Bound states in the continuum (BICs) are spatially localized states embedded in the continuous spectrum without hybridizing with extended bulk modes. Recent advances in topological band theory have greatly enriched the understanding of BICs, which gives rise to boundary-localized topological BICs with extremely high robustness against disorders. However, there remains a challenge in realizing corner-localized topological BICs in a three-dimensional system due to the absence of both realistic theoretical models and effective topological characterization schemes. In particular, how to engineer a controllable number of corner-localized topological BIC is still an open question. Here, we propose that the corner-localized topological BICs can emerge in a class of generalized breathing pyrochlore lattice with general inter-cell hoppings. We further show that the number of BICs at each corner can be arbitrarily adjusted by changing the parameters of inter-cell hoppings. Remarkably, although these corner-localized topological BICs are intertwined with a substantial number of bulk modes, we can accurately characterize them through the polarized topological charges, which are nodal points with topological properties in Brillouin zone and are measurable in experiments. We also reveal three types of topological phase transitions of corner-localized BICs, which are associated with the different ways of closing the bulk energy gap and can be intuitively captured by the polarized topological charges. This work not only promotes the theoretical research of corner-localized topological BICs, but also opens an avenue for their experimental observation in the future.
Bound states in the continuum (BICs) are spatially localized states embedded in the continuous spectrum without hybridizing with extended bulk modes. Recent advances in topological band theory have greatly enriched the understanding of BICs, which gives rise to boundary-localized topological BICs with extremely high robustness against disorders. However, there remains a challenge in realizing corner-localized topological BICs in a three-dimensional system due to the absence of both realistic theoretical models and effective topological characterization schemes. In particular, how to engineer a controllable number of corner-localized topological BIC is still an open question. Here, we propose that the corner-localized topological BICs can emerge in a class of generalized breathing pyrochlore lattice with general inter-cell hoppings. We further show that the number of BICs at each corner can be arbitrarily adjusted by changing the parameters of inter-cell hoppings. Remarkably, although these corner-localized topological BICs are intertwined with a substantial number of bulk modes, we can accurately characterize them through the polarized topological charges, which are nodal points with topological properties in Brillouin zone and are measurable in experiments. We also reveal three types of topological phase transitions of corner-localized BICs, which are associated with the different ways of closing the bulk energy gap and can be intuitively captured by the polarized topological charges. This work not only promotes the theoretical research of corner-localized topological BICs, but also opens an avenue for their experimental observation in the future.
Abstract Bound states in the continuum (BICs), referring to spatially localized bound states with energies falling within the range of extended modes, have been extensively investigated in single-particle systems, leading to diverse applications in photonics, acoustics, and other classical-wave systems. Recently, there has been theoretical interest in exploring many-body BICs in interacting quantum systems, which necessitate the careful design of impurity potentials or spatial profiles of interaction. Here, we propose a type of many-body BICs localized at boundaries, which can be purely induced by the uniform onsite interaction without requiring any specific design of impurity potential or nonlocal interaction. We numerically show that three or more interacting bosons can concentrate on the boundary of a homogeneous one-dimensional lattice, which is absent at single- and two-particle counterparts. Moreover, the eigenenergy of multi-boson bound states can embed within the continuous energy spectra of extended scattering states, thereby giving rise to interaction-induced boundary many-body BICs. Furthermore, by mapping Fock states of three and four bosons to nonlinear circuit networks, we experimentally simulate boundary many-body BICs. Our findings enrich the comprehension of correlated BICs beyond the single-particle level, and have the potential to inspire future investigations on exploring many-body BICs.
Simulating higher-order topological materials in synthetic quantum matter is an active research frontier for its theoretical significance in fundamental physics and promising applications in quantum technologies. Here we experimentally implement two-dimensional (2D) momentum lattices with highly programmable ability using ultracold 87Rb atoms. Through precise control of experimental parameters, we simulate a 2D Su-Schrieffer-Heeger model with this technique, and observe the characteristic dynamics of corner and edge-bound states, where the corner state is identified as a higher-order topological bound state in the continuum. We further study the adiabatic preparation of the corner state by engineering evolutions with time-dependent Hamiltonians. We also demonstrate the higher-order topological phase transition by measuring both the bulk topological invariant and the topological corner state. Our new platform opens the avenue for exploring the exotic dynamics and topology in higher synthetic dimensions, making use of the rich degrees of freedom of cold atoms systems.
Topological insulators lie outside the standard Landau paradigm: Instead of being characterized by local order parameters and spontaneous symmetry breaking, their defining properties are encoded in the global structure of their quantum states and manifested as robust boundary states. Crystalline higher-order topological insulators can extend this principle by hosting localized corner modes in two and higher dimensions. Although these boundary modes can be detected spectroscopically through the local density of states, determining the underlying bulk topology, for example through nested Wilson loops, remains an outstanding experimental challenge. Here we use up to 728 qubits in a superconducting analogue-digital quantum simulator to realize and probe a hierarchy of one-, two-, and three-dimensional topological insulators governed by effective tight-binding Hamiltonians. By reconstructing complex propagators from real-space measurements, we obtain complementary boundary and bulk characterizations: local densities of states reveal localized boundary modes, whereas experimentally reconstructed band projectors yield bulk topological invariants, culminating in a three-dimensional octupole moment extracted through third nested Wilson loops. These results establish a route to realizing, characterizing, and manipulating topologically protected states in programmable three-dimensional quantum matter.
Simulating higher-order topological materials in synthetic quantum matter is an active research frontier for its theoretical significance in fundamental physics and promising applications in quantum technologies. Here we experimentally implement two-dimensional (2D) momentum lattices with highly programmable ability using ultracold 87Rb atoms. Through precise control of experimental parameters, we simulate a 2D Su-Schrieffer-Heeger model with this technique, and observe the characteristic dynamics of corner and edge-bound states, where the corner state is identified as a higher-order topological bound state in the continuum. We further study the adiabatic preparation of the corner state by engineering evolutions with time-dependent Hamiltonians. We also demonstrate the higher-order topological phase transition by measuring both the bulk topological invariant and the topological corner state. Our new platform opens the avenue for exploring the exotic dynamics and topology in higher synthetic dimensions, making use of the rich degrees of freedom of cold atoms systems.
One-dimensional crystals serve as a versatile platform for engineering nontrivial states, which can be easily explored in transport configurations. In this work, we analyze the properties of a periodic structure composed of an H-shaped unit cell, which forms a periodic ladder-shaped system. Using tight-binding models, group-theoretical considerations, and standard band topology, we uncover the influence of bound states in the continuum (BICs) and quasi-BICs formed in the original finite geometry on the creation of nontrivial band states. By designing various textures for the onsite energies, we discovered a topological band inversion between quasi-BIC-induced bands, leading to the emergence of topologically protected edge states that are characterized by a quantized Zak phase. Additionally, we found an on-site configuration that exhibits robust flat bands, induced by a symmetry-protected BIC and linked to special one-sided localized edge states. We present a detailed analysis of the mechanisms driving both effects and discuss the crucial role of symmetry in characterizing the topological phases of these systems.
Non-Abelian topological charges (NATCs), characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. While higher-order topological phases (HOTPs) host boundary states at corners or hinges, their characterization has largely relied on Abelian invariants such as winding and Chern numbers. Here, we propose a coupled-wire scheme of constructing non-Abelian HOTPs and analyze a non-Abelian second-order topological insulator as its minimal model. The resulting Hamiltonian supports hybridized corner modes, protected by parity-time-reversal plus sublattice symmetries and described by a topological vector that unites a non-Abelian quaternion charge with an Abelian winding number. Corner states emerge only when both invariants are nontrivial, whereas weak topological edge states of non-Abelian origins arise when the quaternion charge is nontrivial, enriching the bulk-edge-corner correspondence. The system further exhibits both non-Abelian and Abelian topological phase transitions, providing a unified platform that bridges these two distinct topological classes. Our work extends the understanding of HOTPs into non-Abelian regimes and suggests feasible experimental realizations in synthetic quantum systems, such as photonic or acoustic metamaterials.