from theory to practice. A straightforward convolutional neural network considering turbulence and misalignment is further constructed to achieve the stable and accurate communication without involving experimental data. We experimentally present that the 32-point dual-ring sampling can realize the 10-bit information transmission in a limited topological charge scope from ±0.6 to ±2.4 with the FOAM resolution of 0.2, which greatly reduce the divergence in AV communications. The infinitely expanded channel capacity is further verified by the improved FOAM resolution of 0.025. Compared with other milestone works, our strategy reaches 3-fold OAM utilization, 4-fold information level, and 5-fold OAM resolution. Because of the extra advantages of high dimension, high speed, and low divergence, this technology may shed light on the next-generation AV communication.

Robustness versus sensitivity in non-Hermitian topological lattices probed by pseudospectra

Non-Hermitian topological systems simultaneously possess two antagonistic features: ultrasensitivity due to exceptional points and robustness of topological zero-energy modes, and it is unclear which one prevails under different perturbations. We study that question by applying the pseudospectrum theory on the prototypical non-Hermitian Su-Schrieffer-Heeger lattice. Topological modes around the underlying third-order exceptional point (EP3) are robust with respect to chiral perturbations but sensitive to diagonal perturbations. In fact, exactly at the EP3 the chiral symmetry leads to a suppressed sensitivity, that corresponds to an EP2. Finally, for nonlinearly induced perturbations we provide a connection between the pseudospectrum approach and a nonlinear phase shift, which is relevant for experiments.

Higher-order topological corner states induced solely by on-site potentials with mirror symmetry

Higher-order topological insulators have triggered a great deal of interest because they exhibit nontrivial bulk topology on lower-dimensional boundaries such as corners and hinges. While such interesting phases have been investigated in a plethora of systems by tuning staggered tunneling strength or manipulating existing topological phases, here we show that a higher-order topological phase can be driven solely by mirror-symmetric on-site potentials. We start with a chain model, and we show that it has nonzero edge states due to the lack of internal symmetries such as chiral and particle-hole symmetries. We then generalize the model to two dimensions, and we demonstrate the emergence of topological corner modes. These corner modes are an intrinsic manifestation of nontrivial bulk band topology protected by mirror symmetry, and thus they are robust against symmetry-preserved perturbations. Our model only requires the tuning of on-site energies, and it provides a realistic platform for studying a class of higher-order topological insulators using state-of-the-art experiment techniques.

Topological lattices realized in superconducting circuit optomechanics.

Cavity optomechanics enables the control of mechanical motion through the radiation-pressure interaction1, and has contributed to the quantum control of engineered mechanical systems ranging from kilogramme-scale Laser Interferometer Gravitational-wave Observatory (LIGO)mirrors to nanomechanical systems, enabling ground-state preparation2,3, entanglement4,5, squeezing of mechanical objects6, position measurements at the standard quantum limit7 and quantum transduction8. Yet nearly all previous schemes have used single- or few-mode optomechanical systems. By contrast, new dynamics and applications are expected when using optomechanical lattices9, which enable the synthesis of non-trivial band structures, and these lattices have been actively studied in the field of circuit quantum electrodynamics10. Superconducting microwave optomechanical circuits2 are a promising platform to implement such lattices, but have been compounded by strict scaling limitations. Here we overcome this challenge and demonstrate topological microwave modes in one-dimensional circuit optomechanical chains realizing the Su-Schrieffer-Heeger model11,12. Furthermore, we realize the strained graphene model13,14 in a two-dimensional optomechanical honeycomb lattice. Exploiting the embedded optomechanical interaction, we show that it is possible to directly measure the mode functions of the hybridized modes without using any local probe15,16. This enables us to reconstruct the full underlying lattice Hamiltonian and directly measure the existing residual disorder. Such optomechanical lattices, accompanied by the measurement techniques introduced, offer an avenue to explore collective17,18, quantum many-body19 and quench20 dynamics, topological properties9,21 and, more broadly, emergent nonlinear dynamics in complex optomechanical systems with a large number of degrees of freedom22-24.

Deformed Honeycomb Lattices of InGaAs Nanowires Grown on Silicon‐on‐Insulator for Photonic Crystal Surface‐Emitting Lasers

AbstractPhotonic crystals can be used to achieve high‐performance surface‐emitting lasers and enable novel photonic topological insulator devices. In this work, a GaAs/InGaAs heterojunction nanowire platform by selective area metalorganic vapor phase epitaxy for such applications is demonstrated. The nanowires are arranged into deformed honeycomb lattices on silicon‐on‐insulator substrate to exploit the quadrupolar photonic band‐edge mode. Core–shell and axial heterostructures are formed with their crystalline properties studied by scanning transmission electron microscopy. Room‐temperature, single mode lasing from both stretched and compressed honeycomb lattices within the telecom‐O band, with lasing threshold as low as 1.25 µJ cm−2 is demonstrated. The potential of using InGaAs nanowire‐based honeycomb lattices for small‐divergence surface‐emitting lasers and topological edge mode lasers is investigated. Finite‐difference time‐domain far field simulations suggest a sub‐10° beam divergence can be achieved thanks to the out‐of‐plane diffraction.

Majorana nanowires for topological quantum computation

Majorana bound states are quasiparticle excitations localized at the boundaries of a topologically nontrivial superconductor. They are zero-energy, charge-neutral, particle–hole symmetric, and spatially-separated end modes which are topologically protected by the particle–hole symmetry of the superconducting state. Due to their topological nature, they are robust against local perturbations and, in an ideal environment, free from decoherence. Furthermore, unlike ordinary fermions and bosons, the adiabatic exchange of Majorana modes is noncommutative, i.e., the outcome of exchanging two or more Majorana modes depends on the order in which exchanges are performed. These properties make them ideal candidates for the realization of topological quantum computers. In this tutorial, I will present a pedagogical review of 1D topological superconductors and Majorana modes in quantum nanowires. I will give an overview of the Kitaev model and the more realistic Oreg–Lutchyn model, discuss the experimental signatures of Majorana modes, and highlight their relevance in the field of topological quantum computation. This tutorial may serve as a pedagogical and relatively self-contained introduction for graduate students and researchers new to the field, as well as an overview of the current state-of-the-art of the field and a reference guide to specialists.

Type-II corner modes in topolectrical circuits

We study the rich properties of a topolectrical (TE) circuit array consisting of lossless basic electrical components, such as capacitors and inductors, which can be designed to exhibit higher-order topological phases (HOTP). The HOTP of the circuit exhibits the characteristics of higher-order topology, i.e., unconventional bulk-boundary correspondence with strongly localized corner modes, and higher winding numbers. More interestingly, a type-II corner mode emerges in the presence of long-range interaction, which is realized in the TE circuit by the introduction of next-nearest neighbor (NNN) coupling capacitances. Unlike the usual (i.e., ``type-I'') corner modes that are localized at a particular sublattice node due to the chiral symmetry, the type-II corner modes possess a spatial extent with an exponential decay length. We analytically derive this decay length as a function of the circuit parameters. The NNN coupling is also associated with the tilt parameter in the admittance spectrum of the circuit. The admittance spectrum is reminiscent of that of Dirac fermions. Changing the tilt parameter can lead to a transition from the type-I to the overtilted type-II Dirac dispersion. This overtilting results in a hybridization of the bulk and corner modes in which the distinct corner modes disappear. Furthermore, the type-I and type-II corner modes can be distinguished by their impedance readout. By virtue of their flexibility, the TE circuits provide an ideal platform to demonstrate unusual features of HOTPs arising from long-range interactions, and to engineer different types of robust topological corner modes.

Controllable topological edge mode in an optically excited exciton-polariton lattice

We propose an all-optical scheme of topological lasing and switching based on the Aubry-Andr\'e-Harper (AAH) model of an exciton-polariton chain. We theoretically show that the phase parameter of the optical potential, with a tunable effective quasimomentum, allows the system to exhibit nontrivial topological properties which are attributed to higher dimensions. The topological modes emerging within the bulk band gaps are spatially localized at the edges of the polariton lattice, and their topological properties are characterized by the nonzero Chern numbers of the bulk bands. Polariton lasing in topological edge modes exhibits a higher efficiency and better robustness than in bulk modes, and can be switched between two opposite edges of the lattice by nonresonant excitation, which paves a way for topologically protected optical circuits.

Propagation and imaging analysis of vortex acoustic waves in ocean turbulence

AbstractVortex acoustic waves (VAW) with helical phase wavefronts could provide a new dimension for the detection and imaging of targets in the ocean. To explore the propagation characteristics of VAW under the effect of ocean turbulence (OT) and the impact on imaging, the phase screen method is used to simulate the propagation of VAW generated by a phase‐modulated uniform circular array under the effect of OT and the imaging of the target. The phase change and detection probability under the influence of the acoustic wave parameters and OT parameters during the propagation process are studied. Second, the azimuth resolution performance and focussing performance of the target imaging are studied. Under the effect of OT, the VAW of different frequencies and topological modes become scattered, and the degree of scattering is different when the parameters are different; and the resolution performance and focussing performance have also deteriorated. However, the VAW still has a reliable resolution under the effect of medium and low‐intensity OT, which provides theoretical support for the practice of the VAW in underwater target imaging.

Long-distance coupling of spin qubits via topological magnons

We consider two distant spin qubits in quantum dots, both coupled to a two-dimensional topological ferromagnet hosting chiral magnon edge states at the boundary. The chiral magnon is used to mediate entanglement between the spin qubits, realizing a fundamental building block of scalable quantum computing architectures: a long-distance two-qubit gate. Previous proposals for long-distance coupling with magnons involved off-resonant coupling, where the detuning of the spin-qubit frequency from the magnonic band edge provides protection against spontaneous relaxation. The topological magnon mode, on the other hand, lies in between two magnonic bands far away from any bulk magnon resonances, facilitating strong and highly tuneable coupling between the two spin qubits. Even though the coupling between the qubit and the chiral magnon is resonant for a wide range of qubit splittings, we find that the magnon-induced qubit relaxation is vastly suppressed if the coupling between the qubit and the ferromagnet is antiferromagnetic. A fast and high-fidelity long-distance coupling protocol is presented capable of achieving spin-qubit entanglement over micrometer distances with $1\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$ gate speed and up to $99.9%$ fidelities. The resulting spin-qubit entanglement may be used as a probe for the long-sought detection of topological edge magnons.

Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems

Studies of topological bands and their associated low-dimensional boundary modes have largely focused on linear systems. This work reports robust dynamical features of three-dimensional (3D) nonlinear systems in connection with intriguing topological bands in 3D. Specifically, for a 3D setting of coupled rock-paper-scissors cycles governed by the antisymmetric Lotka-Volterra equation (ALVE) that is inherently nonlinear, we unveil distinct characteristics and robustness of surface-polarized masses and analyze them in connection with the dynamics and topological bands of the linearized Lotka-Volterra equation. Our results show that insights learned from Weyl semimetal phases with type-I and type-II Weyl singularities based on a linearized version of the ALVE are still remarkably useful, even though the system dynamics is far beyond the linear regime. This work indicates the relevance and importance of the concept of topological boundary modes in analyzing high-dimensional nonlinear systems and hopes to stimulate further topological studies where various topological gapless phases of matter may emerge in higher-dimensional nonlinear systems.

Realization of Photonic Topological Insulators at Terahertz Frequencies Characterized by Time-Domain Spectroscopy

Topological systems are inherently robust to disorder and continuous perturbations, resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless guiding of photons and phonons in classical wave systems characterized by topological invariants. Realization of robust, lossless topological insulators in the technologically important terahertz (THz) frequency range has drawn immense attention. In this paper, we propose a Kagome lattice structure that supports topological edge states with valley-dependent transport. Optical topological insulators are subsequently fabricated, in which mirror symmetry is broken and degenerate states are lifted at $K({K}^{\ensuremath{'}})$ valleys in the band structure. Theoretical and numerical analyses show that four types of edge states can be obtained. The performance of the fabricated topological waveguides is characterized with THz time-domain spectroscopy (TDS). Nearly identical THz wave transmission in the 0.437--0.453-THz range is verified with a straight-line topological waveguide and Z-shaped waveguides with multiple sharp turning corners, which quantitatively illustrate the strong backscattering suppression effects from the nontrivial topology edge states of the structures. Particularly, the THz TDS measurements provide important extra time-domain information about the topological waveguiding mode, which is generally unavailable from previous topological insulator investigations solely replying on power spectrum measurements.

Organic Higher-Order Topological Insulators: Heterotriangulene-Based Covalent Organic Frameworks.

The ability to design and control the chemical characteristics of covalent organic frameworks (COFs) offers a new avenue for the development of functional materials, especially with respect to topological properties. Based on density functional theory calculations, by varying the core units through the choice of bridging groups [O, C═O, CH2, or C(CH3)2] and the linker units [acetylene, diacetylene, or benzene], we have designed heterotriangulene-based COFs that are predicted to be two-dimensional higher-order topological insulators (TIs). The higher-order TI characteristics of these COFs are identified via their topological invariants and the presence of in-gap topological corner modes and gapped edge states. The frontier molecular orbital energies of the building moieties play an important role in determining the size of the higher-order TI gap, which we find to be highly dependent on linker units. We also examined the deposition of the COFs on a boron nitride substrate to assess the feasibility of experimental observation of a higher-order TI phase in the organic layer. This work thus provides new insights into heterotriangulene-based COFs and guidance for the exploration of purely organic topological materials.

Observing the quantum topology of light.

Topological photonics provides a powerful platform to explore topological physics beyond traditional electronic materials and shows promising applications in light transport and lasers. Classical degrees of freedom are routinely used to construct topological light modes in real or synthetic dimensions. Beyond the classical topology, the inherent quantum nature of light provides a wealth of fundamentally distinct topological states. Here we implement experiments on topological states of quantized light in a superconducting circuit, with which one- and two-dimensional Fock-state lattices are constructed. We realize rich topological physics including topological zero-energy states of the Su-Schrieffer-Heeger model, strain-induced pseudo-Landau levels, valley Hall effect, and Haldane chiral edge currents. Our study extends the topological states of light to the quantum regime, bridging topological phases of condensed-matter physics with circuit quantum electrodynamics, and offers a freedom in controlling the quantum states of multiple resonators.

Direct measurement of topological invariants in photonic superlattices

Since the discovery of topological insulators, topological phases have generated considerable attention across the physics community. The superlattices in particular offer a rich system with several degrees of freedom to explore a variety of topological characteristics and control the localization of states. Albeit their importance, characterizing topological invariants in superlattices consisting of a multi-band structure is challenging beyond the basic case of two-bands as in the Su–Schreifer–Heeger model. Here, we experimentally demonstrate the direct measurement of the topological character of chiral superlattices with broken inversion symmetry. Using a CMOS-compatible nanophotonic chip, we probe the state evolving in the system along the propagation direction using novel nanoscattering structures. We employ a two-waveguide bulk excitation scheme to the superlattice, enabling the identification of topological zero-energy modes through measuring the beam displacement. Our measurements reveal quantized beam displacement corresponding to 0.088 and −0.245, in the cases of trivial and nontrivial photonic superlattices, respectively, showing good agreement with the theoretical values of 0 and −0.25. Our results provide direct identification of the quantized topological numbers in superlattices using a single-shot approach, paving the way for direct measurements of topological invariants in complex photonic structures using tailored excitations with Wannier functions.

Steering of one-way large-area waveguide modes in topological heterostructures with gyromagnetic photonic crystals

We study the steering of one-way and large-area topological waveguide modes in heterostructures consisting of a domain of ordinary photonic crystals sandwiched between two domains of magnetic-optical photonic crystals. Taking advantage of the band and mode properties of the topological heterostructures, we first demonstrate the design of four basic steering units which can realize the functionalities of forward-guiding, T-splitting, upward turning and downward turning. We demonstrate in detailed characteristic with the high-efficiency and broad-bandwidth of these basic steering units designed. Moreover, by combining these basic steering units, we implement a series of multifunctional waveguide devices, such as one-way large-area waveguide splitters with multiple channels and different angles, a highly bended large-area waveguide with five 90° corners along the propagation path, and waveguide structures supporting waveguide-cavity interaction, delay, splitting as well as storage functionalities. Importantly, all these different functionaries could be realized in a single system platform by simply reconfiguring the underlying magnetic field distributions. Our work opens up a new venue towards designing multi-functional waveguide devices by exploiting the width degree of freedom of the large-area waveguide modes.