We investigate cluster synchronization in experiments with a multilayer network of electronic Colpitts oscillators, specifically a network with two interaction layers. We observe and analytically characterize the appearance of several cluster states as we change coupling in the layers. In this study, we innovatively combine bifurcation analysis and the computation of transverse Lyapunov exponents. We observe four kinds of synchronized states, from fully synchronous to a clustered quasiperiodic state—the first experimental observation of the latter state. Our work is the first to study fundamentally dissimilar kinds of coupling within an experimental multilayer network.

Continuous-wave-driven Kerr nonlinear microresonators give rise to self-organization in terms of dissipative Kerr solitons, which constitute optical frequency combs that can be used to generate low-noise microwave signals. Here, by applying either amplitude or phase modulation to the driving laser we create an intracavity potential trap to discipline the repetition rate of the solitons. We demonstrate that this effect gives rise to a novel spectral purification mechanism of the external microwave signal frequency, leading to reduced phase noise of the output signal. We experimentally observe that the microwave signal generated from disciplined solitons is injection locked by the external drive at long timescales, but exhibits an unexpected suppression of the fast timing jitter. Counterintuitively, this filtering takes place for frequencies that are substantially lower than the cavity decay rate. As a result, while the long timescale stability of the Kerr frequency comb’s repetition rate is improved by more than 4 orders of magnitude, the purified microwave signal shows a reduction of the phase noise by 30 dB at offset frequencies above 10 kHz.

We investigate the impact of liquid drops on deep pools of aqueous glycerol solutions with variable pool viscosity and air pressure both experimentally and numerically. With this approach, we are able to address drop impacts on substrates that continuously transition from low-viscosity liquids to almost solids. We show that the generic corolla spreading out from the impact point consists of two distinct sheets, namely an ejecta sheet fed by the drop liquid and a second sheet fed by the substrate liquid, which evolve on separated timescales. These two sheets contribute to a varying extent to the corolla overall dynamics and splashing, depending on the viscosity ratio between the two liquids.

We study lasing at the high-symmetry points of the Brillouin zone in a honeycomb plasmonic lattice. We use symmetry arguments to define singlet and doublet modes at the $K$ points of the reciprocal space. We experimentally demonstrate lasing at the $K$ points that is based on plasmonic lattice modes and two-dimensional feedback. By comparing polarization properties to $T$-matrix simulations, we identify the lasing mode as one of the singlets with an energy minimum at the $K$ point enabling feedback. Our results offer prospects for studies of topological lasing in radiatively coupled systems.

Flatband systems typically host “compact localized states” (CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice (LL), such conventional localized flatband states are found to be inherently incomplete, with the missing modes manifested as extended line states that form noncontractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially tailored boundaries and, thereby, directly observe the unusually extended flatband line states. Such unconventional line states cannot be expressed as a linear combination of the previously observed boundary-independent bulk CLS but rather arise from the nontrivial real-space topology. The robustness of the line states to imperfect excitation conditions is discussed, and their potential applications are illustrated.

The wide-range application of photonic crystals and metamaterials benefits from the enormous design space of three-dimensional subwavelength structures. In this Letter, we study the space group constraints on photonic dispersions for all 230 space groups with time-reversal symmetry. Our theory carefully treats the unique singular point of photonic bands at zero frequency and momentum, which distinguishes photonic bands from their electronic counterpart. The results are given in terms of minimal band connectivities at zero ($M$) and nonzero frequencies ($M^{\prime }$). Topological band degeneracies are guaranteed to be found in space groups that do not allow band gaps between the second and third photonic bands ($M>2$). Our Letter provides theoretical guidelines for the choice of spatial symmetries in photonics design.

We investigate the collective dynamics and nondegenerate parametric resonance (NPR) of coplanar, interdigitated arrays of microcantilevers distinguished by their cantilevers having linearly expanding lengths and thus varying natural frequencies. Within a certain excitation frequency range, the resonators begin oscillating via NPR across the entire array consisting of 200 single-crystal silicon cantilevers. Tunable coupling generated from fringing electrostatic fields provides a mechanism to vary the scope of the NPR. Our experimental results are supported by a reduced-order model that reproduces the leading features of our data including the NPR band. The potential for tailoring the coupled response of suspended mechanical structures using NPR presents new possibilities in mass, force, and energy sensing applications, energy harvesting devices, and optomechanical systems.

The intermittency of a passive scalar advected by three-dimensional Navier-Stokes turbulence at a Taylor-scale Reynolds number of 650 is studied using direct numerical simulations on a $4096^3$ grid; the Schmidt number is unity. By measuring scalar increment moments of high orders, while ensuring statistical convergence, we provide unambiguous evidence that the scaling exponents saturate to 1.2 for moment orders beyond about 12, indicating that scalar intermittency is dominated by the most singular shocklike cliffs in the scalar field. We show that the fractal dimension of the spatial support of steep cliffs is about 1.8, whose sum with the saturation exponent value of 1.2 adds up to the space dimension of 3, thus demonstrating a deep connection between the geometry and statistics in turbulent scalar mixing. The anomaly for the fourth and sixth order moments is comparable to that in the Kraichnan model for the roughness exponent of $4/3$.

Metamaterials with an effective zero refractive index associated with their electromagnetic response are sought for a number of applications in communications and nonlinear optics. A promising way that this can be achieved in all-dielectric photonic crystals is through the design of a Dirac cone at zero Bloch wave vector in the photonic band structure. In the optical frequency range, the natural way to implement this design is through the use of a photonic crystal slab. In the existing implementation, however, the zero-index photonic modes also radiate strongly into the environment due to intrinsic symmetry properties. This has resulted in large losses in recent experimental realizations of this zero-index paradigm. Here, we propose a photonic crystal slab with zero-index modes which are also symmetry-protected bound states in the continuum. Our approach thus eliminates the associated radiation loss. This could enable, for the first time, large-scale integration of zero-index materials in photonic devices.

The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well-defined classical limit as well as by systems with no classical correspondence, such as locally interacting spins or fermions. Despite great phenomenological success, a general mechanism explaining the emergence of RMT without reference to semiclassical concepts is still missing. Here we provide the example of a quantum many-body system with no semiclassical limit (no large parameter) where the emergence of RMT spectral correlations is proven exactly. Specifically, we consider a periodically driven Ising model and write the Fourier transform of spectral density’s two-point function, the spectral form factor, in terms of a partition function of a two-dimensional classical Ising model featuring a space-time duality. We show that the self-dual cases provide a minimal model of many-body quantum chaos, where the spectral form factor is demonstrated to match RMT for all values of the integer time variable $t$ in the thermodynamic limit. In particular, we rigorously prove RMT form factor for an odd $t$, while we formulate a precise conjecture for an even $t$. The results imply ergodicity for any finite amount of disorder in the longitudinal field, rigorously excluding the possibility of many-body localization. Our method provides a novel route for obtaining exact nonperturbative results in nonintegrable systems.

The breakup of low-viscosity droplets like water is a ubiquitous and rich phenomenon. Theory predicts that in the inviscid limit one observes a finite-time singularity, giving rise to a universal power law, with a prefactor that is universal for a given density and surface tension. This universality has been proposed as a powerful tool to determine the dynamic surface tension at short time scales. We combine high-resolution experiments and simulations to show that this universality is unobservable in practice: in contrast to previous studies, we show that fluid and system parameters do play a role; notably a small amount of viscosity is sufficient to alter the breakup dynamics significantly.

The qualitative behavior of charged particles in a vacuum is given by Earnshaw’s theorem, which states that there is no steady configuration of charged particles in a vacuum that is asymptotically stable to perturbations. In a viscous fluid, examples of stationary configurations of sedimenting uncharged particles are known, but they are unstable or neutrally stable—they are not attractors. In this Letter, it is shown by example that two charged particles settling in a fluid may have a configuration that is asymptotically stable to perturbations for a wide range of charges, radii, and densities. The existence of such “bound states” is essential from a fundamental point of view and it can be significant for dilute charged particulate systems in various biological, medical, and industrial contexts.

A bound state in the continuum (BIC) is a localized state of an open structure with access to radiation channels, yet it remains highly confined with, in theory, an infinite lifetime and quality factor. There have been many realizations of such exceptional states in dielectric systems without loss. However, realizing BICs in lossy systems such as those in plasmonics remains a challenge. In this Letter, we explore the possibility of realizing BICs in a hybrid plasmonic-photonic structure consisting of a plasmonic grating coupled to a dielectric optical waveguide with diverging radiative quality factors. The plasmonic-photonic system supports two distinct groups of BICs: symmetry-protected BICs at the $\mathrm{\Gamma }$ point and off-$\mathrm{\Gamma }$ Friedrich-Wintgen BICs. The photonic waveguide modes are strongly coupled to the gap plasmons in the grating, leading to an avoided crossing behavior with a high value of Rabi splitting of 150 meV. Moreover, we show that the strong coupling significantly alters the band diagram of the hybrid system, revealing opportunities for supporting stopped light at an off-$\mathrm{\Gamma }$ wide angular span.

The optical properties of small metallic particles allow us to bridge the gap between the myriad of subdiffraction local phenomena and macroscopic optical elements. The optomechanical coupling between mechanical vibrations of Au nanoparticles and their optical response due to collective electronic oscillations leads to the emission and the detection of surface acoustic waves (SAWs) by single metallic nanoantennas. We take two Au nanoparticles, one acting as a source and the other as a receptor of SAWs and, even though these antennas are separated by distances orders of magnitude larger than the characteristic subnanometric displacements of vibrations, we probe the frequency content, wave speed, and amplitude decay of SAWs originating from the damping of coherent mechanical modes of the source. Two-color pump-probe experiments and numerical methods reveal the characteristic Rayleigh wave behavior of emitted SAWs, and show that the SAW-induced optical modulation of the receptor antenna allows us to accurately probe the frequency of the source, even when the eigenmodes of source and receptor are detuned.

A single origami crease pattern can be folded into many different structures from the flat-unfolded state, effectively transforming in shape and function. This makes origami engineering a promising approach to transforming machines, but predicting and controlling this transformation is difficult because the fundamental dynamics of origami systems at the flat-unfolded state are not well understood. Working with Miura-inspired mechanisms, we identify and validate a model to predict configuration switching in mechanical origami systems. The model incorporates a hidden degree of freedom introduced by material compliance in the Miura mechanism. We characterize this pseudojoint statically and dynamically to identify its lumped stiffness and inertia and use it to create a new dynamic model. This model can be used to predict which configuration an origami mechanism will settle in by balancing the kinetic and potential energy of the system. We apply this model to design a branching origami structure with 17 distinct configurations controlled by a single actuator and demonstrate reliable switching between these configurations with tailored dynamic inputs. Given the fact that origami can replicate almost any shape, we expect that this framework will be applicable to transformation in arbitrary structures and mechanisms.

We demonstrate nonlinear emission from molecular layers strongly coupled to extended light fields in arrays of plasmonic nanoparticles in the presence of structural imperfections. Hybrid light-matter states, known as plasmon-exciton polaritons (PEPs), are formed by the strong coupling of Frenkel excitons in molecules to surface lattice resonances. These resonances result from the radiative coupling of localized surface plasmon polaritons in silver nanoparticles enhanced by diffraction on the array. By designing arrays with different lattice constants, we show that the nonlinear emission frequency is solely determined by the relaxation of exciton polaritons through vibrational quanta in the molecules. We also observe long-range spatial coherence in the samples, which supports the explanation in terms of a nonlinear collective emission of strongly coupled PEPs. In contrast to recent observations of exciton-polariton lasing and condensation in organic systems, photonic modes play a minor role at the emission frequency in our system, and this emission has an undefined momentum because of the structural imperfections. This remarkable result reveals the rich and distinct physics of strongly coupled organic molecules to photonic cavities.

Although the conservation of momentum is a fundamental law in physics, its constraints are not fulfilled for wave propagation at material boundaries, where incident waves give rise to evanescent field distributions. While nonlinear susceptibility tensor terms can provide solutions in the optical regime, this framework cannot be applied directly to acoustic waves. Now, by considering a complete representation of wave interactions and scattering at boundaries, we are able to show a generic formalism of sum-frequency mixing for the whole scattering field including all evanescent waves. This general case was studied analytically and verified both numerically and experimentally for ultrasonic waves, showing that considering evanescent waves leads to an anomalous nonlinear interaction which enhances sum-frequency generation. This new interpretation not only provides a deeper understanding of the momentum conservation laws in acoustics but also promises translation of this new understanding into optics and photonics, to enhance nonlinear interactions.

We demonstrate a novel response of a nonlinear micromechanical resonator when operated in a region of strong, nonlinear mode coupling. The system is excited with a single drive signal and its response is characterized by periodic amplitude modulations that occur at timescales based on system parameters. The periodic amplitude modulations of the resonator are a consequence of nonlinear mode coupling and are responsible for the emergence of a “frequency-comb” regime in the spectral response. By considering a generic model for a 1∶3 internal resonance, we demonstrate that the novel behavior results from a saddle node on an invariant circle (SNIC) bifurcation. The ability to control the operating parameters of the micromechanical structures reported here makes the simple micromechanical resonator an ideal test bed to study the dynamic response of SNIC behavior demonstrated in mechanical, optical, and biological systems.

We investigate points of circular polarization in the far field of elliptically polarized dipoles and establish a relation between the angular position and helicity of these $C$ points and the dipole moment. In the case of highly eccentric dipoles, the $C$ points of opposite handedness exhibit only a small angular separation and occur in the low intensity region of the emission pattern. In this regard, we introduce an optical weak measurement approach that utilizes the transverse electric (azimuthal) and transverse magnetic (radial) far-field polarization basis. Projecting the far field onto a spatially varying postselected polarization state reveals the angular separation and the helicity of the $C$ points. We demonstrate the applicability of this approach and determine the elliptical dipole moment of a particle sitting on an interface by measuring the $C$ points in its far field.