A programmable topological photonic chip

Controlling topological phases of light allows the observation of abundant topological phenomena and the development of robust photonic devices. The prospect of more sophisticated control with topological photonic devices for practical implementations requires high-level programmability. Here we demonstrate a fully programmable topological photonic chip with large-scale integration of silicon photonic nanocircuits and microresonators. Photonic artificial atoms and their interactions in our compound system can be individually addressed and controlled, allowing the arbitrary adjustment of structural parameters and geometrical configurations for the observation of dynamic topological phase transitions and diverse photonic topological insulators. Individual programming of artificial atoms on the generic chip enables the comprehensive statistical characterization of topological robustness against relatively weak disorders, and counterintuitive topological Anderson phase transitions induced by strong disorders. This generic topological photonic chip can be rapidly reprogrammed to implement multifunctionalities, providing a flexible and versatile platform for applications across fundamental science and topological technologies.

programming each artificial atom as well as the atom-atom interactions may represent the ultimate control of the system.This however remains challenging in many natural and artificial topological systems, so as in photonics.Second, most of previous observations of topological phenomena rely on static analysis of single or several samples.Comprehensively certificating topological robustness by statistical measurements, and probing interesting statistical topological phenomena such as topological Anderson insulators [46][47][48] and amorphous topological insulators 49,50 , require the ability to individually program artificial atoms and their interactions so as to control disorders.Fabricating a large number of samples with precisely controlled disorders for such statistical analysis is impractical.Third, as topology in matters derives from the collective behavior of atoms in the lattice, the geometry of lattice determines the interrelationships between neighboring atoms and the overall topological properties.Topology of bands varies in dimensions 5 , and lattices with various geometries also make different symmetries 6 , resulting in TIs in different classes.Previous investigations on TIs in diverse lattices however rely on completely different samples, which necessarily needs custom design and fabrication of samples.
In this work, we report a highly programmable topological photonic chip.The chip has generically integrated a lattice of large-scale silicon photonic nano-waveguide circuits and microring resonators, and is fabricated by the complementary metal-oxide-semiconductor (CMOS) processes.When we consider each ring as an artificial atom, our photonic chip can be regarded as an artificial lattice that allows arbitrary individual control of atoms as well as the coupling strength and hopping phase between atoms.The generic chip can be rapidly reprogrammed to implement different functionalities, such as to dynamically transform topological phases of Floquet TIs, observe statistical topological phenomena (statistical analysis of topological robustness and topological Anderson phase transitions), and realise a diverse class of topological insulators with various lattices (e.g, 1D Su-Schrieffer-Heeger TIs, and 2D Floquet TIs in square and honeycomb lattices).Our work prototypes a flexible, versatile and instantreprogrammable topological photonic platform.Figure 1 illustrates an overall concept.The photonic topological insulating chip is devised on a two-dimensional lattice of coupledmicroring resonators and nanophotonic circuits, as shown in Fig. 1a.Each microring emulates one atom and the photonic chip emulates the artificial atom lattice.In experiment, we realised a 6 × 6 square lattice, embedding in total 96 microrings, each of which has intrinsic quality factors in the order of 10 5 .As shown in Fig. 1e, resonance of each microring can be individually controlled, and the coupling between microrings (both strength and phase) can be arbitrarily controlled by Mach-Zehnder interferometers (MZIs) with ultra-high extinction ratio of about 50dB.The device operates at the wavelength of 1525 nm.One fabricated and packaged chip is shown in Figs.1b-d.The high-level controllability and programmability of generic photonic chip enable sophisticated implementations of dynamic topological phase transitions, statistical topological processes, and diverse topological lattices, see Fig. 1g.As an initial test of the flexible and fast programmability of the generic chip, Fig. 1f shows imaged field distributions of "@PKU" symbols, and a Supplementary Video shows real-time modulations of "HELLO" letters.
We first report arbitrary controls of the bandstructure of Floquet TIs in the three-particle model.The famous Floquet theory provides an effective temporal approach for TIs with no need of truly breaking time-reversal symmetry 26,51 .Demonstrating the full modulation capability requires comprehensive controls of structural parameters, which remains experimentally exclusive.A zoom-in view of a threering unit is shown in Fig. 2a and the real structure is shown in Fig. 1d.By reconfiguring four parameters on the coupling strength (i.e, θ 1−4 ) and five parameters on the phase (i.e, φ L1−L4 and φ S ) in a three-ring unit cell, arbitrary topology in the three-band structure can be constructed based on the Floquet band theory.We experimentally characterise two types of Floquet TPTs which are driven by the coupling strength (θ) and resonant phase (φ S ), respectively.
θ-driven topological phase transitions: Simultaneously tuning all coupling parameters of θ 1−4 = θ and across the TPT critical point (θ = 2 arcsin( √ 2 − 1) ≈ 0.272π), the bandgaps close and reopen, resulting in disappearance of topological edge modes (indicated by ❶  .Boundary states at bandgaps ❶ disappear with a continuous variation of θ near the critical point at θ = 0.272π, while edge modes in bandgaps ❷ and ❸ exist throughout the entire range of θ variation.The attenuation of light for large θ in experiment is due to resonant enhancement in rings, which increases the effective optical length so as loss.c,d, Measured spectra at θ = 0.1π (strong coupling) and θ = 0.32π (weak coupling), and e,f, their calculated bandstructures, respectively.The windows of edge modes are visually enhanced.g-j, Imaged real-space distributions of electromagnetic field under different points marked in spectra in (c,d): TPT from (g) topological edge modes to (h) forbidden bandgaps at bandgap ❶, (i) edge modes at bandgaps ❷ in weak coupling regime, (j) randomly distributed bulk mode from the non-degenerate bulk bands.k, A boundary cell in FTI is removed by adjusting its coupling to the "bar" state, which forms a lattice defect.High-transmission topological edge modes bypass the hole and present its robustness against atomic vacancies.Note that on the link ring paths, we tapped out -35dB light using diffractive grating couplers for better imaging of light fields, which results in the appearance of regularly distributed bright spots.Noises at the top right come from light reflection from input fiber. in Fig. 2b) and the phase transition at bandgap ❶ from an topological phase to trivial phase.The topological invariant winding number (W) is used to explicitly portray the topology (i.e, W = 1 for nontrivial phase, while W = 0 for trivial phase).Topological invariants also intuitively reflect in transport properties.Figure 2b shows the theoretical and experimental transmission spectra with a fine tuning of θ from 0 to π (i.e, transmittance of MZIs from 1 to 0).The flat and high-transmission regimes (outlined by dashed lines) indicate topological edge modes in one free spectral range (FSR).One FSR corresponds to one 2π/T period in quasi-energy ϵ, where T is the period of Floquet evolution.Figures 2c and 2d show two measured spectra before and after TPT point, corresponding to their calculated projected bands plotted in Figs.2e,f.At some typical points in the spectra, real-space distributions of electromagnetic fields are imaged by infrared camera, see examples in Figs.2g-j.Figures 2g and 2h record light distributions before and after TPTs, while Fig. 2i displays an always existing edge mode at bandgaps ❷.In bulk modes, light dissipates into the bulk, in Fig. 2j.Topological immunity against structure defects is tested in Fig. 2k, where one cell is removed by adjusting its coupling to the bar state forming a lattice defect.It indicates an unique ability to withstand and tolerate structure defects.Our topological chip could provide a fertile ground for studying the critical conditions for the emergence of defect-induced states 9,10,52 .
φ S -driven topological phase transitions: For typical Floquet TIs, introducing local phase modulations is challenging, owning to the globally consistent Floquet period in time domain.On our chip, Floquet TPTs also can be realised by finely altering the resonant phases (φ s ) in all the site rings.In Fig. 3a, by turning φ s from 0 to π, we continue to reduce the number of non-trivial bandgaps in one FSR from two to one in the φ s -TPT (when we set θ = 0.4π and phase in link rings φ L1−L4 = 0).Band deformations and changes of topological invariants are shown in the calculated band-structures.Bandgaps ❸ become trivial after across the critical point φ s = 0.58π.As there is a 2π period on resonant phases, it is expected that the spectra will return to its original state when φ s = 2π.Consequently, there must be another TPT to regenerate topological edge modes at the forbidden bandgaps when increasing φ s from π to 2π. Figure 3b displays consistent spectra both in theory and experiment, showing the disof edge states at bandgaps ❸ within [0, π] evolution and the re-emergence of edge states at bandgaps ❶ within [π, 2π] evolution.Interestingly, the seemingly negligible 2π phase in site rings in fact leads to a reversing of band-structure and a global phase shift to lower quasi-energy that corresponds to longer wavelength.That being said, the non-trivial bandgaps ❷ and ❸ at φ s = 0 correspond to non-trivial bandgaps ❶ and ❷ at φ s = 2π, respectively.
Robustness, as the most intriguing property of topological edge modes, allows the protection of transport immune to imperfections.As long as the presence of disorders does not interrupt the bandstructure and the bandgaps keep open, the topological invariants always remain constant and light transport along the edge modes are robust.This property has led to many potential applications 21,[31][32][33][34][35][36][37][38] .Previously, single or several samples are fabricated, or together with numerical simulation, to verify topological robustness.By harnessing the individual programmability, we experimentally certificate the robustness of topological edge modes by statistic measurements.Random perturbations on resonant phases with uniform distribution of δ × [−0.5, 0.5] are added to all microrings.We consider a nontrivial device with an initial configuration of φ s = 0.8π, see its bandstructure in Fig. 3c.A set of 100 samples with precisely controlled disorders at δ = 0.1π are generated and tested on a single chip.The collections of these statistic measurements (gray lines) are shown in Fig. 3d.And the spectra for an ideal device with no disorder (blue line) is plot for comparison, in which the topological edge modes in bandgaps ❷ are wide and flat high-transmission plateaus.In the presence of disorders, the high-transmittance plateaus in topological edge modes exhibit only small fluctuations, but high fluctuations in bulk modes.We then estimate the normalised standard deviation of transmittance over 100 samples for different level of disorders, see Fig. 3.With these statistic measurements, the observation of low-noise windows for topological edge modes unambiguously certificates the topological robustness against a certain degree of disorders.
Despite the superiority of topological transport, strong disorders may lead to drastic deformation of bands and even disrupt the band topology.But it does not mean the properties of the original topological insulator will completely disappear.Interestingly, under specific conditions, the transport the boundary states will still occur in the presence of strong disorders or even amorphous structures 46,47,49,50 .Exploring order within disorders is the charm of topology, which exactly requires a highly programmable platform with individual controllability.Recently, the emergence of counterintuitive topological Anderson insulators (TAIs) from trivial phases has been successfully observed, by inducing sufficiently strong disorders in one sample 46 .Similar to Anderson localisation 53 , topological Anderson insulating is also a statistical phenomenon for waves in disordered lattices.Such statistical measurement and verification of TAIs have not been reported in optical systems, to the best of our knowledge.Figure 4b illustrates the random phase distribution in the TAI lattice in the presence of strong disorders.We firstly consider an ideal lattice in the absence of disorders, the coupling θ is set as 0.3π, constructing one trivial bandgap within one FSR.We here interest in the bandgaps used to be forbidden, i.e, the dips of blue spectra in Figs.4c,d.Experiment and simulation results of averaged transmission spectra over 100 samples with different levels of disorders in resonant phase are reported in Figs.4c,d, respectively.A peak gradually emerges at the windows of forbidden bandgaps (indicated by the red arrow), as the strength of disorders reaches a sufficiently large value, indicating the occurrence of topological Anderson phase transitions.The emergence of TAI phase can be portrayed by real-space topological invariants 26,54,55 .Analogous to the winding number W ϵ in momentum space, the real-space W real related to non-trivial bandgaps approaches one, while it fluctuates around zero for trivial bandgaps.According to the averaged W real in Fig. ??, a non-zero plateau obviously raises from the ordinary zero dip in forbidden bandgaps.Moreover, Fig. 4e shows the imaged realspace field distributions as an increase of disorders, each of which are overlaid distributions of all 100 samples for better characterising the dynamics of phase transitions.The TAI boundary modes break free from the localisation near the input, and unidirectionally transport along boundaries with an exponential decay into the bulk lattice.In contrast, the same measurements were conducted in a trivial CROW (see inset in Figs.4f,g).The shape of spectra remains unchanged and no TAI boundary modes are observed, as shown in Figs.4f,g.We further benchmark photonic TIs in various lattice structures.Experimental results for the well-known Su-Schrieffer-Heeger (SSH) 1D TIs are shown in Fig. ?? in Supplementary Information.The redundant dimension for the 1D models in a 2D lattice allows observations of the non-Hermitian skin effect in Fig. ??, and other unordinary experiments such as non-reciprocity and next-nearest-neighbor coupling are implementable.Moreover, it is also possible to achieve other 2D lattice geometries beyond the inherent square lattice by reprogramming microrings.Figure 5 illustrates an example of equivalent Floquet TIs in the honeycomb lattice.A perfect correspondence between the measured transmission spectra and simulated projected band-structures in the strong coupling regime (θ = 0.08π) and weak coupling regime (θ = 0.24π) are shown in Figs.5e-h, respectively.When the coupling parameter θ is larger than 0.19π, TPTs happen at the bandgaps across ϵ = π/T and the flat high-transmission plateau turns into a blocked dip.Distinct real-space field distributions for different modes are shown in Figs.5b-d, including topological edge modes conducting along the honeycomb boundaries, dissipatively distributed bulk modes, and inhibitively forbidden bandgaps.By distinguishing the winding number, we observe phase transitions in a five-bulk-band structure.Such multiple non-trivial topological phases in standard honeycomb lattices have been achieved in another recent work 56 , using chain-driven laser-written waveguides.That effectively validates the correctness and reliability of our programmable topological chip.
This work has shown a flexibly and rapidly programmable topological photonic chip.Mutlifunctionalities are benchmarked by reprograming the generic chip, including dynamic topological phase transitions, realisations of diverse topological lattices, and implementations of statistical measurement of topological processes.Our generic chip could be directly used to discover topological phases of light and understand exotic phenomena.Different to conventional linear-optical circuits with only forward operations of classical 57,58 and quantum 59,60 states of light , our device possesses unique backwards operations with a lattice of optical resonators and it may provide an alternative solution for classical [61][62][63][64] and quantum 65,66 information processing and computing tasks.With the ultimate scalability of silicon photonics manufacturing and photonics-electronics cointegration 67 , topological phases of light can be freely programmed through electronic input, and such programmable topological photonic chips could provide a universal platform for fundamental science and topological technologies.

Fig. 1 A
Fig.1A fully programmable topological photonic chip.a, Conceptual diagram.It integrates large-scale photonic nanowaveguide circuits and microring resonators.In total, 96 microrings with high quality factors are regularly positioned in a 6×6 square lattice.All rings (artificial atom) can be individually controlled by integrated thermo-optical phase shifters (gold parts), achieving arbitrary resonant phases in all rings, phase differences between the two paths of link rings and coupling strength between neighboring rings.At the boundaries, 24-in-by-24-out ports are connected to the lattice.b, Photograph of a fabricated topological chip.The silicon chip is fabricated using CMOS processes and it monolithically integrates 2712 components in a 11mm × 7mm footprint, including 408 low-loss directional couplers, 300 phase-shifters with 528 thermal isolators, 48 grating couplers for optical access and 120 tapping ports for light field imaging, 600 electronic access and 708 transmission lines.c, Photograph of a packaged chip.The chip is wire bonded on a multilayer printed circuit board (PCB).External electronic drivers with a number of 600 channels are used to individually control 300 phase shifters.d, Optical microscopy image of a three-ring unit cell.e, Diagrams of reconfigurable optical components, including MZIs and phase shifters.f, Imaging of real-space distributions of electromagnetic field.As examples, the chip is flexibly reprogrammed to display "@PKU" respectively.g, The generic chip is reprogrammed to implement multifunctionalities: dynamic topological phase transitions, observation of statistical topological phenomena, and benchmarking of TIs in various lattices.

Fig. 2
Fig.2Coupling-strength-controlled TPTs in Floquet TIs.a, A three-ring model for Floquet TIs.Using 9 parameters in a single unit cell, it fully describes the quasi-energy bandstructure.b, TPTs driven by coupling strength.Transmission spectra as functions of wavelength λ and the parameter θ on coupling strength are shown, where θ is negatively correlated with the coupling strength and the amplitude transmittance of a MZI is cos(θ/2).The boundaries of nontrivial bandgaps in one FSR are indicated by purple dashed lines.Theoretical results (left panel) are in good agreement with experimental results (right panel).Boundary states at bandgaps ❶ disappear with a continuous variation of θ near the critical point at θ = 0.272π, while edge modes in bandgaps ❷ and ❸ exist throughout the entire range of θ variation.The attenuation of light for large θ in experiment is due to resonant enhancement in rings, which increases the effective optical length so as loss.c,d, Measured spectra at θ = 0.1π (strong coupling) and θ = 0.32π (weak coupling), and e,f, their calculated bandstructures, respectively.The windows of edge modes are visually enhanced.g-j, Imaged real-space distributions of electromagnetic field under different points marked in spectra in (c,d): TPT from (g) topological edge modes to (h) forbidden bandgaps at bandgap ❶, (i) edge modes at bandgaps ❷ in weak coupling regime, (j) randomly distributed bulk mode from the non-degenerate bulk bands.k, A boundary cell in FTI is removed by adjusting its coupling to the "bar" state, which forms a lattice defect.High-transmission topological edge modes bypass the hole and present its robustness against atomic vacancies.Note that on the link ring paths, we tapped out -35dB light using diffractive grating couplers for better imaging of light fields, which results in the appearance of regularly distributed bright spots.Noises at the top right come from light reflection from input fiber.

Fig. 3
Fig. 3 Resonant-phase-controlled TPTs and statistic verification of topological robustness.a, Calculated bandstructures in φ S -controlled TPT.Starting from the weak coupling regime (θ = 0.4π), by increasing φ S from 0 to π, site rings and link rings become detuned, reaching a maximum detuning at φ S = π.TPT happens at bandgap ❸ when φ S = 0.58π, making it a trivial forbidden bandgap.b, Theoretical (left panel) and experimental (right panel) transmission spectra as functions of wavelength λ and phase φ S .As a global phase shift is introduced by φ S , TPT happens at bandgap ❶.The mapping of bandgaps changes from {❶, ❷, ❸} to {❸, ❶, ❷} after a 2π-evolution of phase φ S .c, Calculated projected bandstructures at φ S = 0.8π.It is plotted as a reference to demonstrate the robustness of topological edge modes.d and e, Experimental verification of topological robustness with statistic measurements by individually controlling the phase disorders in all rings.In (d), a sets of 100 samples with uniformly distributed random phases are chosen in the range of δ × [−0.5, 0.5] and δ = 0.1π in measurement.Measured transmission spectra for disordered device are shown as the gray background, and the spectrum for an ideal device without disorders is plot as a blue line.In the topological edge modes, the flat plateaus with high transmission are slightly influenced, while in all other regimes, severe broadening and small dips owing to obstruction from random local modes appear.The measured standard deviation (normalised) of transmission spectra under different strength of disorders are plot in (e).Evident windows with low fluctuations are exactly corresponding to the regimes of topological edge modes.Standard deviations are colour coded and the key is provided at the right bottom.

Fig. 4
Fig. 4 Observation of topological Anderson phase transitions with statistical measurements by individually programming the TI with strong disorders.a, Ideal Floquet TI in weak coupling regime(θ = 0.3π) with no disorder.All microrings are matched to resonance.There is a forbidden bandgap within one FSR.b, TAI induced by strong disorders.Topological Anderson phase transitions happen at the forbidden bandgaps and connect them with TAI boundary modes.Statistic measurements of the TAI with a large variety of disorders are necessary to observe the topological Anderson phase transitions, which are realised on a single device by individually controlling phase disorders in all rings in our experiment.c and d, Measured and simulated transmission spectra of the TAI with different disorders.For each disorder, 100 samples are generated on the chip for statistic measurements, and the mean spectra is plotted.As an increase of disorders, an intriguing peak that represents the TAI boundary mode (indicated by the red arrow) gradually emerges at the lowtransmission dip where used to be the forbidden bandgaps in the ideal lattices with no disorders.e, Imaging the dynamic process of topological Anderson phase transitions.Each image is an accumulated field distributions of 100 samples.The phase transition from a forbidden mode to a transported TAI boundary mode along the upper boundary is observed.Simulation results are shown for comparsion, which are in good agreement with experimental results.Different to random diffusions of bulk modes, the TAI boundary modes propagate along the boundary and rapidly decay into the bulk.f and g, Measured and simulated transmission spectra of a 1D trivial device.The shape of transmission spectra does not change with increasing disorders, and the low-transmission dip corresponding to the forbidden bandgaps remained a dip (indicated by the blue arrow), i.e, no phase transition occurred.

Fig. 5
Fig. 5 Floquet topological insulators in the honeycomb lattice by reconfiguring the lattice geometry.a, A reconfigured square lattice that is equivalent to the honeycomb lattice.b-d, Measured real-space distributions of light field in different modes: (b) topological edge mode, (c) bulk mode, and (d) forbidden bandgap.e and f, Measured transmission spectrum and calculated projected band when the device works in θ = 0.08π.There are five bulk bands in one FSR, distinct from the three-particle model in a square lattice.The winding numbers W in all bulk bandbaps are one, implying the existence of non-trivial boundary modes.g and h, Measured transmission spectrum and calculated projected band when the device works in θ = 0.24π.When decreasing the coupling strength down to the critical point of θ = 0.19π, TPTs happen at the bandgap across ϵ = π/T, turning it a trivial forbidden bandgap (W=0), while other bandgaps remain nontrivial.