arXiv subjects

Shiqi Xia

Publications and source records attributed to Shiqi Xia.

At least 19 recordsLinked to original sources

arXiv2026

Topological photonics in one-dimensional settings

Over the past decade, topological photonics has emerged as a vibrant field, attracting significant attention and witnessing remarkable advancements. This growth can be attributed to its fundamental appeal and the unique opportunities it offers for unconventional control of light, promising innovations in next-generation photonic devices. At the heart of topological photonics lies the one-dimensional (1D) SSH model. Originally conceived to elucidate the physics of a molecular chain of polyacetylene, this model has found widespread applications in exploring a wide range of topological phenomena in photonics and beyond. In this chapter, we aim to provide an overview of topological photonics in one-dimensional (1D) settings. After briefly introducing paradigmatic 1D models, including the SSH, Rice-Mele, and AAH models, we review recent advances in experimental studies and applications of topological photonics based on 1D platforms. Our discussion highlights demonstrated examples, such as the nonlinear tuning of topological states in both Hermitian and non-Hermitian photonic SSH lattices, as well as nonlinear harmonic generation and topological lasing in SSH-type photonic microstructures. We further discuss characteristic topological phenomena in other representative 1D settings, including Floquet systems, topological pumping, quasicrystals, and synthetic non-Hermitian systems. Finally, we examine selected examples of two-dimensional (2D) photonic topological crystalline insulators that are closely linked to the SSH model. Towards the end, we summarize the chapter and provide a list of key contributions, together with an outlook on possible future directions in 1D topological photonics. While this review focuses specifically on 1D topological photonics, it is not intended to be comprehensive or exhaustive.

physics.optics↗

arXiv2025

Strain-Induced Boundary States and Phase Transitions in Graphene Flakes

Strain has been extensively employed to tailor graphene's properties and has emerged as a powerful tool for engineering gauge fields and exploring fundamental phenomena in artificial platforms like photonic graphene. Here we discover that, in graphene flakes with custom boundaries, one can create or destroy edge states depending on the direction of the applied uniaxial strain. This is experimentally demonstrated in a photonic platform with two specific examples: one flake structure with pairs of twig and zigzag edges, and the other with pairs of armchair and bearded edges. We find that the existence of the edge states and their positions in momentum space are accurately predicted with appropriate winding numbers, unveiling the underlying topology of such edge states. Furthermore, when a graphene flake supports the maximum number of edge states along boundaries after a semimetal-to-insulator transition, both compact localized edge and corner states emerge, indicating the realization of a photonic minimal-model higher-order topological insulator based on such strained graphene flakes.

physics.optics↗

arXiv2025

Unveiling prethermalization and thermal processes through the simplest one-dimensional topological model

Drawing on classical thermodynamic principles-such as the equipartition of energy and entropy maximization-extensive research has shown that the evolution of optical power in multimode optical systems tends toward a Rayleigh-Jeans distribution at thermal equilibrium. Understanding of the processes associated with the thermalization dynamics are of fundamental importance in analyzing and controlling such complex systems. In this work, we utilize a one-dimensional Su-Schrieffer-Heeger lattice as the simplest topological model to investigate the thermalization process of multiband systems in both topologically trivial and nontrivial regimes. Specifically, we identify that thermalization develops in three stages: (i) out-of-equilibrium dynamics, (ii) prethermal stage and (iii) final thermalization. Each individual band constitutes a subsystem that prethermalizes to the Rayleigh-Jeans distribution predicted from its power and internal energy. We find that this leads to a continuously varying prethermalization that eventually relaxes to the final thermal state (a dynamically evolving prethermal state). The presence of topological edge states can accelerate the thermalization process, although prethermal states exist both in the topologically trivial and nontrivial regimes. Factors such as bandgap width, temperature and nonlinearity that can influence the thermalization dynamics are examined in detail. Our work may offer valuable physical insights into understanding and controlling the thermalization process in multiband optical systems, paving the way for more efficient manipulation of light in complex settings.

physics.optics↗

arXiv2025

Observation of doubly-degenerate topological flatbands of edge states in strained graphene

Flat bands are of significant interest due to their potential for energy confinement and their ability to enable strongly correlated physics. Incorporating topology into flatband systems further enhances flatband mode robustness against perturbations. Here, we present the first realization of doubly degenerate topological flatbands of edge states in chiral-symmetric strained graphene. The flatband degeneracy stems from Dirac point merging, achieved by tuning the coupling ratios in a honeycomb lattice with twig boundary conditions. The nontrivial topology of these modes is characterized by the winding of the Berry connection, which ensures their robustness against disorder. Experimentally, two types of topological edge states are observed in a strained photonic graphene lattice, consistent with numerical simulations. Moreover, the degeneracy of the topological flatbands doubles the density of states for zero-energy modes, facilitating the formation of compact edge states and enhancing control over edge states and light confinement. Our findings underscore the interplay among lattice geometry, symmetry, and topology in shaping doubly degenerate topological flatbands. This opens new possibilities for advancements in correlated effects, nonlinear optical phenomena, and efficient energy transfer in materials science, photonic crystals, and quantum devices.

physics.optics↗

arXiv2025

Observation of Topological Armchair Edge States in Photonic Biphenylene Network

Edge states in 2D materials are vital for advancements in spintronics, quantum computing, and logic transistors. For graphene nanoribbons, it is well known that the zigzag edges can host edge states, but realization of armchair edge states has been challenging without breaking the time-reversal symmetry. Here, by using a photonic analog of recently synthesized graphene-like biphenylene network (BPN), we demonstrate topological in-gap edge states particularly at the armchair edges. Interestingly, several bulk states preserve the characteristics of edge states along the armchair boundaries, manifesting an unusual hybridization between the edge and bulk states. Experimentally, we observe both zigzag and armchair edge states in photonic BPN lattices written in a nonlinear crystal. Furthermore, we clarify the different features of the armchair boundary between the BPN and graphene lattices. Our results demonstrated here may be applicable to carbon-based BPNs and other artificial platforms beyond photonics, holding promise for expanding the application scope of 2D materials.

physics.optics↗

arXiv2024

Bulk-hole correspondence and inner robust boundary modes in singular flatband lattices

Topological entities based on bulk-boundary correspondence are ubiquitous, from conventional to higher-order topological insulators, where the protected states are typically localized at the outer boundaries (edges or corners). A less explored scenario involves protected states that are localized at the inner boundaries, sharing the same energy as the bulk states. Here, we propose and demonstrate what we refer to as the bulk-hole correspondence - a relation between the inner robust boundary modes (RBMs) and the existence of multiple "holes" in singular flatband lattices, mediated by the immovable discontinuity of the bulk Bloch wavefunctions. We find that the number of independent flatband states always equals the sum of the number of independent compact localized states and the number of nontrivial inner RBMs, as captured by the Betti number that also counts the hole number from topological data analysis. This correspondence is universal for singular flatband lattices, regardless of the lattice shape and the hole shape. Using laser-written Kagome lattices as a platform, we experimentally observe such inner RBMs, demonstrating their real-space topological nature and robustness. Our results may extend to other singular flatband systems beyond photonics, including non-Euclidean lattices, providing a new approach for understanding nontrivial flatband states and topology in hole-bearing lattice systems.

physics.optics↗

arXiv2024

Soft-Matter-Based Topological Vertical Cavity Surface Emitting Lasers

Polarized topological vertical cavity surface-emitting lasers (VCSELs), as stable and efficient on-chip light sources, play an important role in the next generation of optical storage and optical communications. However, most current topological lasers demand complex design and expensive fabrication processes, and their semiconductor-based structures pose challenges for flexible device applications. By use of an analogy with two-dimensional Semenov insulators in synthetic parametric space, we design and realize a one-dimensional optical superlattice (stacked polymerized cholesteric liquid crystal films and Mylar films), thereby we demonstrate a flexible, low threshold, circularly polarized topological VCSEL with high slope efficiency. We show that such a laser maintains a good single-mode property under low pump power and inherits the transverse spatial profile of the pump laser. Thanks to the soft-matter-based flexibility, our topological VCSEL can be "attached" to substrates of various shapes, enabling desired laser properties and robust beam steering even after undergoing hundreds of bends. Our results may find applications in consumer electronics, laser scanning and displays, as well as wearable devices.

physics.optics↗

arXiv2024

Optical Vortex Ladder via Sisyphus Pumping of Pseudospin

Robust higher-order optical vortices are much in demand for applications in optical manipulation, optical communications, quantum entanglement and quantum computing. However, in numerous experimental settings, a controlled generation of optical vortices with arbitrary orbital angular momentum (OAM) remains a substantial challenge. Here, we present a concept of "optical vortex ladder" for stepwise generation of optical vortices through Sisyphus pumping of pseudospin modes in photonic graphene. Instead of conical diffraction and incomplete pseudospin conversion under traditional Gaussian beam excitations, the vortices produced in the ladder arise from non-trivial topology and feature diffraction-free Bessel profiles, thanks to the refined excitation of the ring spectrum around the Dirac cones. By employing a periodic "kick" to the photonic graphene, effectively inducing the Sisyphus pumping, the ladder enables tunable generation of optical vortices of any order even when the initial excitation does not involve any OAM. The optical vortex ladder stands out as an intriguing non-Hermitian dynamical system, and, among other possibilities, opens up a pathway for applications of topological singularities in beam shaping and wavefront engineering.

physics.optics↗

arXiv2023

Observation of topologically distinct corner states in "bearded" photonic Kagome lattices

Kagome lattices represent an archetype of intriguing physics, attracting a great deal of interest in different branches of natural sciences, recently in the context of topological crystalline insulators. Here, we demonstrate two distinct classes of corner states in breathing Kagome lattices (BKLs) with "bearded" edge truncation, unveiling their topological origin. The in-phase corner states are found to exist only in the topologically nontrivial regime, characterized by a nonzero bulk polarization. In contrast, the out-of-phase corner states appear in both topologically trivial and nontrivial regimes, either as bound states in the continuum or as in-gap states depending on the lattice dimerization conditions. Furthermore, the out-of-phase corner states are highly localized, akin to flat-band compact localized states, and they manifest both real- and momentum-space topology. Experimentally, we observe both types of corner states in laser-written photonic bearded-edge BKLs, corroborated by numerical simulations. Our results not only deepen the current understanding of topological corner modes in BKLs, but also provide new insight into their physical origins, which may be applied to other topological BKL platforms beyond optics.

physics.optics↗

arXiv2023

Deep learning empowered synthetic dimension dynamics: morphing of light into topological modes

Synthetic dimensions (SDs) opened the door for exploring previously inaccessible phenomena in high-dimensional synthetic space. However, construction of synthetic lattices with desired coupling properties is a challenging and unintuitive task, largely limiting the exploration and current application of SD dynamics. Here, we overcome this challenge by using deep learning artificial neural networks (ANNs) to validly design the dynamics in SDs. We use ANNs to construct a lattice in real space that has a predesigned spectrum of mode eigenvalues. By employing judiciously chosen perturbations (wiggling of waveguides), we show experimentally and theoretically resonant mode coupling and tailored dynamics in SDs, which leads to effective transport or confinement of a complex beam profile. As an enlightening example, we demonstrate morphing of light into a topologically protected edge mode in ANN-designed Su-Schrieffer-Heeger photonic lattices. Such ANN-assisted construction of SDs advances towards utopian networks, opening new avenues in fundamental research beyond geometric limitations. Our findings may offer a flexible and efficient solution for mode lasing, optical switching, and communication technologies.

physics.optics↗

arXiv2023

Photonic realization of a generic type of graphene edge states exhibiting topological flat band

Cutting a honeycomb lattice (HCL) can end up with three types of edges (zigzag, bearded and armchair), as is well known in the study of graphene edge states. Here we theoretically investigate and experimentally demonstrate a class of graphene edges, namely, the twig-shaped edges, using a photonic platform, thereby observing edge states distinctive from those observed before. Our main findings are: (i) the twig edge is a generic type of HCL edges complementary to the armchair edge, formed by choosing the right primitive cell rather than simple lattice cutting or Klein edge modification; (ii) the twig edge states form a complete flat band across the Brillouin zone with zero-energy degeneracy, characterized by nontrivial topological winding of the lattice Hamiltonian; (iii) the twig edge states can be elongated or compactly localized along the boundary, manifesting both flat band and topological features. Such new edge states are realized in a laser-written photonic graphene and well corroborated by numerical simulations. Our results may broaden the understanding of graphene edge states, bringing about new possibilities for wave localization in artificial Dirac-like materials.

physics.optics↗

arXiv2022

Mapping and manipulation of topological singularities: from photonic graphene to T-graphene

Topological singularities (TSs) in momentum space give rise to intriguing fundamental phenomena as well as unusual material properties, attracting a great deal of interest in the past decade. Recently, we have demonstrated universal momentum-to-real-space mapping of TSs and pseudospin angular momentum conversion using photonic honeycomb (graphene-like) and Lieb lattices. Such mapping arises from the Berry phase encircling the Dirac or Dirac-like cones, and is thus of topological origin. In this paper, we briefly present previous observations of topological charge conversion, and then we present our first theoretical analysis and experimental demonstration of TS mapping in a new T-graphene lattice. Unlike other lattices, there are two coexisting but distinct TSs located at different high-symmetry points in the first Brillouin zone of T-graphene, which enables controlled topological charge conversion in the same lattice. We show active manipulation of the TS mapping, turning the two TSs into vortices of different helicities, or one into a high-order vortex but the other into a quadrupole. Such TS manipulation and pseudospin-to-orbital conversion may find applications in optical communications and quantum information, and may bring insight into the study of other Dirac-like structures with multiple TSs beyond the 2D photonic platform.

physics.optics↗

arXiv2022

Persistent homology analysis of a generalized Aubry-André-Harper model

Observing critical phases in lattice models is challenging due to the need to analyze the finite time or size scaling of observables. We study how the computational topology technique of persistent homology can be used to characterize phases of a generalized Aubry-André-Harper model. The persistent entropy and mean squared lifetime of features obtained using persistent homology behave similarly to conventional measures (Shannon entropy and inverse participation ratio) and can distinguish localized, extended, and crticial phases. However, we find that the persistent entropy also clearly distinguishes ordered from disordered regimes of the model. The persistent homology approach can be applied to both the energy eigenstates and the wavepacket propagation dynamics.

cond-mat.dis-nn↗

arXiv2022

Photonic p-orbital higher-order topological insulators

The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals. Despite tremendous efforts in engineering synthetic cold-atom, electronic and photonic lattices to explore orbital physics, thus far high orbitals in an important class of materials, namely, the higher-order topological insulators (HOTIs), have not been realized. Here, we demonstrate p-orbital corner states in a photonic HOTI, unveiling their underlying topological invariant, symmetry protection, and nonlinearity-induced dynamical rotation. In a Kagome-type HOTI, we find that topological protection of the p-orbital corner states demands an orbital-hopping symmetry, in addition to the generalized chiral symmetry. Due to orbital hybridization, the nontrivial topology of the p-orbital HOTI is hidden if bulk polarization is used as the topological invariant, but well manifested by the generalized winding number. Our work opens a pathway for the exploration of intriguing orbital phenomena mediated by higher band topology applicable to a broad spectrum of systems.

physics.optics↗

arXiv2022

Topological flatband loop states in fractal-like photonic lattices

Noncontractible loop states (NLSs) are recently realized topological entity in flatband lattices, arising typically from band touching at a point where a flat band intersects one or more dispersive bands. There exists also band touching across a plane, where one flat band overlaps another all over the Brillouin zone without crossing a dispersive band. Such isolated plane-touching flat bands remain largely unexplored. For example, what are the topological features associated with such flatband degeneracy? Here, we demonstrate for the first time to our knowledge nontrivial NLSs and robust boundary modes in a system with such degeneracy. Based on a tailored photonic lattice constructed from the well-known fractal Sierpinski gasket, we theoretically analyze the wavefunction singularities and the conditions for the existence of the NLSs. We show that the NLSs can exist in both singular and nonsingular flat bands, as a direct reflection of the real-space topology. Experimentally, we observe directly such flatband NLSs in a laser-written Corbino-shaped fractal-like lattice. This work not only leads to a deep understanding of the mechanism behind the nontrivial flatband states, but also opens up new avenues to explore fundamental phenomena arising from the interplay of flatband degeneracy, fractal structures and band topology.

physics.optics↗

arXiv2021

Topologically tuned terahertz confinement in a nonlinear photonic chip

Compact terahertz (THz) functional devices are greatly sought after for high-speed wireless communication, biochemical sensing, and non-destructive inspection. However, conventional devices to generate and guide THz waves are afflicted with diffraction loss and disorder due to inevitable fabrication defects. Here, based on the topological protection of electromagnetic waves, we demonstrate nonlinear generation and topologically tuned confinement of THz waves in a judiciously-patterned lithium niobate chip forming a wedge-shaped Su-Schrieffer-Heeger lattice. Experimentally measured band structures provide direct visualization of the generated THz waves in momentum space, and their robustness to chiral perturbation is also analyzed and compared between topologically trivial and nontrivial regimes. Such chip-scale control of THz waves may bring about new possibilities for THz integrated topological circuits, promising for advanced photonic applications.

physics.optics↗

arXiv2021

Realization of second-order photonic square-root topological insulators

Square-root higher-order topological insulators (HOTIs) are recently discovered new topological phases, with intriguing topological properties inherited from a parent lattice Hamiltonian. Different from conventional HOTIs, the square-root HOTIs typically manifest two paired non-zero energy corner states. In this work, we experimentally demonstrate the second-order square-root HOTIs in photonics for the first time to our knowledge, thereby unveiling such distinct corner states. The specific platform is a laser-written decorated honeycomb lattice (HCL), for which the squared Hamiltonian represents a direct sum of the underlying HCL and breathing Kagome lattice. The localized corner states residing in different bandgaps are observed with characteristic phase structures, in sharp contrast to discrete diffraction in a topologically trivial structure. Our work illustrates a scheme to study fundamental topological phenomena in systems with coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions, and may bring about new possibilities in topology-driven photonic devices.

physics.optics↗

arXiv2021

Fractal-like photonic lattices and localized states arising from singular and nonsingular flatbands

We realize fractal-like photonic lattices using cw-laser-writing technique, thereby observe distinct compact localized states (CLSs) associated with different flatbands in the same lattice setting. Such triangle-shaped lattices, akin to the first generation Sierpinski lattices, possess a band structure where singular non-degenerate and nonsingular degenerate flatbands coexist. By proper phase modulation of an input excitation beam, we demonstrate experimentally not only the simplest CLSs but also their superimposition into other complex mode structures. Furthermore, we show by numerical simulation a dynamical oscillation of the flatband states due to beating of the CLSs that have different eigenenergies. These results may provide inspiration for exploring fundamental phenomena arising from fractal structure, flatband singularity, and real-space topology.

physics.optics↗