Designing metamaterials that carry out advanced computations poses a significant challenge. A powerful design strategy splits the problem into two steps: First, encoding the desired functionality in a discrete or tight-binding model, and second, identifying a metamaterial geometry that conforms to the model. Applying this approach to information-processing tasks requires accurately mapping nonlinearity -- an essential element for computation -- from discrete models to geometries. Here we formulate this mapping through a nonlinear coordinate transformation that accurately connects tight-binding degrees of freedom to metamaterial excitations in the nonlinear regime. This transformation allows us to design information-processing metamaterials across the broad range of computations that can be expressed as tight-binding models, a capability we showcase with three examples based on three different computing paradigms: a coherent Ising machine that approximates combinatorial optimization problems through energy minimization, a mechanical racetrack memory exemplifying in-memory computing, and a speech classification metamaterial based on analog neuromorphic computing.

The ability to quantify the directional flow of information is vital to understanding natural systems and designing engineered information-processing systems. A widely used measure to quantify this information flow is the transfer entropy. However, until now, this quantity could only be obtained in dynamical models using approximations that are typically uncontrolled. Here we introduce a computational algorithm called Transfer Entropy-Path Weight Sampling (TE-PWS), which makes it possible, for the first time, to quantify the transfer entropy and its variants exactly for any stochastic model, including those with multiple hidden variables, nonlinearity, transient conditions, and feedback. By leveraging techniques from polymer and path sampling, TE-PWS efficiently computes the transfer entropy as a Monte-Carlo average over signal trajectory space. We use our exact technique to demonstrate that commonly used approximate methods to compute transfer entropies incur large systematic errors and high computational costs. As an application, we use TE-PWS in linear and nonlinear systems to reveal how transfer entropy can overcome naive applications of the data processing inequality in the presence of feedback.

Learning to change shape is a fundamental strategy of adaptation and evolution of living organisms, from bacteria and cells to tissues and animals. Human-made materials can also exhibit advanced shape morphing capabilities, but lack the ability to learn. Here, we build metamaterials that can learn complex shape-changing responses using a contrastive learning scheme. By being shown examples of the target shape changes, our metamaterials are able to learn those shape changes by progressively updating internal learning degrees of freedom -- the local stiffnesses. Unlike traditional materials that are designed once and for all, our metamaterials have the ability to forget and learn new shape changes in sequence, to learn multiple shape changes that break reciprocity, and to learn multistable shape changes, which in turn allows them to perform reflex gripping actions and locomotion. Our findings establish metamaterials as an exciting platform for physical learning, which in turn opens avenues for the use of physical learning to design adaptive materials and robots.

Multistable order parameters provide a natural means of encoding non-volatile information in spatial domains, a concept that forms the foundation of magnetic memory devices. However, this stability inherently conflicts with the need to move information around the device for processing and readout. While in magnetic systems, domains can be transported using currents or external fields, mechanisms to robustly shuttle information-bearing domains across neutral systems are scarce. Here, we experimentally realize a topological boundary ratchet in an elastic metamaterial, where digital information is encoded in buckling domains and transported in a quantized manner via cyclic loading. The transport is topological in origin: neighboring domains act as different topological pumps for their Bogoliubov excitations, so their interface hosts topological boundary modes. Cyclic loading renders these modes unstable through inter-domain pressure, which in turn drives the motion of the domain wall. We demonstrate that the direction of information propagation can be controlled through adjustable mechanical constraints on the buckling beams, and numerically investigate buckling-based domain-wall logic circuits in an elastic metamaterial network. The underlying tight-binding structure with low-order nonlinearities makes this approach a general pathway toward racetrack memories in neutral systems.

Efficient information processing is crucial for both living organisms and engineered systems. The mutual information rate, a core concept of information theory, quantifies the amount of information shared between the trajectories of input and output signals, and enables the quantification of information flow in dynamic systems. A common approach for estimating the mutual information rate is the Gaussian approximation which assumes that the input and output trajectories follow Gaussian statistics. However, this method is limited to linear systems, and its accuracy in nonlinear or discrete systems remains unclear. In this work, we assess the accuracy of the Gaussian approximation for non-Gaussian systems by leveraging Path Weight Sampling (PWS), a recent technique for exactly computing the mutual information rate. In two case studies, we examine the limitations of the Gaussian approximation. First, we focus on discrete linear systems and demonstrate that, even when the system's statistics are nearly Gaussian, the Gaussian approximation fails to accurately estimate the mutual information rate. Second, we explore a continuous diffusive system with a nonlinear transfer function, revealing significant deviations between the Gaussian approximation and the exact mutual information rate as nonlinearity increases. Our results provide a quantitative evaluation of the Gaussian approximation's performance across different stochastic models and highlight when more computationally intensive methods, such as PWS, are necessary.

Frequency upconversion is a cornerstone of electromagnetic signal processing, analysis and detection. It is used to transfer energy and information from one frequency domain to another where transmission, modulation or detection is technically easier or more efficient. Optomechanical transduction is emerging as a flexible approach to coherent frequency upconversion; it has been successfully demonstrated for conversion from radio- and microwaves (kHz to GHz) to optical fields. Nevertheless, optomechanical transduction of multi-THz and mid-infrared signals remains an open challenge. Here, we utilize molecular cavity optomechanics to demonstrate upconversion of sub-microwatt continuous-wave signals at $\sim$32~THz into the visible domain at ambient conditions. The device consists in a plasmonic nanocavity hosting a small number of molecules. The incoming field resonantly drives a collective molecular vibration, which imprints an optomechanical modulation on a visible pump laser and results in Stokes and anti-Stokes upconverted Raman sidebands with sub-natural linewidth, indicating a coherent process. The nanocavity offers 13 orders of magnitude enhancement of upconversion efficiency per molecule compared to free space, with a measured phonon-to-photon internal conversion efficiency larger than $10^{-4}$ per milliwatt of pump power. Our results establish a flexible paradigm for optomechanical frequency conversion using molecular oscillators coupled to plasmonic nanocavities, whose vibrational and electromagnetic properties can be tailored at will using chemical engineering and nanofabrication.

Cs2AgBiBr6 (CABB) has been proposed as a promising non-toxic alternative to lead halide perovskites. However, low charge carrier collection efficiencies remain an obstacle for the incorporation of this material in optoelectronic applications. In this work, we study the optoelectronic properties of CABB thin films using steady state and transient absorption and reflectance spectroscopy. We find that optical measurements on such thin films are distorted as a consequence of multiple reflections within the film. Moreover, we discuss the pathways behind conductivity loss in these thin films, using a combination of microsecond transient absorption and time-resolved microwave conductivity spectroscopy. We demonstrate that a combined effect of carrier loss and localization results in the conductivity loss in CABB thin films. Moreover, we find that the charge carrier diffusion length and sample thickness are of the same order. This suggests that the materials surface is an important contributor to charge carrier loss.

We studied the interaction between salts and surfactants on the water surface using heterodyne-detected vibrational sum frequency generation (HD-VSFG) spectroscopy. We used sodium dodecyl sulfate (SDS) as a prototype surfactant system at 75 micromolar bulk concentration in water. The vibrational response of the OH band of near-surface oriented water molecules and the CH bands of the hydrophobic tails of the surfactant are measured. We observed a dramatic enhancement of the surface density of the negatively charged SDS (DS-) within a narrow range of added salt concentrations. We demonstrated this increase is strongly ion-specific, and induced by the screening of the lateral Coulomb repulsion of the sulfate headgroups by the added cations, followed by strong hydrophobic interactions (hydrophobic collapse) when the DS- surface density reaches a critical value. For a solution of 75 micromolar SDS, the required concentrations of CsCl, KCl, and NaCl for this transition are 2, 5, and 10 mM, respectively.

Physical reservoir computing is a promising framework for efficient neuromorphic in and near-sensor computing applications. Here, we demonstrate a multimodal optoelectronic reservoir network based on halide perovskite semiconductor devices, capable of processing both voltage and light inputs. The devices consist of micrometer-sized, asymmetric crossbars covered with a MAPbI3 perovskite film. In a network, we simulate the performance by transforming MNIST images and videos based on the NMNIST dataset using 4-bit inputs and training linear readout layers for classification. We demonstrate multimodal networks capable of processing both voltage and light inputs, reaching mean accuracies up to 95.3 p/m 0.1% and 87.8 p/m 0.1% for image and video classification, respectively. We observed only minor deterioration due to measurement noise. The networks significantly outperformed linear classifier references, by 3.1% for images and 14.6% for video. We show that longer retention times benefit classification accuracy for single-mode networks, and give guidelines for choosing optimal experimental parameters. Moreover, the microscale device architecture lends itself well to further downscaling in high-density sensor arrays, making the devices ideal for efficient in-sensor computing.

Integrated photonics has revolutionized fields such as telecommunications, quantum optics, and metrology by enabling compact, scalable circuits through highly confined optical modes. Within the field of quantum acoustics, phonons have emerged as a compelling alternative, offering advantages such as lower energy, smaller mode volume, and low propagation speeds, which make them ideal for interfacing diverse quantum systems. Developing integrated phononic circuits is thus essential for unlocking the full potential of quantum acoustics and advancing technologies such as quantum computing and hybrid systems. In this work, we demonstrate the first 4-port directional coupler for quantum mechanical excitations - a key building block for phononic circuits. By tuning the coupling region length, we achieve phononic beam splitters with controllable splitting ratios. We validate quantum-level performance by sending a single-phonon Fock state through the device. This work represents a foundational advance toward scalable, integrated phononic platforms for both classical and quantum applications.

Frequency upconversion is a cornerstone of electromagnetic signal processing, analysis and detection. It is used to transfer energy and information from one frequency domain to another where transmission, modulation or detection is technically easier or more efficient. Optomechanical transduction is emerging as a flexible approach to coherent frequency upconversion; it has been successfully demonstrated for conversion from radio- and microwaves (kHz to GHz) to optical fields. Nevertheless, optomechanical transduction of multi-THz and mid-infrared signals remains an open challenge. Here, we utilize molecular cavity optomechanics to demonstrate upconversion of sub-microwatt continuous-wave signals at $\sim$32~THz into the visible domain at ambient conditions. The device consists in a plasmonic nanocavity hosting a small number of molecules. The incoming field resonantly drives a collective molecular vibration, which imprints an optomechanical modulation on a visible pump laser and results in Stokes and anti-Stokes upconverted Raman sidebands with sub-natural linewidth, indicating a coherent process. The nanocavity offers 13 orders of magnitude enhancement of upconversion efficiency per molecule compared to free space, with a measured phonon-to-photon internal conversion efficiency larger than $10^{-4}$ per milliwatt of pump power. Our results establish a flexible paradigm for optomechanical frequency conversion using molecular oscillators coupled to plasmonic nanocavities, whose vibrational and electromagnetic properties can be tailored at will using chemical engineering and nanofabrication.

Metal halide perovskites (MHPs) have emerged as attractive optoelectronic materials because of high fluorescence quantum yield, broad color tunability, and excellent color purity. However, the ionic nature of MHPs makes them susceptible to polar solvents, leading to defect-induced nonradiative recombination and photoluminescence (PL) quenching. Here, we present a combined in-synthesis ($\textit{in situ}$) and post-synthesis ion engineering to suppress nonradiative recombination and integrate multicolor MHP arrays on-chip through a perovskite-compatible photolithography process and $\textit{in situ}$ vapor-phase anion exchange. CsPbBr$_{3}$@CsPbBr$_{3-x}$TFA$_{x}$ nanoplatelets were grown on-chip via a single-step solution process incorporating trifluoroacetate (TFA$^{-}$) pseudohalides. X-ray photoelectron spectroscopy revealed that TFA$^{-}$ passivate uncoordinated Pb$^{2+}$ ions on nanoplatelet surface and suppresses the formation of metallic lead (Pb$^{0}$). This decreases the non-radiative recombination centers and yields a PL peak at 520 nm with a linewidth of 14.56$\% \pm$ 0.5 nm. The nanoplatelets were patterned via a top-down photolithography process and selectively masked with a PMMA/Al$_{2}$O$_{3}$ stack to enable vapor-phase anion exchange. The PL peak shifted in the unmasked regions from 520 nm to 413 nm, resulting in distinct green and blue emission arrays. Our method enables the scalable fabrication of highly luminescent, two-color MHP arrays with tailored optical properties, advancing their integration into next-generation optoelectronic devices.

Pulsed optomechanical measurements enable squeezing, non-classical state creation and backaction-free sensing. We demonstrate pulsed measurement of a cryogenic nanomechanical resonator with record precision close to the quantum regime. We use these to prepare thermally squeezed and purified conditional mechanical states, and to perform full state tomography. These demonstrations exploit large photon-phonon coupling in a nanophotonic cavity to reach a single-pulse imprecision of 9 times the mechanical zero-point amplitude $x_\mathrm{zpf}$. We study the effect of other mechanical modes which limit the conditional state width to 58 $x_\mathrm{zpf}$, and show how decoherence causes the state to grow in time.

Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior, such as large shape changes, effect of pre-tension, negative stiffness and instabilities. While traditional finite element analysis is capable of simulating a specific nonlinear structure quantitatively, it can be costly and cumbersome to use due to the high number of degrees of freedom involved. We propose a framework to facilitate the exploration of highly nonlinear structures under quasistatic conditions. In our framework, models are simplified by introducing `flexels', elements capable of intrinsically representing the complex mechanical responses of compound structures. By extending the concept of nonlinear springs, flexels can be characterized by multi-valued response curves, and model various mechanical deformations, interactions and stimuli, e.g., stretching, bending, contact, pneumatic actuation, and cable-driven actuation. We demonstrate that the versatility of the formulation allows to model and simulate, with just a few elements, complex mechanical systems such as pre-stressed tensegrities, tape spring mechanisms, interaction of buckled beams and pneumatic soft gripper actuated using a metafluid. With the implementation of the framework in an easy-to-use Python library, we believe that the flexel formulation will provide a useful modeling approach for understanding and designing nonlinear mechanical structures.

One way for solar cell efficiencies to overcome the Shockley-Queisser limit is downconversion of high-energy photons using singlet fission (SF) in polyacenes like tetracene (Tc). SF enables generation of multiple excitons from the high-energy photons which can be harvested in combination with Si. In this work we investigate the use of lead sulfide quantum dots (PbS QDs) with a band gap close to Si as an interlayer that allows Foerster Resonant Energy Transfer (FRET) from Tc to Si, a process that would be spin-forbidden without the intermediate QD step. We investigate how the conventional FRET model, most commonly applied to the description of molecular interactions, can be modified to describe the geometry of QDs between Tc and Si and how the distance between QD and Si, and the QD bandgap affects the FRET efficiency. By extending the acceptor dipole in the FRET model to a 2D plane, and to the bulk, we see a relaxation of the distance dependence of transfer. Our results indicate that FRET efficiencies from PbS QDs to Si well above 50 % are be possible at very short, but possibly realistic distances of around 1 nm, even for quantum dots with relatively low photoluminescence quantum yield.

The hysteretic snapping under lateral forcing of a compressed, buckled beam is fundamental for many devices and mechanical metamaterials. For a single-tip lateral pusher, an important limitation is that snapping requires the pusher to cross the centerline of the beam. Here, we show that dual-tip pushers allow accelerated snapping, where the beam snaps before the pusher reaches the centerline. As a consequence, we show that when a buckled beam under increased compression comes in contact with a dual-tip pusher, it can snap to the opposite direction -- this is impossible with a single-tip pusher. Additionally, we reveal a novel two-step snapping regime, in which the beam sequentially loses contact with the two tips of the dual-tip pusher. To characterize this class of snapping instabilities, we employ a systematic modal expansion of the beam shape. This expansion allows us to capture and analyze the transition from one-step to two-step snapping geometrically. Finally we demonstrate how to maximize the distance between the pusher and the beam's centerline at the moment of snapping. Together, our work opens up a new avenue for quantitatively and qualitatively controlling and modifying the snapping of buckled beams, with potential applications in mechanical sensors, actuators, and metamaterials.

Collections of bistable elements called hysterons provide a powerful model to capture the sequential response and memory effects of frustrated, multistable media in the athermal, quasistatic limit. While a century of work has elucidated, in great detail, the properties of ensembles of non-interacting hysterons - the so-called Preisach model - comparatively little is known about the behavior and properties of interacting hysterons. Here we discuss a general framework for interacting hysterons, focussing on the relation between the design parameters that specify the hysterons and their interactions, and the resulting transition graphs (t-graphs). We show how the structure of such t-graphs can be thought of as being composed of a scaffold that is dressed by (avalanche) transitions selected from finite binary trees. Moreover, we provide a systematic framework to straightforwardly determine the design inequalities for a given t-graph, and discuss an effective method to determine if a certain t-graph topology is realizable by a set of interacting hysterons. Altogether, our work builds on the Preisach model by generalizing the hysteron-dependent switching fields to the state-dependent switching fields. As a result, while in the Preisach model, the main loop identifies the critical hysterons that trigger a transition, in the case of interacting hysterons, the scaffold contains this critical information and assumes a central role in determining permissible transitions. In addition, our work suggests strategies to deal with the combinatorial explosion of the number and variety of t-graphs for interacting hysterons. This approach paves the way for a deeper theoretical understanding of the properties and statistics of t-graphs, and opens a route to materializing complex pathways, memory effects and embodied computations in (meta)materials based on interacting hysterons.

Mechanical systems played a foundational role in computing history, and have regained interest due to their unique properties, such as low damping and the ability to process mechanical signals without transduction. However, recent efforts have primarily focused on elementary computations, implemented in systems based on pre-defined reservoirs, or in periodic systems such as arrays of buckling beams. Here, we numerically demonstrate a passive mechanical system -- in the form of a nonlinear mass-spring model -- that tackles a real-world benchmark for keyword spotting in speech signals. The model is organized in a hierarchical architecture combining feature extraction and continuous-time convolution, with each individual stage tailored to the physics of the considered mass-spring systems. For each step in the computation, a subsystem is designed by combining a small set of low-order polynomial potentials. These potentials act as fundamental components that interconnect a network of masses. In analogy to electronic circuit design, where complex functional circuits are constructed by combining basic components into hierarchical designs, we refer to this framework as springtronics. We introduce springtronic systems with hundreds of degrees of freedom, achieving speech classification accuracy comparable to existing sub-mW electronic systems.

When cyclically driven, certain disordered materials exhibit transient and multiperiodic responses that are difficult to reproduce in synthetic materials. Here, we show that elementary multiperiodic elements with period T=2, togglerons, can serve as building blocks for such responses. We experimentally realize metamaterials composed of togglerons with tunable transients and periodic responses - including odd periods. Our approach suggests a hierarchy of increasingly complex elements in frustrated media, and opens a new strategy for rational design of sequential metamaterials.

The optical cross sections of plasmonic nanoparticles are intricately linked to the morphology of the particle. If this connection can be made accurately enough, it would become possible to determine a particles shape solely from its measured optical cross sections. For that, electromagnetic simulations can be used to bridge the morphology and optical properties assuming that they can be performed in an accurate manner. In this paper, we study key factors that influence the accuracy of electromagnetic simulations. First, we compare several standard electromagnetic simulation methods and discuss in detail the effects of the meshing accuracy, choice of dielectric function and inclusion of a substrate for the boundary element method. To help the boundary element methods complex parametrization, we develop a workflow including reconstruction, meshing and mesh simplification steps to be able to use electron tomography data as input for these simulations. In particular, we analyze how the choice of reconstruction algorithm and the intricacies of image segmentation influence the simulated optical cross sections and correlate it to induced shape errors, which can be minimized in the data processing pipeline. In our case, optimal results could be obtained by using the Total Variation Minimization (TVM) reconstruction method in combination with Otsu thresholding and slight smoothing, which was important to create a reliable and watertight surface mesh using the marching cubes algorithm, especially for more complex shapes.