分类: 光学 >> 量子光学 提交时间: 2023-02-23
摘要: 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.
分类: 光学 >> 量子光学 提交时间: 2023-02-19
摘要: 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.
分类: 光学 >> 量子光学 提交时间: 2023-02-19
摘要: 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-Andr\'{e}-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.
分类: 光学 >> 量子光学 提交时间: 2023-02-19
摘要: 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.
分类: 光学 >> 量子光学 提交时间: 2023-02-19
摘要: 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.