Photonic Waveguide Arrays Research Articles

Two-dimensional non-Abelian Thouless pump

Non-Abelian Thouless pumps are periodically driven systems designed by the non-Abelian holonomy principle, in which quantized transport of degenerate eigenstates emerges, exhibiting noncommutative features such that the outcome depends on the pumping sequence. The study of non-Abelian Thouless pump is currently restricted to 1D systems, while extending it to higher-dimensional systems will not only provide effective means to probe non-Abelian physics in high-dimensional topological systems, but also expand the dimension and type of associated non-Abelian geometric phase matrix for potential applications. Here, we propose the design and experimental realization of 2D non-Abelian Thouless pumps on a photonic chip with 2D photonic waveguide arrays, where degenerate photonic modes are topologically pumped simultaneously along two real-space directions. We reveal the associated non-Abelian group and experimentally demonstrate the non-Abelian feature by measuring the pumping sequence dependent output. The proposed 2D non-Abelian Thouless pump shows promising applications for robust optical interconnections and optical computing.

Programmable high-dimensional Hamiltonian in a photonic waveguide array

Waveguide lattices offer a compact and stable platform for a range of applications, including quantum walks, condensed matter system simulation, and classical and quantum information processing. However, to date, waveguide lattice devices have been static and designed for specific applications. We present a programmable waveguide array in which the Hamiltonian terms can be individually electro-optically tuned to implement various Hamiltonian continuous-time evolutions on a single device. We used a single array with 11 waveguides in lithium niobate, controlled via 22 electrodes, to perform a range of experiments that realized the Su-Schriffer-Heeger model, the Aubrey-Andre model, and Anderson localization, which is equivalent to over 2500 static devices. Our architecture’s micron-scale local electric fields overcome the cross-talk limitations of thermo-optic phase shifters in other platforms such as silicon, silicon-nitride, and silica. Electro-optic control allows for ultra-fast and more precise reconfigurability with lower power consumption, and with quantum input states, our platform can enable the study of multiple condensed matter quantum dynamics with a single device.

Observation of delocalization transition in topological waveguide arrays with long-range interactions.

Topological edge states are a generic feature of topological insulators, and the long-range interactions, which break certain properties of topological edge states, are always non-negligible in real physical systems. In this Letter, we investigate the influence of next-nearest-neighbor (NNN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) model by extracting the survival probabilities at the boundary of the photonic lattices. By introducing a series of integrated photonic waveguide arrays with different strengths of long-range interactions, we experimentally observe delocalization transition of light in SSH lattices with nontrivial phase, which is in good agreement with our theoretical predictions. The results indicate that the NNN interactions can significantly affect the edge states, and that the localization of these states can be absent in topologically nontrivial phase. Our work provides an alternative way to investigate the interplay between long-range interactions and localized states, which may stimulate further interest in topological properties in relevant structures.

Floquet engineering of the non-Hermitian skin effect in photonic waveguide arrays

The non-Hermitian skin effect (NHSE), which involves an extensive number of bulk modes collapsing to open boundaries as skin modes, unveils a variety of unprecedented topological physics. However, achieving this effect in photonic waveguides has been challenging due to the difficulty of establishing the required non-Hermitian asymmetric couplings. Here, we investigate NHSE in photonic waveguide arrays via Floquet engineering. By periodically driving the waveguides along the propagation direction, we create an artificial gauge field (AGF) that interacts with on-site dissipation, yielding non-Hermitian asymmetric coupling and eventually giving rise to NHSE. The localization direction of NHSE is tunable by AGFs and can be detected from light propagation. In particular, we explore the interplay between NHSE and dynamical localization, whereby NHSE is suppressed by dynamical localization due to the collapse of quasienergies. Our proposed method can be extended to explore the non-Bloch Su-Schrieffer--Heeger model, with potential implications for steering light transport with the aid of NHSE.

Steering edge currents through a Floquet topological insulator

Periodic driving may cause topologically protected, chiral transport along edges of a two-dimensional (2D) lattice that, without driving, would be topologically trivial. We study what happens if one adds a different on-site potential along the diagonal of such a 2D grid. In addition to the usual bulk and edge states, the system then also exhibits doublon states, analogous to two interacting particles in one dimension. A particle initially located at an edge propagates along the system's boundary. Its wave function splits when it hits the diagonal and continues propagating simultaneously along the edge and the diagonal. The strength of the diagonal potential determines the ratio between both parts. We show that for specific values of the diagonal potential, hopping onto the diagonal is prohibited so that the system effectively separates into two triangular lattices. For other values of the diagonal potential, we find a temporal delay between the two contributions traveling around and through the system. This behavior could enable the steering of topologically protected transport of light along the edges and through the bulk of laser-inscribed photonic waveguide arrays.

Observation of Square‐Root Higher‐Order Topological States in Photonic Waveguide Arrays

AbstractRecently, higher‐order topological insulators (HOTIs), accompanied by topologically nontrivial boundary states with a codimension larger than one, have been extensively explored because of unconventional bulk‐boundary correspondences. As a novel type of HOTIs, very recent works have explored the square‐root HOTIs, where the topologically nontrivial nature of bulk bands stems from the square of the Hamiltonian. In this paper, 2D square‐root HOTIs are experimentally demonstrated in photonic waveguide arrays written in glass using femtosecond laser direct‐write techniques. Edge and corner states are clearly observed at visible light spectra. The dynamical evolutions of topological boundary states are experimentally demonstrated, which verify the existence of photonic corner states in two band gaps. The symmetry‐protected corner states in the photonic square‐root HOTI may have potential applications in information processing and lasing.

Oscillating bound states in non-Markovian photonic lattices

It is known that the superposition of two bound states in the continuum (BIC) leads to the phenomenon of an oscillating bound state, where excitations mediated by the continuum modes oscillate persistently. We perform exact calculations for the oscillating BICs in a 1D photonic lattice coupled to a "giant atom" at multiple points. Our work is significantly distinct from previous proposals of oscillating BICs in continuous waveguide systems due to the presence of a finite energy band contributing band-edge effects. In particular, we show that the bound states outside the energy band are detrimental to the oscillating BIC phenomenon, and can be suppressed by increasing either the number of coupling points or the separation between each coupling point. Crucially, non-Markovianity is necessary for the existence of oscillating BIC, and the oscillation amplitude increases with the characteristic delay time of the giant atom interactions. We also propose a novel initialization scheme in the BIC subspace. Our work be experimentally implemented on current photonic waveguide array platforms and opens up new prospects in utilizing reservoir engineering for the storage of quantum information in photonic lattices.

Floquet engineering of two dimensional photonic waveguide arrays with [formula omitted] or [formula omitted] corner states

In this paper, we theoretically study the Floquet engineering of two dimensional photonic waveguide arrays in three types of lattices: honeycomb lattice with Kekulé distortion, breathing square lattice and breathing Kagome lattice. The Kekulé distortion factor or the breathing factor in the corresponding lattice is periodically changed along the axial direction of the photonic waveguide with frequency ω. Within certain ranges of ω, the Floquet corner states in the Floquet band gap of quasi-energy spectrum are found, which are localized at the corner of the finite two-dimensional arrays. Due to particle-hole symmetry in the model of honeycomb and square lattice, the quasi-energy level of the Floquet π corner states is ±ω/2. On the other hand, Kagome lattice does not have particle-hole symmetry, so that the quasi-energy level of the Floquet ±2π/3 corner states is near to ±1ω/3. The corner states are either protected by crystalline symmetry or reflection symmetry. The finding of Floquet fractional-π corner states could provide more options for engineering of on-chip photonic devices.

Edge State, Localization Length, and Critical Exponent from Survival Probability in Topological Waveguides.

Edge states in topological phase transitions have been observed in various platforms. To date, verification of the edge states and the associated topological invariant are mostly studied, and yet a quantitative measurement of topological phase transitions is still lacking. Here, we show the direct measurement of edge states and their localization lengths from survival probability. We employ photonic waveguide arrays to demonstrate the topological phase transitions based on the Su-Schrieffer-Heeger model. By measuring the survival probability at the lattice boundary, we show that in the long-time limit, the survival probability is P=(1-e^{-2/ξ_{loc}})^{2}, where ξ_{loc} is the localization length. This length derived from the survival probability is compared with the distance from the transition point, yielding a critical exponent of ν=0.94±0.04 at the phase boundary. Our experiment provides an alternative route to characterizing topological phase transitions and extracting their key physical quantities.

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.

Higher-order topological pumping and its observation in photonic lattices

The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a topological invariant characterizing the quantum Hall effect in two-dimensional electron gases, with the topology of dynamical periodic systems in one dimension. Here, we demonstrate its counterpart for higher-order topology. Specifically, we show that adiabatic cycles in two-dimensional crystals with vanishing dipole moments (and therefore zero overall particle transport) can nevertheless be topologically nontrivial. These cycles are associated with higher-order topology and can be diagnosed by their ability to produce corner-to-corner transport in certain metamaterial platforms. We experimentally verify the corner to corner transport associated with this topological pump by using an array of photonic waveguides adiabatically modulated in their separations and refractive indices. By mapping the dynamical phenomenon demonstrated here from two spatial and one temporal dimensions to three spatial dimensions, our observations are equivalent to the observation of chiral hinge states in a three-dimensional second-order topological insulator.

Non-Abelian braiding on photonic chips

Non-Abelian braiding has attracted significant attention because of its pivotal role in describing the exchange behaviors of anyons--a candidate for realizing quantum logics. The input and outcome of non-Abelian braiding are connected by a unitary matrix which can also physically emerge as a geometric-phase matrix in classical systems. Hence it is predicted that non-Abelian braiding should have analogues in photonics, but a feasible platform and the experimental realization remain out of reach. Here, we propose and experimentally realize an on-chip photonic system that achieves the non-Abelian braiding of up to five photonic modes. The braiding is realized by controlling the multi-mode geometric-phase matrix in judiciously designed photonic waveguide arrays. The quintessential effect of braiding--sequence-dependent swapping of photon dwell sites is observed in both classical-light and single-photon experiments. Our photonic chips are a versatile and expandable platform for studying non-Abelian physics, and we expect the results to motivate next-gen non-Abelian photonic devices.

Parylene Photonic Microimager for Implantable Imaging.

We have recently introduced a fully flexible, compact photonic platform, Parylene photonics. Here, we demonstrate a Parylene photonic waveguide array microimager with a light source localization accuracy of 17.04 µm along the x-axis and 30.07 µm along the y-axis over a 200 µm×1000 µm region. We show the feasibility of fluorescent imaging from mouse brain tissue using the microimager array.Clinical Relevance- Implantable microimagers can be used for clinical intraoperative monitoring as well as structural and functional imaging with cell-type specificity in research.

Nonlinear topological valley Hall edge states arising from type-II Dirac cones

Type-II Dirac/Weyl points, although impermissible in particle physics due to Lorentz covariance, were uncovered in condensed matter physics, driven by fundamental interest and intriguing applications of topological materials. Recently, there has been a surge of exploration of such generic points using various engineered platforms including photonic crystals, waveguide arrays, metasurfaces, magnetized plasma and polariton micropillars, aiming towards relativistic quantum emulation and understanding of exotic topological phenomena. Such endeavors, however, have focused mainly on linear topological states in real or synthetic Dirac/Weyl materials. Here, we demonstrate nonlinear valley Hall edge states (VHESs) in laser-writing anisotropic photonic lattices hosting type-II Dirac points. These self-trapped VHESs, manifested as topological gap quasi-solitons, are fundamentally distinct from their linear counterparts in type-I lattices and from all previously found topological solitons. Our finding may provide a route for understanding nonlinear phenomena in Lorentz-violating topological systems and for developing advanced light sources from topological insulator lasers.

Topological photonics in 3D micro-printed systems

Topological materials have been at the forefront of research across various fields of physics in hopes of harnessing properties such as scatter-free transport due to protection from defects and disorder. Photonic systems are ideal test beds for topological models and seek to profit from the idea of topological robustness for applications. Recent progress in 3D-printing of microscopic structures has allowed for a range of implementations of topological systems. We review recent work on topological models realized particularly in photonic crystals and waveguide arrays fabricated by 3D micro-printing. The opportunities that this technique provides are a result of its facility to tune the refractive index, compatibility with infiltration methods, and its ability to fabricate a wide range of flexible geometries.

Photonic realization of the κ -deformed Dirac equation

We show an implementation of a kappa-deformed Dirac equation in tight-binding arrays of photonic waveguides. This is done with a special configuration of couplings extending to second nearest neighbors. Geometric manipulations can control these evanescent couplings. A careful study of wave packet propagation is presented, including the effects of deformation parameters on Zitterbewegung or trembling motion. In this way, we demonstrate how to recreate the effects of a flat noncommutative spacetime -i.e., kappa-Minkowski spacetime -in simple experimental setups. We touch upon elastic realizations in the section of Conclusions.

Observation of Bloch oscillations and Wannier-Stark localization on a superconducting quantum processor

The Bloch oscillation (BO) and Wannier-Stark localization (WSL) are fundamental concepts about metal-insulator transitions in condensed matter physics. These phenomena have also been observed in semiconductor superlattices and simulated in platforms such as photonic waveguide arrays and cold atoms. Here, we report experimental investigation of BOs and WSL simulated with a 5-qubit programmable superconducting processor, of which the effective Hamiltonian is an isotropic XY spin chain. When applying a linear potential to the system by properly tuning all individual qubits, we observe that the propagation of a single spin on the chain is suppressed. It tends to oscillate near the neighborhood of their initial positions, which demonstrates the characteristics of BOs and WSL. We verify that the WSL length is inversely correlated to the potential gradient. Benefiting from the precise single-shot simultaneous readout of all qubits in our experiments, we can also investigate the thermal transport, which requires the joint measurement of more than one qubits. The experimental results show that, as an essential characteristic for BOs and WSL, the thermal transport is also blocked under a linear potential. Our experiment would be scalable to more superconducting qubits for simulating various of out-of-equilibrium problems in quantum many-body systems.

Braiding photonic topological zero modes

A remarkable property of quantum mechanics in two-dimensional (2D) space is its ability to support "anyons," particles that are neither fermions nor bosons. Theory predicts that these exotic excitations can be realized as bound states confined near topological defects, like Majorana zero modes trapped in vortices in topological superconductors. Intriguingly, in the simplest cases the nontrivial phase that arises when such defects are "braided" around one another is not intrinsically quantum mechanical; rather, it can be viewed as a manifestation of the geometric (Pancharatnam-Berry) phase in wave mechanics, enabling the simulation of such phenomena in classical systems. Here we report the first experimental measurement in any system, quantum or classical, of the geometric phase due to such a braiding process. These measurements are obtained using an interferometer constructed from highly tunable 2D arrays of photonic waveguides. Our results introduce photonic lattices as a versatile playground for the experimental study of topological defects and their braiding, complementing ongoing efforts in solid-state systems and cold atomic gases.

Novel phenomena in flatband photonic structures: from localized states to real-space topology

In recent years, flatband systems have aroused considerable interest in different branches of physics, from condensed-matter physics to engineered flatband structures such as in ultracold atoms, various metamaterials, electronic materials, and photonic waveguide arrays. Flatband localization, as an important phenomenon in solid state physics, is of broad interest in the exploration of many fundamental physics of many-body systems. We briefly review the recent experimental advances in light localization in engineered flatband lattices, with the emphasis on the optical induction technique of various photonic lattices and unconventional flatband states. The photonic lattices, established by various optical induction techniques, include quasi-one-dimensional diamond lattices and two-dimensional super-honeycomb, Lieb and Kagome lattices. Nontrivial flatband line states, independent of linear superpositions of conventional compact localized states, are demonstrated in photonic Lieb and super-honeycomb lattices, and they can be considered as an indirect illustration of the non-contractible loop states. Furthermore, we discuss alternative approaches to directly observing the non-contractible loop states in photonic Kagome lattices. These robust loop states are direct manifestation of real-space topology in such flatband systems. In this paper we do not intend to comprehensively account the vast flatband literature, but we briefly review the relevant work on photonic lattices mainly from our group. We hope that the mentioned concepts and techniques can be further explored and developed for subsequent applications in other structured photonic media such as photonic crystals, metamaterials, and other synthetic nanophotonic materials.

Experimental observation of topologically protected defect states in silicon waveguide arrays

Photonic waveguide arrays provide a simple and versatile platform for simulating conventional topological systems. Here, we investigate a novel one-dimensional (1D) topological band structure, a dimer chain, consisting of silicon waveguides with alternating self-coupling and inter-coupling. Coupled mode theory is used to study topological features of such a model. It is found that topological invariants of our proposed model are described by the global Berry phase instead of the Berry phase of the upper or lower energy band, which is commonly used in the 1D topological models such as the Su–Schrieffer–Heeger model. Next, we design an array configuration composed of two dimer patterns with different global Berry phases to realize the topologically protected waveguiding. The topologically protected propagation feature is simulated based on the finite-difference time-domain method and then observed in the experiment. Our results provide an in-depth understanding of the dynamics of the topological defect state in a 1D silicon waveguide array, and may provide different routes for on-chip lightwave shaping and routing.