Observation of Non-Abelian Thouless Pump.

Thouless pump provides robust ways to realize quantized transport of waves and particles, and it casts the static 2D quantum Hall effect onto 1D dynamic systems where one of the momentum dimensions is replaced by the evolution time or path parameter. In the past few decades, various types of Abelian Thouless pump have been achieved theoretically and experimentally. However, the study of non-Abelian Thouless pump is scarce, which tells us that the order of two evolution loops with the same base point cannot be changed, and there has been no experimental observation of non-Abelian Thouless pump. Here we report the observation of a non-Abelian Thouless pump in coupled acoustic waveguide array. The non-Abelian property originates from the noncommutative combination of two different ℤ_{3} pump cycles that traverse across multiple band degeneracies in the parameter space in a three-band system. Moreover, we can pump a specific initial state to any state on any lattice site by applying these two ℤ_{3} pump cycles multiple times in a well-designed sequence. Our study paves the way for exploring and utilizing non-Abelian dynamical effects in classical wave systems and may offer different recipes for quantum walking, quantum optics, and quantum computation.

Vortical Reflection and Spiraling Fermi Arcs with Weyl Metamaterials.

Scatterings and transport in Weyl semimetals have caught growing attention in condensed matter physics, with observables including chiral zero modes and the associated magnetoresistance and chiral magnetic effects. Measurement of electrical conductance is usually performed in these studies, which, however, cannot resolve the momentum of electrons, preventing direct observation of the phase singularities in scattering matrix associated with Weyl point. Here we experimentally demonstrate a helical phase distribution in the angle (momentum) resolved scattering matrix of electromagnetic waves in a photonic Weyl metamaterial. It further leads to spiraling Fermi arcs in an air gap sandwiched between a Weyl metamaterial and a metal plate. Benefiting from the alignment-free feature of angular vortical reflection, our findings establish a new platform in manipulating optical angular momenta with photonic Weyl systems.

Observation of Non-Abelian Nodal Links in Photonics.

In crystals, two bands may cross each other and form degeneracies along a closed loop in the three-dimensional momentum space, which is called nodal line. Nodal line degeneracy can be designed to exhibit various configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian band topology was proposed in nodal link systems, where the nodal lines formed by consecutive pairs of bands exhibit interesting braiding structures and the underlying topological charges are described by quaternions. Here, we experimentally demonstrate non-Abelian nodal links in a biaxial hyperbolic metamaterial. The linked nodal lines threading through each other are formed by the crossings between three adjacent bands. Based on the non-Abelian charges, we further analyze various admissible nodal link configurations for the three-band system. On the interface between the metamaterial and air, surface bound states in the continuum are observed, which serves as the symmetry-enforced derivative of drumhead surface states from the linked nodal lines. Our work serves as a direct observation of the global topological structures of nodal links, and provides a platform for studying non-Abelian topological charge in the momentum space.

Observation of Three-Dimensional Photonic Dirac Points and Spin-Polarized Surface Arcs.

Three-dimensional (3D) Dirac points inheriting relativistic effects from high-energy physics appear as gapless excitations in the topological band theory. Hosting fourfold linear dispersion, they play the central role among various topological phases, such as representing the degeneracy of paired Weyl nodes carrying opposite chiralities. While they have been extensively investigated in solid state systems for electrons, 3D Dirac points have not yet been observed in any classical systems. Here, we experimentally demonstrate 3D photonic Dirac points in the microwave region with an elaborately designed metamaterial, where two symmetrically placed Dirac points are stabilized by electromagnetic duality symmetry. Furthermore, spin-polarized surface arcs (counterparts of Fermi arcs in electronic systems) are demonstrated, which opens the gate toward implementing spin-multiplexed topological surface wave propagation. Closely linked to other exotic states through topological phase transitions, our system offers an effective medium platform for topological photonics.

Versatile and tunable surface plasmon polariton excitation over a broad bandwidth with a simple metaline by external polarization modulation.

Surface plasmon polariton (SPP) sources and launchers are highly demanded in various applications of nanophotonics. Here, we propose a general approach that can realize complete control of the complex extinction ratio (including amplitude and phase) of any two linearly independent SPP modes excited by any elementary SPP excitation architecture just by manipulating the incident polarization state. In an optical system, it suffices to simply tune the orientation angles of a linear polarizer and a quarter wave plate, which may greatly simplify the design and application of SPP launchers and diversify their functionalities. As an example to show the broad application prospect of this method, we design and realize a metaline consisting of Δ-shaped plasmonic nanoantennas, which can effectively realize dual functionalities, i.e., the tunable directional SPP excitation at an arbitrarily chosen wavelength and the complete unidirectional SPP excitation over a broad bandwidth. This general approach can also be extended to the control of the complex extinction ratio of any two linearly independent excited modes in many other linear optical systems, such as two modes in a waveguide or two diffraction orders in a grating, over a broad bandwidth.

A simple method for generating unidirectional surface plasmon polariton beams with arbitrary profiles.

The efficient steering of surface plasmon polariton (SPP) fields is a vital issue in various plasmonic applications, such as plasmonic circuitry. We present a straightforward and efficient method for generating unidirectionally propagating SPP beams with arbitrary amplitude and phase profiles by manipulating Δ-shaped nanoantennas. As an example, a second-order Hermite-Gauss SPP beam is generated with this method. The near-field distribution of the generated SPP beam is experimentally characterized to validate the effectiveness of the method.

M-shaped grating by nanoimprinting: a replicable, large-area, highly active plasmonic surface-enhanced Raman scattering substrate with nanogaps.

Plasmonic nanostructures separated by nanogaps enable strong electromagnetic-field confinement on the nanoscale for enhancing light-matter interactions, which are in great demand in many applications such as surface-enhanced Raman scattering (SERS). A simple M-shaped nanograting with narrow V-shaped grooves is proposed. Both theoretical and experimental studies reveal that the electromagnetic field on the surface of the M grating can be pronouncedly enhanced over that of a grating without such grooves, due to field localization in the nanogaps formed by the narrow V grooves. A technique based on room-temperature nanoimprinting lithography and anisotropic reactive-ion etching is developed to fabricate this device, which is cost-effective, reliable, and suitable for fabricating large-area nanostructures. As a demonstration of the potential application of this device, the M grating is used as a SERS substrate for probing Rhodamine 6G molecules. Experimentally, an average SERS enhancement factor as high as 5×108 has been achieved, which verifies the greatly enhanced light-matter interaction on the surface of the M grating over that of traditional SERS surfaces.

Magneto-optical chiral metasurfaces for achieving polarization-independent nonreciprocal transmission.

Nonreciprocal transmission, resulting from the breaking of Lorentz reciprocity, plays a pivotal role in nonreciprocal communication systems by enabling asymmetric forward and backward propagations. Metasurfaces endowed with nonreciprocity represent a compact and facile platform for manipulating electromagnetic waves in an unprecedented manner. However, most passive metasurfaces that achieve nonreciprocal transmissions are polarization dependent. While incorporation of active elements or nonlinear materials can achieve polarization-independent nonreciprocal metasurfaces, the complicated configurations limit their practical applications. To address this issue, we propose and demonstrate a passive and linear metasurface that combines magneto-optical and chiral effects, enabling polarization-independent isolation. The designed metasurface achieves a transmittance of up to 80%, with a high contrast between forward and backward propagations. Our work introduces a novel mechanism for nonreciprocal transmission and lays the foundation for the development of compact, polarization-insensitive nonreciprocal devices.

Fast topological pumps via quantum metric engineering on photonic chips.

Topological pumps have garnered substantial attention in physics. However, the requirement for slow evolution speed to satisfy adiabaticity greatly restricts their application in on-chip devices. Here, we discover a direct link between adiabaticity and quantum metric, the real part of quantum geometry that has been relatively less explored compared to its imaginary counterpart, the Berry curvature. We demonstrate that the evolution speed of topological pumps between nontrivial edge states can be increased by reducing the quantum metric via introduction of long-range coupling to the celebrated Rice-Mele model. This fast topological pump can occur without affecting the bulk state evolution, which challenges the common understanding. We experimentally confirm our findings by using a platform consisting of bilayer integrated silicon waveguides operating at telecommunication wavelengths. Our work provides possibilities for lifting topological pumps from the constraints of slow evolution and paves the way toward compact photonic integration.

Chiral transmission by an open evolution trajectory in a non-Hermitian system.

Exceptional points (EPs), at which two or more eigenvalues and eigenstates of a resonant system coalesce, are associated with non-Hermitian Hamiltonians with gain and/or loss elements. Dynamic encircling of EPs has received significant interest in recent years, as it has been shown to lead to highly nontrivial phenomena, such as chiral transmission in which the final state of the system depends on the encircling handedness. Previously, chiral transmission for a pair of eigenmodes has been realized by establishing a closed dynamical trajectory in parity-time- (PT-) or anti-PT-symmetric systems. Although chiral transmission of symmetry-broken modes, more accessible in practical photonic integrated circuits, has been realized by establishing a closed trajectory encircling EPs in anti-PT-symmetric systems, the demonstrated transmission efficiency is very low due to path-dependent losses. Here, we demonstrate chiral dynamics in a coupled waveguide system that does not require a closed trajectory. Specifically, we explore an open trajectory linking two infinite points having the same asymptotic eigenmodes (not modes in PT- and anti-PT-symmetric systems), demonstrating that this platform enables high-efficiency chiral transmission, with each eigenmode localized in a single waveguide. This concept is experimentally implemented in a coupled silicon waveguide system at telecommunication wavelengths. Our work provides a new evolution strategy for chiral dynamics with superior performance, laying the foundation for the development of practical chiral-transmission devices.

Non-Hermitian Skin Effect in a Non-Hermitian Electrical Circuit.

The conventional bulk-boundary correspondence directly connects the number of topological edge states in a finite system with the topological invariant in the bulk band structure with periodic boundary condition (PBC). However, recent studies show that this principle fails in certain non-Hermitian systems with broken reciprocity, which stems from the non-Hermitian skin effect (NHSE) in the finite system where most of the eigenstates decay exponentially from the system boundary. In this work, we experimentally demonstrate a 1D non-Hermitian topological circuit with broken reciprocity by utilizing the unidirectional coupling feature of the voltage follower module. The topological edge state is observed at the boundary of an open circuit through an impedance spectra measurement between adjacent circuit nodes. We confirm the inapplicability of the conventional bulk-boundary correspondence by comparing the circuit Laplacian between the periodic boundary condition (PBC) and open boundary condition (OBC). Instead, a recently proposed non-Bloch bulk-boundary condition based on a non-Bloch winding number faithfully predicts the number of topological edge states.

Linked Weyl surfaces and Weyl arcs in photonic metamaterials.

Generalization of the concept of band topology from lower-dimensional to higher-dimensional (n > 3) physical systems is expected to introduce new bulk and boundary topological effects. However, theoretically predicted topological singularities in five-dimensional systems-Weyl surfaces and Yang monopoles-have either not been demonstrated in realistic physical systems or are limited to purely synthetic dimensions. We constructed a system possessing Yang monopoles and Weyl surfaces based on metamaterials with engineered electromagnetic properties, leading to the observation of several intriguing bulk and surface phenomena, such as linking of Weyl surfaces and surface Weyl arcs, via selected three-dimensional subspaces. The demonstrated photonic Weyl surfaces and Weyl arcs leverage the concept of higher-dimension topology to control the propagation of electromagnetic waves in artificially engineered photonic media.

Momentum space toroidal moment in a photonic metamaterial.

Berry curvature, the counterpart of the magnetic field in the momentum space, plays a vital role in the transport of electrons in condensed matter physics. It also lays the foundation for the emerging field of topological physics. In the three-dimensional systems, much attention has been paid to Weyl points, which serve as sources and drains of Berry curvature. Here, we demonstrate a toroidal moment of Berry curvature with flux approaching to π in judiciously engineered metamaterials. The Berry curvature exhibits a vortex-like configuration without any source and drain in the momentum space. Experimentally, the presence of Berry curvature toroid is confirmed by the observation of conical-frustum shaped domain-wall states at the interfaces formed by two metamaterials with opposite toroidal moments.

Octupole corner state in a three-dimensional topological circuit.

Higher-order topological insulators (HOTIs) represent a new family of topological materials featuring quantized bulk polarizations and zero-dimensional corner states. In recent years, zero-dimensional corner states have been demonstrated in two-dimensional systems in the form of quadrupole modes or dipole modes. Due to the challenges in designing and constructing three-dimensional systems, octupole corner modes in 3D have not been observed. In this work, we experimentally investigate octupole topological phases in a three-dimensional electrical circuit, which can be viewed as a cubic lattice version of the Hofstadter model with a π-flux threading each plaquette. We experimentally observe in our higher-order topological circuit a 0D corner state manifested as a localized impedance peak. The observed corner state in the electrical circuit is induced by the octupole moment of the bulk circuit and is topologically protected by anticommuting spatial symmetries of the circuit lattice. Our work provides a platform for investigating higher-order topological effects in three-dimensional electrical circuits.