Observation of dynamic non-Hermitian skin effects.

Non-Hermitian physics has emerged as a new paradigm that profoundly changes our understanding of non-equilibrium systems, introducing novel concepts such as exceptional points, spectral topology, and non-Hermitian skin effects (NHSEs). Most existing studies focus on non-Hermitian eigenstates, whereas dynamic properties have been discussed only recently, and the dynamic NHSEs are not yet confirmed in experiments. Here, we report the experimental observation of non-Hermitian skin dynamics using tunable one-dimensional nonreciprocal double-chain mechanical systems with glide-time symmetry. Remarkably, dynamic NHSEs are observed with various behaviors in different dynamic phases, which can be understood via the generalized Brillouin zone and the related concepts. Moreover, the observed dynamic NHSEs, amplifications, bulk unidirectional wave propagation, and boundary wave trapping provide promising ways to manipulate waves in a controllable and robust way. Our findings open a new pathway toward non-Hermitian dynamics, which will fertilize the study of non-equilibrium phases of matter.

Observation of Topological Transition in Floquet Non-Hermitian Skin Effects in Silicon Photonics.

Non-Hermitian physics has greatly enriched our understanding of nonequilibrium phenomena and uncovered novel effects such as the non-Hermitian skin effect (NHSE) that has profoundly revolutionized the field. NHSE has been predicted in systems with nonreciprocal couplings which, however, are challenging to realize in experiments. Without nonreciprocal couplings, the NHSE can also emerge in systems with coexisting gauge fields and loss or gain (e.g., in Floquet non-Hermitian systems). However, such Floquet NHSE remains largely unexplored in experiments. Here, we realize the Floquet NHSEs in periodically modulated optical waveguides integrated on a silicon photonic platform. By engineering the artificial gauge fields induced by the periodical modulation, we observe various Floquet NHSE phases and unveil their rich topological transitions. Remarkably, we discover the transitions between the unipolar NHSE phases and an unconventional bipolar NHSE phase, which is accompanied by the directional reversal of the NHSEs. The underlying physics is revealed by the band winding in complex quasienergy space which undergoes a topology change from isolated loops with the same winding to linked loops with opposite windings. Our work unfolds a new route toward Floquet NHSEs originating from the interplay between gauge fields and dissipation effects, and thus offers fundamentally new ways for steering light and other waves.

Observation of an acoustic topological Euler insulator with meronic waves.

Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features: First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone. Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via. the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via. pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena.

Measuring entanglement entropy and its topological signature for phononic systems.

Entanglement entropy is a fundamental concept with rising importance in various fields ranging from quantum information science, black holes to materials science. In complex materials and systems, entanglement entropy provides insight into the collective degrees of freedom that underlie the systems' complex behaviours. As well-known predictions, the entanglement entropy exhibits area laws for systems with gapped excitations, whereas it follows the Gioev-Klich-Widom scaling law in gapless fermion systems. However, many of these fundamental predictions have not yet been confirmed in experiments due to the difficulties in measuring entanglement entropy in physical systems. Here, we report the experimental verification of the above predictions by probing the nonlocal correlations in phononic systems. We obtain the entanglement entropy and entanglement spectrum for phononic systems with the fermion filling analog. With these measurements, we verify the Gioev-Klich-Widom scaling law. We further observe the salient signatures of topological phases in entanglement entropy and entanglement spectrum.

Observation of D-class topology in an acoustic metamaterial.

Topological materials and metamaterials opened new paradigms to create and manipulate phases of matter with unconventional properties. Topological D-class phases (TDPs) are archetypes of the ten-fold classification of topological phases with particle-hole symmetry. In two dimensions, TDPs support propagating topological edge modes that simulate the elusive Majorana elementary particles. Furthermore, a piercing of π-flux Dirac-solenoids in TDPs stabilizes localized Majorana excitations that can be braided for the purpose of topological quantum computation. Such two-dimensional (2D) TDPs have been a focus in the research frontier, but their experimental realizations are still under debate. Here, with a novel design scheme, we realize 2D TDPs in an acoustic crystal by synthesizing both the particle-hole and fermion-like time reversal symmetries for a wide range of frequencies. The design scheme leverages an enriched unit cell structure with real-valued couplings that emulate the targeted Hamiltonian of TDPs with complex hoppings: A technique that could unlock the realization of all topological classes with passive metamaterials. In our experiments, we realize a pair of TDPs with opposite Chern numbers in two independent sectors that are connected by an intrinsic fermion-like time-reversal symmetry built in the system. We measure the acoustic Majorana-like helical edge modes and visualize their robust topological transport, thus revealing the unprecedented D and DIII class topologies with direct evidence. Our study opens up a new pathway for the experimental realization of two fundamental classes of topological phases and may offer new insights in fundamental physics, materials science, and phononic information processing.

Electrical tuning of branched flow of light.

Branched flows occur ubiquitously in various wave systems, when the propagating waves encounter weak correlated scattering potentials. Here we report the experimental realization of electrical tuning of the branched flow of light using a nematic liquid crystal (NLC) system. We create the physical realization of the weakly correlated disordered potentials of light via the inhomogeneous orientations of the NLC. We demonstrate that the branched flow of light can be switched on and off as well as tuned continuously through the electro-optical properties of NLC film. We further show that the branched flow can be manipulated by the polarization of the incident light due to the optical anisotropy of the NLC film. The nature of the branched flow of light is revealed via the unconventional intensity statistics and the rapid fidelity decay along the light propagation. Our study unveils an excellent platform for the tuning of the branched flow of light which creates a testbed for fundamental physics and offers a new way for steering light.

Topological phononic metamaterials.

The concept of topological energy bands and their manifestations have been demonstrated in condensed matter systems as a fantastic paradigm toward unprecedented physical phenomena and properties that are robust against disorders. Recent years, this paradigm was extended to phononic metamaterials (including mechanical and acoustic metamaterials), giving rise to the discovery of remarkable phenomena that were not observed elsewhere thanks to the extraordinary controllability and tunability of phononic metamaterials as well as versatile measuring techniques. These phenomena include, but not limited to, topological negative refraction, topological 'sasers' (i.e. the phononic analog of lasers), higher-order topological insulating states, non-Abelian topological phases, higher-order Weyl semimetal phases, Majorana-like modes in Dirac vortex structures and fragile topological phases with spectral flows. Here we review the developments in the field of topological phononic metamaterials from both theoretical and experimental perspectives with emphasis on the underlying physics principles. To give a broad view of topological phononics, we also discuss the synergy with non-Hermitian effects and cover topics including synthetic dimensions, artificial gauge fields, Floquet topological acoustics, bulk topological transport, topological pumping, and topological active matters as well as potential applications, materials fabrications and measurements of topological phononic metamaterials. Finally, we discuss the challenges, opportunities and future developments in this intriguing field and its potential impact on physics and materials science.

In situ Simulation of Thermal Reality.

Simulated reality encompasses virtual, augmented, and mixed realities-each characterized by different degrees of truthfulness in the visual perception: "all false," "coexistence of true and false," and "difficult distinction between true and false," respectively. In all these technologies, however, the temperature rendering of virtual objects is still an unsolved problem. Undoubtedly, the lack of thermal tactile functions substantially reduces the quality of the user's real-experience perception. To address this challenge, we propose theoretically and realize experimentally a technological platform for the in situ simulation of thermal reality. To this purpose, we design a thermal metadevice consisting of a reconfigurable array of radiating units, capable of generating the thermal image of any virtual object, and thus rendering it in situ together with its thermal signature. This is a substantial technological advance, which opens up new possibilities for simulated reality and its applications to human activities.

Geometric Phase in Twisted Topological Complementary Pair.

Geometric phase enabled by spin-orbit coupling has attracted enormous interest in optics over the past few decades. However, it is only applicable to circularly-polarized light and encounters substantial challenges when applied to wave fields lacking the intrinsic spin degree of freedom. Here, a new paradigm is presented for achieving geometric phase by elucidating the concept of topological complementary pair (TCP), which arises from the combination of two compact phase elements possessing opposite intrinsic topological charge. Twisting the TCP leads to the generation of a linearly-varying geometric phase of arbitrary order, which is quantified by the intrinsic topological charge. Notably distinct from the conventional spin-orbit coupling-based theories, the proposed geometric phase is the direct result of the cyclic evolution of orbital-angular-momentum transformation in mode space, thereby exhibiting universality across classical wave systems. As a proof of concept, the existence of this geometric phase is experimentally demonstrated using scalar acoustic waves, showcasing the remarkable ability in the precise manipulation of acoustic waves at subwavelength scales. These findings engender a fresh understanding of wave-matter interaction in compact structures and establish a promising platform for exploring geometric phase, offering significant opportunities for diverse applications in wave systems.

Hybrid topological photonic crystals.

Topologically protected photonic edge states offer unprecedented robust propagation of photons that are promising for waveguiding, lasing, and quantum information processing. Here, we report on the discovery of a class of hybrid topological photonic crystals that host simultaneously quantum anomalous Hall and valley Hall phases in different photonic band gaps. The underlying hybrid topology manifests itself in the edge channels as the coexistence of the dual-band chiral edge states and unbalanced valley Hall edge states. We experimentally realize the hybrid topological photonic crystal, unveil its unique topological transitions, and verify its unconventional dual-band gap topological edge states using pump-probe techniques. Furthermore, we demonstrate that the dual-band photonic topological edge channels can serve as frequency-multiplexing devices that function as both beam splitters and combiners. Our study unveils hybrid topological insulators as an exotic topological state of photons as well as a promising route toward future applications in topological photonics.

Optical parity-time induced perfect resonance transmission in zero index metamaterials.

Non-Hermitian photonic systems with balanced gain and loss have become significantly more popular due to their potential applications in communications and lasing. In this study, we introduce the concept of optical parity-time (PT) symmetry to zero-index metamaterials (ZIMs) to investigate the transport of electromagnetic (EM) waves through a PT-ZIM junction in a waveguide system. The PT-ZIM junction is formed by doping two dielectric defects of the same geometry in the ZIM, with one being the gain and the other being the loss. It is found that the balanced gain and loss can induce a perfect transmission resonance in a perfect reflection background, and the resonant linewidth is controllable and determined by the gain/loss. The smaller the gain/loss, the narrower the linewidth and the larger the quality (Q) factor of the resonance. This finding originates from the fact that the introduced PT symmetry breaks the spatial symmetry of the structure, leading to the excitation of quasi-bound states in the continuum (quasi-BIC). Additionally, we also show that the lateral displacements of the two cylinders play a crucial role in the electromagnetic transport properties in ZIMs with PT symmetry, which breaks the common sense that the transport effect in ZIMs is location-independent. Our results provide a new approach to manipulate the interaction of EM waves with defects in ZIMs using gain and loss to achieve anomalous transmission, and a pathway to investigate non-Hermitian photonics in ZIMs with potential applications in sensing, lasing, and nonlinear optics.

Thermoelectric Rectification and Amplification in Interacting Quantum-Dot Circuit-Quantum-Electrodynamics Systems.

Thermoelectric rectification and amplification were investigated in an interacting quantum-dot circuit-quantum-electrodynamics system. By applying the Keldysh nonequilibrium Green's function approach, we studied the elastic (energy-conserving) and inelastic (energy-nonconserving) transport through a cavity-coupled quantum dot under the voltage biases in a wide spectrum of electron-electron and electron-photon interactions. While significant charge and Peltier rectification effects were found for strong light-matter interactions, the dependence on electron-electron interaction could be nonmonotonic and dramatic. Electron-electron interaction-enhanced transport was found under certain resonance conditions. These nontrivial interaction effects were found in both linear and nonlinear transport regimes, which manifested in charge and thermal currents, rectification effects, and the linear thermal transistor effect.

Tunable liquid-solid hybrid thermal metamaterials with a topology transition.

Thermal metamaterials provide rich control of heat transport which is becoming the foundation of cutting-edge applications ranging from chip cooling to biomedical. However, due to the fundamental laws of physics, the manipulation of heat is much more constrained in conventional thermal metamaterials where effective heat conduction with Onsager reciprocity dominates. Here, through the inclusion of thermal convection and breaking the Onsager reciprocity, we unveil a regime in thermal metamaterials and transformation thermotics that goes beyond effective heat conduction. By designing a liquid-solid hybrid thermal metamaterial, we demonstrate a continuous switch from thermal cloaking to thermal concentration in one device with external tuning. Underlying such a switch is a topology transition in the virtual space of the thermotic transformation which is achieved by tuning the liquid flow via external control. These findings illustrate the extraordinary heat transport in complex multicomponent thermal metamaterials and pave the way toward an unprecedented regime of heat manipulation.

Observation of fractal higher-order topological states in acoustic metamaterials.

Topological phases of matter have been extensively investigated in solid-state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain almost unexplored. Fractals, being self-similar on different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate fractal higher-order topological states with unprecedented emergent phenomena in a Sierpinski acoustic metamaterial. We uncover abundant topological edge and corner states in the acoustic metamaterial due to the fractal geometry. Interestingly, the numbers of the edge and corner states depend exponentially on the system size, and the leading exponent is the Hausdorff fractal dimension of the Sierpinski carpet. Furthermore, the results reveal the unconventional spectrum and rich wave patterns of the corner states with consistent simulations and experiments. This study thus unveils unconventional topological states in fractal geometry and may inspire future studies of topological phenomena in non-Euclidean geometries.

Experimental Realization of Nonreciprocal Adiabatic Transfer of Phonons in a Dynamically Modulated Nanomechanical Topological Insulator.

High quality nanomechanical oscillators are promising platforms for quantum entanglement and quantum technology with phonons. Realizing coherent transfer of phonons between distant oscillators is a key challenge in phononic quantum information processing. Here, we report on the realization of robust unidirectional adiabatic pumping of phonons in a parametrically coupled nanomechanical system engineered as a one-dimensional phononic topological insulator. By exploiting three nearly degenerate local modes-two edge states and an interface state between them-and the dynamic modulation of their mutual couplings, we achieve nonreciprocal adiabatic transfer of phononic excitations from one edge to the other with near unit fidelity. We further demonstrate the robustness of such adiabatic transfer of phonons in the presence of various noises in the control signals. Our experiment paves the way toward nonreciprocal phonon dynamics via adiabatic pumping and is valuable for phononic quantum information processing.

Possible realization of optical Dirac points in woodpile photonic crystals.

The simulation of fermionic relativistic physics, e.g., Dirac and Weyl physics, has led to the discovery of many unprecedented phenomena in photonics, of which the optical-frequency realization is, however, still challenging. Here, surprisingly, we discover that the woodpile photonic crystals commonly used for optical frequency applications host exotic fermion-like relativistic degeneracies: a Dirac nodal line and a fourfold quadratic point, as protected by the nonsymmorphic crystalline symmetry. Deforming the woodpile photonic crystal leads to the emergence of type-II Dirac points from the fourfold quadratic point. Such type-II Dirac points can be detected by its anomalous refraction property which is manifested as a giant birefringence in a slab setup. Our findings provide a promising route towards 3D optical Dirac physics in all-dielectric photonic crystals.

Observation of Topological p-Orbital Disclination States in Non-Euclidean Acoustic Metamaterials.

Disclinations-topological defects ubiquitously existing in various materials-can reveal the intrinsic band topology of the hosting material through the bulk-disclination correspondence. In low-dimensional materials and nanostructure such as graphene and fullerenes, disclinations yield curved surfaces and emergent non-Euclidean geometries that are crucial in understanding the properties of these materials. However, the bulk-disclination correspondence has never been studied in non-Euclidean geometry, nor in systems with p-orbital physics. Here, by creating p-orbital topological acoustic metamaterials with disclination-induced conic and hyperbolic surfaces, we demonstrate the rich emergent bound states arising from the interplay among the real-space geometry, the bulk band topology, and the p-orbital physics. This phenomenon is confirmed by clear experimental evidence that is consistent with theory and simulations. Our experiment paves the way toward topological phenomena in non-Euclidean geometries and will stimulate interesting research on, e.g., topological phenomena for electrons in nanomaterials with curved surfaces.

Observation of Emergent Dirac Physics at the Surfaces of Acoustic Higher-Order Topological Insulators.

Using 3D sonic crystals as acoustic higher-order topological insulators (HOTIs), 2D surface states described by spin-1 Dirac equations at the interfaces between the two sonic crystals with distinct topology but the same crystalline symmetry are discovered. It is found that the Dirac mass can be tuned by the geometry of the two sonic crystals. The sign reversal of the Dirac mass reveals a surface topological transition where the surface states exhibit zero refractive index behavior. When the surface states are gapped, 1D hinge states emerge due to the topology of the gapped surface states. The zero refractive index behavior and the emergent topological hinge states are confirmed experimentally. This study reveals a multidimensional Wannier orbital control that leads to extraordinary properties of surface states and unveils an interesting topological mechanism for the control of surface waves.