Fermionic time-reversal symmetry in a photonic topological insulator

Parity-time-symmetric photonic topological insulator

Topological insulators are a concept that originally stems from condensed matter physics. As a corollary to their hallmark protected edge transport, the conventional understanding of such systems holds that they are intrinsically closed, that is, that they are assumed to be entirely isolated from the surrounding world. Here, by demonstrating a parity-time-symmetric topological insulator, we show that topological transport exists beyond these constraints. Implemented on a photonic platform, our non-Hermitian topological system harnesses the complex interplay between a discrete coupling protocol and judiciously placed losses and, as such, inherently constitutes an open system. Nevertheless, even though energy conservation is violated, our system exhibits an entirely real eigenvalue spectrum as well as chiral edge transport. Along these lines, this work enables the study of the dynamical properties of topological matter in open systems without the instability arising from complex spectra. Thus, it may inspire the development of compact active devices that harness topological features on-demand.

Dynamical Detection of Topological Spectral Density

Local density of states (LDOS) is emerging as powerful means of exploring classical-wave topological phases. However, the current LDOS detection method remains rare and merely works for static situations. Here, we introduce a generic dynamical method to detect both the static and Floquet LDOS, based on an elegant connection between dynamics of chiral density and local spectral densities. Moreover, we find that the Floquet LDOS allows to measure out Floquet quasienergy spectra and identify topological π modes. As an example, we demonstrate that both the static and Floquet higher-order topological phase can be universally identified via LDOS detection, regardless of whether the topological corner modes are in energy gaps, bands, or continuous energy spectra without band gaps. Our study opens a new avenue utilizing dynamics to detect topological spectral densities and provides a universal approach of identifying static and Floquet topological phases.

Fractal photonic anomalous Floquet topological insulators to generate multiple quantum chiral edge states

Anomalous Floquet topological insulators with vanishing Chern numbers but supporting chiral edge modes are attracting more and more attention. Since the existing anomalous Floquet topological insulators usually support only one kind of chiral edge mode even at a large lattice size, they are unscalable and unapplicable for multistate topological quantum systems. Recently, fractal topological insulators with self-similarity have been explored to support more nontrivial modes. Here, we demonstrate the first experimental realization of fractal photonic anomalous Floquet topological insulators based on dual Sierpinski carpet consisting of directional couplers using the femtosecond laser direct writing. The fabricated lattices support much more kinds of chiral edge states with fewer waveguides and enable perfect hopping of quantum states with near unit transfer efficiency. Instead of zero-dimensional bound modes for quantum state transport in previous laser direct-written topological insulators, we generate multiple propagating single-photon chiral edge states in the fractal lattice and observe high-visibility quantum interferences. These suggest the successful realization of highly indistinguishable single-photon chiral edge states, which can be applied in various quantum operations. This work provides the potential for enhancing the multi-fold manipulation of quantum states, enlarging the encodable quantum information capacity in a single lattice via high-dimensional encoding and many other fractal applications.

A second wave of topological phenomena in photonics and acoustics

Light and sound are the most ubiquitous forms of waves, associated with a variety of phenomena and physical effects such as rainbows and echoes. Light and sound, both categorized as classical waves, have lately been brought into unexpected connections with exotic topological phases of matter. We are currently witnessing the onset of a second wave of active research into this topic. The past decade has been marked by fundamental advances comprising two-dimensional quantum Hall insulators and quantum spin and valley Hall insulators, whose topological properties are characterized using linear band topology. Here, going beyond these conventional topological systems, we focus on the latest frontiers, including non-Hermitian, nonlinear and non-Abelian topology as well as topological defects, for which the characterization of the topological features goes beyond the standard band-topology language. In addition to an overview of the current state of the art, we also survey future research directions for valuable applications.

Ideal acoustic quantum spin Hall phase in a multi-topology platform

Fermionic time-reversal symmetry ([Formula: see text])-protected quantum spin Hall (QSH) materials feature gapless helical edge states when adjacent to arbitrary trivial cladding materials. However, due to symmetry reduction at the boundary, bosonic counterparts usually exhibit gaps and thus require additional cladding crystals to maintain robustness, limiting their applications. In this study, we demonstrate an ideal acoustic QSH with gapless behaviour by constructing a global T_f on both the bulk and the boundary based on bilayer structures. Consequently, a pair of helical edge states robustly winds several times in the first Brillouin zone when coupled to resonators, promising broadband topological slow waves. We further reveal that this ideal QSH phase behaves as a topological phase transition plane that bridges trivial and higher-order phases. Our versatile multi-topology platform sheds light on compact topological slow-wave and lasing devices.

Photonic Z_{2} Topological Anderson Insulators

That disorder can induce nontrivial topology is a surprising discovery in topological physics. As a typical example, Chern topological Anderson insulators (TAIs) have been realized in photonic systems, where the topological phases exist without symmetry protection. In this Letter, by taking transverse magnetic and transverse electric polarizations as pseudospin degrees of freedom, we theoretically propose a scheme to realize disorder-induced symmetry-protected topological phase transitions in two-dimensional photonic crystals with a combined time-reversal, mirror, and duality symmetry T_{f}=TM_{z}D. In particular, we demonstrate that the disorder-induced symmetry-protected topological phase persists even without pseudospin conservation, thereby realizing a photonic Z_{2} TAI, in contrast to a Z-classified quantum spin Hall (QSH) TAI with decoupled spins. By formulating a new scattering approach, we show that the topology of both the QSH and Z_{2} TAIs can be manifested by the accumulated spin rotations of the reflected waves from the photonic crystals. Using a transmission structure, we also illustrate the trivialization of a disordered QSH phase with an even integer topological index caused by spin coupling.

On-chip beam rotators, adiabatic mode converters, and waveplates through low-loss waveguides with variable cross-sections

Photonics integrated circuitry would benefit considerably from the ability to arbitrarily control waveguide cross-sections with high precision and low loss, in order to provide more degrees of freedom in manipulating propagating light. Here, we report a new method for femtosecond laser writing of optical-fiber-compatible glass waveguides, namely spherical phase-induced multicore waveguide (SPIM-WG), which addresses this challenging task with three-dimensional on-chip light control. Fabricating in the heating regime with high scanning speed, precise deformation of cross-sections is still achievable along the waveguide, with shapes and sizes finely controllable of high resolution in both horizontal and vertical transversal directions. We observed that these waveguides have high refractive index contrast of 0.017, low propagation loss of 0.14 dB/cm, and very low coupling loss of 0.19 dB coupled from a single-mode fiber. SPIM-WG devices were easily fabricated that were able to perform on-chip beam rotation through varying angles, or manipulate the polarization state of propagating light for target wavelengths. We also demonstrated SPIM-WG mode converters that provide arbitrary adiabatic mode conversion with high efficiency between symmetric and asymmetric nonuniform modes; examples include circular, elliptical modes, and asymmetric modes from ppKTP (periodically poled potassium titanyl phosphate) waveguides which are generally applied in frequency conversion and quantum light sources. Created inside optical glass, these waveguides and devices have the capability to operate across ultra-broad bands from visible to infrared wavelengths. The compatibility with optical fiber also paves the way toward packaged photonic integrated circuitry, which usually needs input and output fiber connections.

Non-Floquet engineering in periodically driven dissipative open quantum systems

Floquet engineering plays a key role in realizing novel dynamical topological states. The conventional Floquet engineering, however, only applies to time-periodic non-dissipative Hermitian systems, and for the open quantum systems, non-Hermitian processes usually occur. So far, it remains unclear how to characterize the topological phases of time-periodic open quantum systems via the frequency space Floquet Hamiltonian. Here, we propose the non-Floquet theory to solve the problem and illustrate it by a continuously time-periodic non-Hermitian bipartite chain. In non-Floquet theory, a temporal non-unitary transformation is exercised on the Floquet states, and the transformed Floquet spectrum restores the form of the Wannier-Stark ladder. Besides, we also show that different choices of the starting points of the driving period can result in different localization behavior, effects of which can reversely be utilized to design quantum detectors of phases in dissipative oscillating fields. Our methods are capable of describing topological features in dynamical open quantum systems with various driving types and can find its applications to construct new types of dynamical topological materials.

Bimorphic Floquet topological insulators

Topological theories have established a unique set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by specifically tailored discrete coupling protocols or helical lattice motions, we introduce a class of bimorphic Floquet topological insulators that leverage connective chains with periodically modulated on-site potentials to reveal rich topological features in the system. In exploring a 'chain-driven' generalization of the archetypical Floquet honeycomb lattice, we identify a rich phase structure that can host multiple non-trivial topological phases associated simultaneously with both Chern-type and anomalous chiral states. Experiments carried out in photonic waveguide lattices reveal a strongly confined helical edge state that, owing to its origin in bulk flat bands, can be set into motion in a topologically protected fashion, or halted at will, without compromising its adherence to individual lattice sites.

Spin-Polarized Fractional Corner Charges and Their Photonic Realization

We demonstrate that a spin degree of freedom can introduce additional texture to higher order topological insulators (HOTIs), manifesting in novel topological invariants and phase transitions. Spin-polarized mid-gap corner states of various multiplicities are predicted for different HOTI phases, and novel bulk-boundary correspondence principles are defined based on bulk invariants such as total and spin corner charge. Those are shown to be robust to spin-flipping perturbations. Photonic realizations of spin-linked topological phases are demonstrated in engineered systems using pseudospin.