Quantum Topological Boundary States in Quasi-Crystals

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.

Topologically Protected Quantum Logic Gates with Valley-Hall Photonic Crystals

Topological photonics provide a promising way to realize more robust optical devices against some defects and environmental perturbations. Quantum logic gates are fundamental units of quantum computers, which are widely used in future quantum information processing. Thus, constructing robust universal quantum logic gates is an important way forward to practical quantum computing. However, the most important problem to be solved is how to construct the quantum-logic-gate-required 2 × 2 beam splitter with topological protection. Here, the experimental realization of the topologically protected contradirectional coupler is reported, which can be employed to realize the quantum logic gates, including control-NOT and Hadamard gates, on the silicon photonic platform. These quantum gates not only have high experimental fidelities but also exhibit a certain degree of tolerances against certain types of defects. This work paves the way for the development of practical optical quantum computations and signal processing.

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.

Observation of the topological phase transition from the spatial correlation of a biphoton in a one-dimensional topological photonic waveguide array

We propose a simple method, using the first singular value (FSV) of the spatial correlation of biphotons, to characterize topological phase transitions (TPTs) in one-dimensional (1D) topological photonic waveguide arrays (PWAs). After analyzing the spatial correlation of biphotons using the singular value decomposition, we found that the FSV of the spatial correlation of biphotons in real space can characterize TPTs and distinguish between the topological trivial and nontrivial phases in PWAs based on the Su-Schrieffer-Heeger model. The analytical simulation results were demonstrated by applying the coupled-mode theory to biphotons and were found to be in good agreement with those of the numerical simulation. Moreover, the numerical simulation of the FSV (of the spatial correlation of biphotons) successfully characterized the TPT in a PWA based on the Aubry-André-Harper and Rice-Mele models, demonstrating the universality of this method for 1D topological PWAs. Our method provides biphotons with the possibility of acquiring information regarding TPTs directly from the spatial correlation in real space, and their potential applications in quantum topological photonics and topological quantum computing as quantum simulators and information carriers.

Asymmetric topological pumping in nonparaxial photonics

Topological photonics was initially inspired by the quantum-optical analogy between the Schrödinger equation for an electron wavefunction and the paraxial equation for a light beam. Here, we reveal an unexpected phenomenon in topological pumping observed in arrays of nonparaxial optical waveguides where the quantum-optical analogy becomes invalid. We predict theoretically and demonstrate experimentally an asymmetric topological pumping when the injected field transfers from one side of the waveguide array to the other side whereas the reverse process is unexpectedly forbidden. Our finding could open an avenue for exploring topological photonics that enables nontrivial topological phenomena and designs in photonics driven by nonparaxiality.

The understanding of the topological properties of light is at the base of the future optical devices development. In this work the authors aim to suggesting a different paradigm for topological transport and manipulation of nonparaxial light, paving the way toward the new developments in the field of topological photonics

Symmetry-Induced Error Filtering in a Photonic Lieb Lattice

Quantum computation promises intrinsically parallel information processing capacity by harnessing the superposition and entanglement of quantum states. However, it is still challenging to realize universal quantum computation due that the reliability and scalability are limited by unavoidable noises on qubits. Nontrivial topological properties like quantum Hall phases are found capable of offering protection, but require stringent conditions of topological band gaps and broken time-reversal symmetry. Here, we propose and experimentally demonstrate a symmetry-induced error filtering scheme, showing a more general role of geometry in protection mechanism and applications. We encode qubits in a superposition of two spatial modes on a photonic Lieb lattice. The geometric symmetry endows the system with topological properties featuring a flat band touching, leading to distinctive transmission behaviors of π-phase qubits and 0-phase qubits. The geometry exhibits a significant effect on filtering phase errors, which also enables it to monitor phase deviations in real time. The symmetry-induced error filtering can be a key element for encoding and protecting quantum states, suggesting an emerging field of symmetry-protected universal quantum computation and noisy intermediate-scale quantum technologies.

Real-space observation of topological invariants in 2D photonic systems

Topological materials are capable of inherently robust transport and propagation of physical fields against disorder and perturbations, holding the promise of revolutionary technologies in a wide spectrum. Higher-order topological insulators are recently predicted as topological phases beyond the standard bulk-edge correspondence principle, however, their topological invariants have been proven very challenging to observe, even not possible yet by indirect ways. Here, we demonstrate theoretically and experimentally that the topological invariants in two-dimensional systems can be directly revealed in real space by measuring single-photon bulk dynamics. By freely writing photonic lattices with femtosecond laser, we construct and identify the predicted second-order topological insulators, as well as first-order topological insulators with fractional topological winding number. Furthermore, we show that the accumulation and statistics on individual single-particle registrations can eventually lead to the same results of light waves, despite the fact that the development of topological physics was originally based on wave theories, sharing the same spirit of wave-particle nature in quantum mechanics. Our results offer a direct fashion of observing topological phases in two-dimensional systems and may inspire topologically protected artificial devices in high-order topology, high-dimension and quantum regime.