Topologically robust transport of photons in a synthetic gauge field

Observation of topological frequency combs

On-chip generation of optical frequency combs using nonlinear ring resonators has enabled numerous applications of combs that were otherwise limited to mode-locked lasers. Nevertheless, on-chip frequency combs have relied predominantly on single-ring resonators. In this study, we experimentally demonstrate the generation of a novel class of frequency combs, the topological frequency combs, in a two-dimensional lattice of hundreds of ring resonators that hosts fabrication-robust topological edge states with linear dispersion. By pumping these edge states, we demonstrate the generation of a nested frequency comb that shows oscillation of multiple edge state resonances across ≈40 longitudinal modes and is spatially confined at the lattice edge. Our results provide an opportunity to explore the interplay between topological physics and nonlinear frequency comb generation in a commercially available nanophotonic platform.

Simultaneous and independent topological control of identical microparticles in non-periodic energy landscapes

Topological protection ensures stability of information and particle transport against perturbations. We explore experimentally and computationally the topologically protected transport of magnetic colloids above spatially inhomogeneous magnetic patterns, revealing that transport complexity can be encoded in both the driving loop and the pattern. Complex patterns support intricate transport modes when the microparticles are subjected to simple time-periodic loops of a uniform magnetic field. We design a pattern featuring a topological defect that functions as an attractor or a repeller of microparticles, as well as a pattern that directs microparticles along a prescribed complex trajectory. Using simple patterns and complex loops, we simultaneously and independently control the motion of several identical microparticles differing only in their positions above the pattern. Combining complex patterns and complex loops we transport microparticles from unknown locations to predefined positions and then force them to follow arbitrarily complex trajectories concurrently. Our findings pave the way for new avenues in transport control and dynamic self-assembly in colloidal science.

Observation of π solitons in oscillating waveguide arrays

Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous π modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous π modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological π solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. π solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such π solitons are determined by their power.

Adiabatic topological photonic interfaces

Topological phases of matter have been attracting significant attention across diverse fields, from inherently quantum systems to classical photonic and acoustic metamaterials. In photonics, topological phases offer resilience and bring novel opportunities to control light with pseudo-spins. However, topological photonic systems can suffer from limitations, such as breakdown of topological properties due to their symmetry-protected origin and radiative leakage. Here we introduce adiabatic topological photonic interfaces, which help to overcome these issues. We predict and experimentally confirm that topological metasurfaces with slowly varying synthetic gauge fields significantly improve the guiding features of spin-Hall and valley-Hall topological structures commonly used in the design of topological photonic devices. Adiabatic variation in the domain wall profiles leads to the delocalization of topological boundary modes, making them less sensitive to details of the lattice, perceiving the structure as an effectively homogeneous Dirac metasurface. As a result, the modes showcase improved bandgap crossing, longer radiative lifetimes and propagation distances.

Experimental realization of chiral Landau levels in two-dimensional Dirac cone systems with inhomogeneous effective mass

Chiral zeroth Landau levels are topologically protected bulk states. In particle physics and condensed matter physics, the chiral zeroth Landau level plays a significant role in breaking chiral symmetry and gives rise to the chiral anomaly. Previous experimental works on such chiral Landau levels are mainly based on three-dimensional Weyl degeneracies coupled with axial magnetic fields. Their realizations using two-dimensional Dirac point systems, being more promising for future applications, were never experimentally realized before. Here we propose an experimental scheme for realizing chiral Landau levels in a two-dimensional photonic system. By introducing an inhomogeneous effective mass through breaking local parity-inversion symmetries, a synthetic in-plane magnetic field is generated and coupled with the Dirac quasi-particles. Consequently, the zeroth-order chiral Landau levels can be induced, and the one-way propagation characteristics are experimentally observed. In addition, the robust transport of the chiral zeroth mode against defects in the system is also experimentally tested. Our system provides a new pathway for the realization of chiral Landau levels in two-dimensional Dirac cone systems, and may potentially be applied in device designs utilizing the chiral response and transport robustness.

Reconfigurable refraction manipulation at synthetic temporal interfaces with scalar and vector gauge potentials

Photonic gauge potentials, including scalar and vector ones, play fundamental roles in emulating photonic topological effects and for enabling intriguing light transport dynamics. While previous studies mainly focus on manipulating light propagation in uniformly distributed gauge potentials, here we create a series of gauge-potential interfaces with different orientations in a nonuniform discrete-time quantum walk and demonstrate various reconfigurable temporal-refraction effects. We show that for a lattice-site interface with the potential step along the lattice direction, the scalar potentials can yield total internal reflection (TIR) or Klein tunneling, while vector potentials manifest direction-invariant refractions. We also reveal the existence of penetration depth for the temporal TIR by demonstrating frustrated TIR with a double lattice-site interface structure. By contrast, for an interface emerging in the time-evolution direction, the scalar potentials have no effect on the packet propagation, while the vector potentials can enable birefringence, through which we further create a "temporal superlens" to achieve time-reversal operations. Finally, we experimentally demonstrate electric and magnetic Aharonov-Bohm effects using combined lattice-site and evolution-step interfaces of either scalar or vector potential. Our work initiates the creation of artificial heterointerfaces in synthetic time dimension by employing nonuniformly and reconfigurable distributed gauge potentials. This paradigm may find applications in optical pulse reshaping, fiber-optic communications, and quantum simulations.

Disordered topological graphs enhancing nonlinear phenomena

Complex networks play a fundamental role in understanding phenomena from the collective behavior of spins, neural networks, and power grids to the spread of diseases. Topological phenomena in such networks have recently been exploited to preserve the response of systems in the presence of disorder. We propose and demonstrate topological structurally disordered systems with a modal structure that enhances nonlinear phenomena in the topological channels by inhibiting the ultrafast leakage of energy from edge modes to bulk modes. We present the construction of the graph and show that its dynamics enhances the topologically protected photon pair generation rate by an order of magnitude. Disordered nonlinear topological graphs will enable advanced quantum interconnects, efficient nonlinear sources, and light-based information processing for artificial intelligence.

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.

Anomalous Single-Mode Lasing Induced by Nonlinearity and the Non-Hermitian Skin Effect

Single-mode operation is a desirable but elusive property for lasers operating at high pump powers. Typically, single-mode lasing is attainable close to threshold, but increasing the pump power gives rise to multiple lasing peaks due to inter-modal gain competition. We propose a laser with the opposite behavior: multimode lasing occurs at low output powers, but pumping beyond a certain value produces a single lasing mode, with all other candidate modes experiencing negative effective gain. This phenomenon arises in a lattice of coupled optical resonators with non-fine-tuned asymmetric couplings, and is caused by an interaction between nonlinear gain saturation and the non-Hermitian skin effect. The single-mode lasing is observed in both frequency domain and time domain simulations. It is robust against on-site disorder, and scales up to large lattice sizes. This finding might be useful for implementing high-power laser arrays.

Multimode interference in topological photonic heterostructure

In this Letter, topological photonic heterostructures, which are composed of finite-size photonic crystals with different topological phases, are proposed. The coupled topological edge states (CTESs), which originate from the coupling between topological edge states, are found. By using the finite element method, the multimode interference effect of CTESs is predicted and investigated. Paired and symmetrical interferences are discussed, and the respective imaging positions are calculated. In addition, the multimode interference effect is topologically protected when introducing disorders. As examples of application, frequency and power splitters of topological edge states based on the multimode interference effect are designed and demonstrated numerically. Our findings pave a new, to the best of our knowledge, way of designing topological photonic integrated circuit applications such as filters, couplers, multiplexers, and so on.

Topological edge state bandwidth tuned by multiple parameters in two-dimensional terahertz photonic crystals with metallic cross structures

Originating from the study of topological photonic crystals (TPCs), analogues of the quantum spin Hall effect have been used as a potential way to control the propagation of electromagnetic waves. Due to the topological robustness of the spin TPCs, the edge states along the interface between the trivial and topological areas are topologically protected and not reflected from structural defects and disorders. Here, on the basis of the time-spatial reversal symmetry and topological defect theory, we demonstrate broadening of the edge state bandwidth in spin TPCs made of regular metallic cross structures by simultaneously deforming the hexagonal honeycomb lattice and adjusting the rotation angle. Due to the simultaneous tuning of the two parameters, the designed spin TPCs possess more flexibility. Topologically protected one-way propagating edge states are observed in the terahertz regime, where electromagnetic waves propagate along sharp corners without backscattering. Our findings offer the potential application for topological devices in terahertz technology and are beneficial for the development of 6G mobile communications.

Light-Matter Interactions in Synthetic Magnetic Fields: Landau-Photon Polaritons

We study light-matter interactions in two-dimensional photonic systems in the presence of a spatially homogeneous synthetic magnetic field for light. Specifically, we consider one or more two-level emitters located in the bulk region of the lattice, where for increasing magnetic field the photonic modes change from extended plane waves to circulating Landau levels. This change has a drastic effect on the resulting emitter-field dynamics, which becomes intrinsically non-Markovian and chiral, leading to the formation of strongly coupled Landau-photon polaritons. The peculiar dynamical and spectral properties of these quasiparticles can be probed with state-of-the-art photonic lattices in the optical and the microwave domain and may find various applications for the quantum simulation of strongly interacting topological models.

Chiral surface plasmon-enhanced chiral spectroscopy: principles and applications

In this review, the development context and scientific research results of chiral surface plasmons (SPs) in recent years are classified and described in detail. First, the principle of chiral SPs is introduced through classical and quantum theory. Following this, the classification and properties of different chiral structures, as well as the superchiral near-field, are introduced in detail. Second, we describe the excitation and propagation properties of chiral SPs, which lays a good foundation for the application of chiral SPs and their chiral spectra in various fields. After that, we have summarized the recent research results of chiral SPs and their applications in the areas of biology, two-dimensional materials, topological materials, analytical chemistry, chiral sensing, chiral optical force, and chiral light detection. Chiral SPs are a new type of optical phenomenon that have useful application potential in many fields and are worth exploring.

Tailoring topological edge states with photonic crystal nanobeam cavities

The realization of topological edge states (TESs) in photonic systems has provided unprecedented opportunities for manipulating light in novel manners. The Su-Schrieffer-Heeger (SSH) model has recently gained significant attention and has been exploited in a wide range of photonic platforms to create TESs. We develop a photonic topological insulator strategy based on SSH photonic crystal nanobeam cavities. In contrast to the conventional photonic SSH schemes which are based on alternately tuned coupling strength in one-dimensional lattice, our proposal provides higher flexibility and allows tailoring TESs by manipulating mode coupling in a two-dimensional manner. We reveal that the proposed hole-array based nanobeams in a dielectric membrane can selectively tailor single or double TESs in the telecommunication region by controlling the coupling strength of the adjacent SSH nanobeams in both transverse and axial directions. Our finding provides an additional degree of freedom in exploiting the SSH model for integrated topological photonic devices and functionalities based on the well-established photonic crystal nanobeam cavity platforms.

Designing disorder into crystalline materials

Crystals are a state of matter characterized by periodic order. Yet, crystalline materials can harbour disorder in many guises, such as non-repeating variations in composition, atom displacements, bonding arrangements, molecular orientations, conformations, charge states, orbital occupancies or magnetic structure. Disorder can sometimes be random but, more usually, it is correlated. Frontier research into disordered crystals now seeks to control and exploit the unusual patterns that persist within these correlated disordered states in order to access functional responses inaccessible to conventional crystals. In this Review, we survey the core design principles that guide targeted control over correlated disorder. We show how these principles - often informed by long-studied statistical mechanical models - can be applied across an unexpectedly broad range of materials, including organics, supramolecular assemblies, oxide ceramics and metal-organic frameworks. We conclude with a forward-looking discussion of the exciting link between disorder and function in responsive media, thermoelectrics and topological phases.

Non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly pairs

The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin-orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

Multidimensional synthetic chiral-tube lattices via nonlinear frequency conversion

Geometrical dimensionality plays a fundamentally important role in the topological effects arising in discrete lattices. Although direct experiments are limited by three spatial dimensions, the research topic of synthetic dimensions implemented by the frequency degree of freedom in photonics is rapidly advancing. The manipulation of light in these artificial lattices is typically realized through electro-optic modulation; yet, their operating bandwidth imposes practical constraints on the range of interactions between different frequency components. Here we propose and experimentally realize all-optical synthetic dimensions involving specially tailored simultaneous short- and long-range interactions between discrete spectral lines mediated by frequency conversion in a nonlinear waveguide. We realize triangular chiral-tube lattices in three-dimensional space and explore their four-dimensional generalization. We implement a synthetic gauge field with nonzero magnetic flux and observe the associated multidimensional dynamics of frequency combs, all within one physical spatial port. We anticipate that our method will provide a new means for the fundamental study of high-dimensional physics and act as an important step towards using topological effects in optical devices operating in the time and frequency domains.

Realization of Anomalous Floquet Insulators in Strongly Coupled Nanophotonic Lattices

We experimentally realized Floquet topological photonic insulators using a square lattice of direct-coupled octagonal resonators. Unlike previously reported topological insulator systems based on microring lattices, the nontrivial topological behaviors of our system arise directly from the periodic evolution of light around each octagon to emulate a periodically driven system. By exploiting asynchronism in the evanescent coupling between adjacent octagonal resonators, we could achieve strong and asymmetric couplings in each unit cell, which are necessary for realizing anomalous Floquet insulator behaviors. Direct imaging of scattered light from fabricated samples confirmed the existence of chiral edge states as predicted by the topological phase map of the lattice. In addition, by exploiting the frequency dispersion of the coupling coefficients, we could also observe topological phase changes of the lattice from a normal insulator to Chern and Floquet insulators. Our lattice thus provides a versatile nanophotonic system for investigating 2D Floquet topological insulators.

Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing

Topological protection in photonics offers new prospects for guiding and manipulating classical and quantum information. The mechanism of spin-orbit coupling promises the emergence of edge states that are helical, exhibiting unidirectional propagation that is topologically protected against back scattering. We directly observe the topological states of a photonic analog of electronic materials exhibiting the quantum spin Hall effect, living at the interface between two silicon photonic crystals with different topological order. Through the far-field radiation that is inherent to the states' existence, we characterize their properties, including linear dispersion and low loss. We find that the edge state pseudospin is encoded in unique circular far-field polarization and linked to unidirectional propagation, thus revealing a signature of the underlying photonic spin-orbit coupling. We use this connection to selectively excite different edge states with polarized light and directly visualize their routing along sharp chiral waveguide junctions.

Four-wave mixing of topological edge plasmons in graphene metasurfaces

We study topologically protected four-wave mixing (FWM) interactions in a plasmonic metasurface consisting of a periodic array of nanoholes in a graphene sheet, which exhibits a wide topological bandgap at terahertz frequencies upon the breaking of time reversal symmetry by a static magnetic field. We demonstrate that due to the significant nonlinearity enhancement and large life time of graphene plasmons in specific configurations, a net gain of FWM interaction of plasmonic edge states located in the topological bandgap can be achieved with a pump power of less than 10 nW. In particular, we find that the effective nonlinear edge-waveguide coefficient is about γ ≃ 1.1 × 10¹³ W^-1 m^-1, i.e., more than 10 orders of magnitude larger than that of commonly used, highly nonlinear silicon photonic nanowires. These findings could pave a new way for developing ultralow-power-consumption, highly integrated, and robust active photonic systems at deep-subwavelength scale for applications in quantum communications and information processing.

Topological Protection and Control of Quantum Markovianity

Under the Born–Markov approximation, a qubit system, such as a two-level atom, is known to undergo a memoryless decay of quantum coherence or excitation when weakly coupled to a featureless environment. Recently, it has been shown that unavoidable disorder in the environment is responsible for non-Markovian effects and information backflow from the environment into the system owing to Anderson localization. This turns disorder into a resource for enhancing non-Markovianity in the system–environment dynamics, which could be of relevance in cavity quantum electrodynamics. Here we consider the decoherence dynamics of a qubit weakly coupled to a two-dimensional bath with a nontrivial topological phase, such as a two-level atom embedded in a two-dimensional coupled-cavity array with a synthetic gauge field realizing a quantum-Hall bath, and show that Markovianity is protected against moderate disorder owing to the robustness of chiral edge modes in the quantum-Hall bath. Interestingly, switching off the gauge field, i.e., flipping the bath into a topological trivial phase, allows one to re-introduce non-Markovian effects. Such a result indicates that changing the topological phase of a bath by a tunable synthetic gauge field can be harnessed to control non-Markovian effects and quantum information backflow in a qubit-environment system.

Synthetic Gauge Field for Two-Dimensional Time-Multiplexed Quantum Random Walks

Temporal multiplexing provides an efficient and scalable approach to realize a quantum random walk with photons that can exhibit topological properties. But two-dimensional time-multiplexed topological quantum walks studied so far have relied on generalizations of the Su-Shreiffer-Heeger model with no synthetic gauge field. In this work, we demonstrate a two-dimensional topological quantum random walk where the nontrivial topology is due to the presence of a synthetic gauge field. We show that the synthetic gauge field leads to the appearance of multiple band gaps and, consequently, a spatial confinement of the quantum walk distribution. Moreover, we demonstrate topological edge states at an interface between domains with opposite synthetic fields. Our results expand the range of Hamiltonians that can be simulated using photonic quantum walks.

Nonlinear Second-Order Topological Insulators

We demonstrate, both theoretically and experimentally, the concept of nonlinear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of nonlinearity. We show that one-dimensional edge states and zero-dimensional corner states can be induced in a trivial crystal insulator made of evanescently coupled resonators with linear and nonlinear coupling coefficients, simply by tuning the intensity. This allows global external control over topological phase transitions and switching to a phase with nonzero bulk polarization, without requiring any structural or geometrical changes. We further show how these nonlinear effects enable dynamic tuning of the spectral properties and localization of the topological edge and corner states. Such self-induced second-order topological insulators, which can be found and implemented in a wide variety of physical platforms ranging from electronics to microwaves, acoustics, and optics, hold exciting promises for reconfigurable topological energy confinement, power harvesting, data storage, and spatial management of high-intensity fields.

Photonic Anomalous Quantum Hall Effect

We experimentally realize a photonic analogue of the anomalous quantum Hall insulator using a two-dimensional (2D) array of coupled ring resonators. Similar to the Haldane model, our 2D array is translation invariant, has a zero net gauge flux threading the lattice, and exploits next-nearest neighbor couplings to achieve a topologically nontrivial band gap. Using direct imaging and on-chip transmission measurements, we show that the band gap hosts topologically robust edge states. We demonstrate a topological phase transition to a conventional insulator by frequency detuning the ring resonators and thereby breaking the inversion symmetry of the lattice. Furthermore, the clockwise or the counterclockwise circulation of photons in the ring resonators constitutes a pseudospin degree of freedom. The two pseudospins acquire opposite hopping phases, and their respective edge states propagate in opposite directions. These results are promising for the development of robust reconfigurable integrated nanophotonic devices for applications in classical and quantum information processing.

Spontaneous Emission and Resonant Scattering in Transition from Type I to Type II Photonic Weyl Systems

Spontaneous emission and scattering behavior of an emitter or a resonant scatterer strongly depend on the density of states of the surrounding medium. It has been shown that the resonant scattering cross section (RSC) may diverge at the Weyl frequency of a type I Weyl system due to the diminishing density of states. Here we study the spontaneous emission (SE) and RSC in a photonic metacrystal across the critical transition between type I and type II Weyl systems. Theoretical results show that the SE rate of an emitter in a type I Weyl system diminishes to zero at the Weyl frequency. When the system is tuned towards the transition point between type I and type II Weyl point, the dip in the SE spectrum at the Weyl frequency becomes infinitely sharp. The dip vanishes at the critical transition, and transforms into a peak when the system changes into a type II Weyl system. We further show that the resonant scattering cross section also exhibits dramatically different spectral features across the transition. Our study demonstrates the ability to tune SE and RSC through altering the dispersion of the Weyl medium between type I and type II, which provides a fundamentally new route in manipulating light-matter interactions.

Dynamically reconfigurable topological edge state in phase change photonic crystals

The observation of topological edge states (TESs) revolutionized our understanding of scattering and propagation of electromagnetic (EM) waves. Supported by topological robustness, the TES at the interface between trivial and non-trivial insulators was not reflected from the structural disorders and imperfections. Recently topological photonic crystals (PhCs) were demonstrated to obtain remarkable one-way propagation of the TES, having the advantages of lossless propagation, dense integration, and high fabrication tolerance over conventional PhCs. Nevertheless, the lack of reversible switching of TES possesses significant limitations in helicity/spin filtering and tunable photonic devices. We proposed a topological PhC based on a prototypical phase-change material, Ge₂Sb₂Te₅ (GST225) to solve the problem. We find that at a particular frequency, the TES within the structure can be reversibly switched between "on" and "off" by transiting the GST225 structural state between amorphous and crystalline. Moreover, the topology of the PhC was maintained since the tuning of TES was achieved by varying the refractive index of GST225 instead of the structural geometry. This provides a continuous change of the spectral position of the photonic bandgap and TES by gradually crystallising the GST225. We show that the phase change of GST225 from amorphous to crystalline and vice versa can be engineered in nanoseconds. Our proof of concept may offer a platform for dynamically tuning the TESs that might otherwise be challenging to attain in photonic systems. We expect it to have potential applications for photonic devices in topological optical circuits and scatter-free one-way light propagation.

Asymptotic Prethermalization in Periodically Driven Classical Spin Chains

We reveal a continuous dynamical heating transition between a prethermal and an infinite-temperature stage in a clean, chaotic periodically driven classical spin chain. The transition time is a steep exponential function of the drive frequency, showing that the exponentially long-lived prethermal plateau, originally observed in quantum Floquet systems, survives the classical limit. Even though there is no straightforward generalization of Floquet's theorem to nonlinear systems, we present strong evidence that the prethermal physics is well described by the inverse-frequency expansion. We relate the stability and robustness of the prethermal plateau to drive-induced synchronization not captured by the expansion. Our results set the pathway to transfer the ideas of Floquet engineering to classical many-body systems, and are directly relevant for photonic crystals and cold atom experiments in the superfluid regime.

Robust topologically protected transport in photonic crystals at telecommunication wavelengths

Photonic topological insulators offer the possibility to eliminate backscattering losses and improve the efficiency of optical communication systems. Despite considerable efforts, a direct experimental demonstration of theoretically predicted robust, lossless energy transport in topological insulators operating at near-infrared frequencies is still missing. Here, we combine the properties of a planar silicon photonic crystal and the concept of topological protection to design, fabricate and characterize an optical topological insulator that exhibits the valley Hall effect. We show that the transmittances are the same for light propagation along a straight topological interface and one with four sharp turns. This result quantitatively demonstrates the suppression of backscattering due to the non-trivial topology of the structure. The photonic-crystal-based approach offers significant advantages compared with other realizations of photonic topological insulators, such as lower propagation losses, the presence of a band gap for light propagating in the crystal-slab plane, a larger operating bandwidth, a much smaller footprint, compatibility with complementary metal-oxide-semiconductor fabrication technology, and the fact that it allows for operation at telecommunications wavelengths.

Pseudo-spin-valley coupled edge states in a photonic topological insulator

Pseudo-spin and valley degrees of freedom engineered in photonic analogues of topological insulators provide potential approaches to optical encoding and robust signal transport. Here we observe a ballistic edge state whose spin–valley indices are locked to the direction of propagation along the interface between a valley photonic crystal and a metacrystal emulating the quantum spin–Hall effect. We demonstrate the inhibition of inter-valley scattering at a Y-junction formed at the interfaces between photonic topological insulators carrying different spin–valley Chern numbers. These results open up the possibility of using the valley degree of freedom to control the flow of optical signals in 2D structures.

Valleys in the photonic band structure provide an additional degree of freedom to engineer topological photonic structures and devices. Here, Kang et al. demonstrate that inter-valley scattering is inhibited at a Y-junction between three sections with different valley topology.

Reconfigurable Topological Phases in Next-Nearest-Neighbor Coupled Resonator Lattices

We present a reconfigurable topological photonic system consisting of a 2D lattice of coupled ring resonators, with two sublattices of site rings coupled by link rings, which can be accurately described by a tight-binding model. Unlike previous coupled-ring topological models, the design is translationally invariant, similar to the Haldane model, and the nontrivial topology is a result of next-nearest couplings with nonzero staggered phases. The system exhibits a topological phase transition between trivial and spin Chern insulator phases when the sublattices are frequency detuned. Such topological phase transitions can be easily induced by thermal or electro-optic modulators, or nonlinear cross phase modulation. We use this lattice to design reconfigurable topological waveguides, with potential applications in on-chip photon routing and switching.

Topological hybrid silicon microlasers

Topological physics provides a robust framework for strategically controlling wave confinement and propagation dynamics. However, current implementations have been restricted to the limited design parameter space defined by passive topological structures. Active systems provide a more general framework where different fundamental symmetry paradigms, such as those arising from non-Hermiticity and nonlinear interaction, can generate a new landscape for topological physics and its applications. Here, we bridge this gap and present an experimental investigation of an active topological photonic system, demonstrating a topological hybrid silicon microlaser array respecting the charge-conjugation symmetry. The created new symmetry features favour the lasing of a protected zero mode, where robust single-mode laser action in the desired state prevails even with intentionally introduced perturbations. The demonstrated microlaser is hybrid implemented on a silicon-on-insulator substrate, and is thereby readily suitable for integrated silicon photonics with applications in optical communication and computing.

Topological effects, first observed in condensed matter physics, are now also studied in optical systems, extending the scope to active topological devices. Here, Zhao et al. combine topological physics with non-Hermitian photonics, demonstrating a topological microlaser on a silicon platform.

Recent advances in the spin Hall effect of light

The spin Hall effect (SHE) of light, as an analogue of the SHE in electronic systems, is a promising candidate for investigating the SHE in semiconductor spintronics/valleytronics, high-energy physics and condensed matter physics, owing to their similar topological nature in the spin-orbit interaction. The SHE of light exhibits unique potential for exploring the physical properties of nanostructures, such as determining the optical thickness, and the material properties of metallic and magnetic thin films and even atomically thin two-dimensional materials. More importantly, it opens a possible pathway for controlling the spin states of photons and developing next-generation photonic spin Hall devices as a fundamental constituent of the emerging spinoptics. In this review, based on the viewpoint of the geometric phase gradient, we give a detailed presentation of the recent advances in the SHE of light and its applications in precision metrology and future spin-based photonics.

Tuning out disorder-induced localization in nanophotonic cavity arrays

Weakly coupled high-Q nanophotonic cavities are building blocks of slow-light waveguides and other nanophotonic devices. Their functionality critically depends on tuning as resonance frequencies should stay within the bandwidth of the device. Unavoidable disorder leads to random frequency shifts which cause localization of the light in single cavities. We present a new method to finely tune individual resonances of light in a system of coupled nanocavities. We use holographic laser-induced heating and address thermal crosstalk between nanocavities using a response matrix approach. As a main result we observe a simultaneous anticrossing of 3 nanophotonic resonances, which were initially split by disorder.

Dynamically Manipulating Topological Physics and Edge Modes in a Single Degenerate Optical Cavity

We propose a scheme to simulate topological physics within a single degenerate cavity, whose modes are mapped to lattice sites. A crucial ingredient of the scheme is to construct a sharp boundary so that the open boundary condition can be implemented for this effective lattice system. In doing so, the topological properties of the system can manifest themselves on the edge states, which can be probed from the spectrum of an output cavity field. We demonstrate this with two examples: a static Su-Schrieffer-Heeger chain and a periodically driven Floquet topological insulator. Our work opens up new avenues to explore exotic photonic topological phases inside a single optical cavity.

Light-Mediated Cascaded Locking of Multiple Nano-Optomechanical Oscillators

Collective phenomena emerging from nonlinear interactions between multiple oscillators, such as synchronization and frequency locking, find applications in a wide variety of fields. Optomechanical resonators, which are intrinsically nonlinear, combine the scientific assets of mechanical devices with the possibility of long distance controlled interactions enabled by traveling light. Here we demonstrate light-mediated frequency locking of three distant nano-optomechanical oscillators positioned in a cascaded configuration. The oscillators, integrated on a chip along a common coupling waveguide, are optically driven with a single laser and oscillate at gigahertz frequency. Despite an initial mechanical frequency disorder of hundreds of kilohertz, the guided light locks them all with a clear transition in the optical output. The experimental results are described by Langevin equations, paving the way to scalable cascaded optomechanical configurations.

Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice

Topological quantum matter can be realized by subjecting engineered systems to time-periodic modulations. In analogy with static systems, periodically driven quantum matter can be topologically classified by topological invariants, whose non-zero value guarantees the presence of robust edge modes. In the high-frequency limit of the drive, topology is described by standard topological invariants, such as Chern numbers. Away from this limit, these topological numbers become irrelevant, and novel topological invariants must be introduced to capture topological edge transport. The corresponding edge modes were coined anomalous topological edge modes, to highlight their intriguing origin. Here we demonstrate the experimental observation of these topological edge modes in a 2D photonic lattice, where these propagating edge states are shown to coexist with a quasi-localized bulk. Our work opens an exciting route for the exploration of topological physics in time-modulated systems operating away from the high-frequency regime.

Driving a Superconductor to Insulator Transition with Random Gauge Fields

Typically the disorder that alters the interference of particle waves to produce Anderson localization is potential scattering from randomly placed impurities. Here we show that disorder in the form of random gauge fields that act directly on particle phases can also drive localization. We present evidence of a superfluid bose glass to insulator transition at a critical level of this gauge field disorder in a nano-patterned array of amorphous Bi islands. This transition shows signs of metallic transport near the critical point characterized by a resistance , indicative of a quantum phase transition. The critical disorder depends on interisland coupling in agreement with recent Quantum Monte Carlo simulations. We discuss how this disorder tuned SIT differs from the common frustration tuned SIT that also occurs in magnetic fields. Its discovery enables new high fidelity comparisons between theoretical and experimental studies of disorder effects on quantum critical systems.

Realizing topological edge states in a silicon nitride microring-based photonic integrated circuit

Topological edge states in a photonic integrated circuit based on the platform of silicon nitride are demonstrated with a two-dimensional coupled resonator optical waveguide array involving the synthetic magnetic field for photons at near-infrared wavelengths. Measurements indicate that the topological edge states can be observed at certain wavelengths, with light travelling around the boundary of the array. Combined with the induced disorders in fabrication near the edge, the system shows the defect immunity under the topological protection of edge states.

Keldysh field theory for driven open quantum systems

Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.

Photonic Weyl degeneracies in magnetized plasma

Weyl particles are elusive relativistic fermionic particles with vanishing mass. While not having been found as an elementary particle, they are found to emerge in solid-state materials where three-dimensional bands develop a topologically protected point-like crossing, a so-called Weyl point. Photonic Weyl points have been recently realised in three-dimensional photonic crystals with complex structures. Here we report the presence of a novel type of plasmonic Weyl points in a naturally existing medium-magnetized plasma, in which Weyl points arise as crossings between purely longitudinal plasma modes and transverse helical propagating modes. These photonic Weyl points are right at the critical transition between a Weyl point with the traditional closed finite equifrequency surfaces and the newly proposed 'type II' Weyl points with open equifrequency surfaces. Striking observable features of plasmon Weyl points include a half k-plane chirality manifested in electromagnetic reflection. Our study introduces Weyl physics into homogeneous photonic media, which could pave way for realizing new topological photonic devices.

Topologically robust transport of entangled photons in a 2D photonic system

We theoretically study the transport of time-bin entangled photon pairs in a two-dimensional topological photonic system of coupled ring resonators. This system implements the integer quantum Hall model using a synthetic gauge field and exhibits topologically robust edge states. We show that the transport through edge states preserves temporal correlations of entangled photons whereas bulk transport does not preserve these correlations and can lead to significant unwanted temporal bunching or anti-bunching of photons. We study the effect of disorder on the quantum transport properties; while the edge transport remains robust, bulk transport is very susceptible, and in the limit of strong disorder, bulk states become localized. We show that this localization is manifested as an enhanced bunching/anti-bunching of photons. This topologically robust transport of correlations through edge states could enable robust on-chip quantum communication channels and delay lines for information encoded in temporal correlations of photons.

Experimental Realization of a Reflections-Free Compact Delay Line Based on a Photonic Topological Insulator

Electromagnetic (EM) waves propagating through an inhomogeneous medium are generally scattered whenever the medium’s electromagnetic properties change on the scale of a single wavelength. This fundamental phenomenon constrains how optical structures are designed and interfaced with each other. Recent theoretical work indicates that electromagnetic structures collectively known as photonic topological insulators (PTIs) can be employed to overcome this fundamental limitation, thereby paving the way for ultra-compact photonic structures that no longer have to be wavelength-scale smooth. Here we present the first experimental demonstration of a photonic delay line based on topologically protected surface electromagnetic waves (TPSWs) between two PTIs which are the EM counterparts of the quantum spin-Hall topological insulators in condensed matter. Unlike conventional guided EM waves that do not benefit from topological protection, TPSWs are shown to experience multi-wavelength reflection-free time delays when detoured around sharply-curved paths, thus offering a unique paradigm for compact and efficient wave buffers and other devices.

Floquet topological insulators for sound

The unique conduction properties of condensed matter systems with topological order have recently inspired a quest for the similar effects in classical wave phenomena. Acoustic topological insulators, in particular, hold the promise to revolutionize our ability to control sound, allowing for large isolation in the bulk and broadband one-way transport along their edges, with topological immunity against structural defects and disorder. So far, these fascinating properties have been obtained relying on moving media, which may introduce noise and absorption losses, hindering the practical potential of topological acoustics. Here we overcome these limitations by modulating in time the acoustic properties of a lattice of resonators, introducing the concept of acoustic Floquet topological insulators. We show that acoustic waves provide a fertile ground to apply the anomalous physics of Floquet topological insulators, and demonstrate their relevance for a wide range of acoustic applications, including broadband acoustic isolation and topologically protected, nonreciprocal acoustic emitters.

One-way sound propagation has been recently proposed in the context of topological acoustics, but is challenged by introducing uniform media motion. Here, Fleury et al. present a practical scheme to achieve topological propagation by modulating in time the acoustic properties of a lattice of resonators, resembling Floquet topological insulators in condensed matter.

Interaction-induced hopping phase in driven-dissipative coupled photonic microcavities

The Bose-Hubbard model (BHM) describes bosons hopping across sites and interacting on-site. Inspired by the success of BHM simulators with atoms in optical lattices, proposals for implementing the BHM with photons in coupled nonlinear cavities have recently emerged. Two coupled semiconductor microcavities constitute a model system where the hopping, interaction and decay of exciton polaritons-mixed light-matter quasiparticles-can be engineered in combination with site-selective coherent driving to implement the driven-dissipative two-site optical BHM. Here we explore the interplay of interference and nonlinearity in this system, in a regime where three distinct density profiles can be observed under identical driving conditions. We demonstrate how the phase acquired by polaritons hopping between cavities can be controlled through polariton-polariton interactions. Our results open new perspectives for synthesizing density-dependent gauge fields using polaritons in two-dimensional multicavity systems.

Probing topological protection using a designer surface plasmon structure

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the ‘topological protection' in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can break the topological protection, but do not exist in electronic topological insulators. This is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants.

The limits of topological protection in photonic systems remain unclear. Here, Gao et al. construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can break the topological protection.

Robust reconfigurable electromagnetic pathways within a photonic topological insulator

The discovery of topological photonic states has revolutionized our understanding of electromagnetic propagation and scattering. Endowed with topological robustness, photonic edge modes are not reflected from structural imperfections and disordered regions. Here we demonstrate robust propagation along reconfigurable pathways defined by synthetic gauge fields within a topological photonic metacrystal. The flow of microwave radiation in helical edge modes following arbitrary contours of the synthetic gauge field between bianisotropic metacrystal domains is unimpeded. This is demonstrated in measurements of the spectrum of transmission and time delay along the topological domain walls. These results provide a framework for freely steering electromagnetic radiation within photonic structures.

Experimental demonstration of topological effects in bianisotropic metamaterials

Existence of robust edge states at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, a topological insulator. Such nontrivial states were originally predicted and discovered in condensed matter physics, but they find their counterparts in other fields of physics, including the physics of classical waves and electromagnetism. Here, we present the first experimental realization of a topological insulator for electromagnetic waves based on engineered bianisotropic metamaterials. By employing the near-field scanning technique, we demonstrate experimentally the topologically robust propagation of electromagnetic waves around sharp corners without backscattering effects.