Topological acoustics enables backscattering-immune wave transport along domain interfaces, whose directionality can be deterministically controlled through spin-momentum locking of the excitation source. In this work, we computationally demonstrate a monolithic two-dimensional Ge2Sb2Te5 (GST) phononic crystal plate in which hexagonally patterned crystalline inclusions are embedded within an amorphous GST host, where the impedance contrast between the two phases opens a topological bandgap. Here we show that the overlap integral between an external excitation source and the Bloch eigenstates governs directional selectivity. The source position and phase determine which topological pseudospin channel is excited, enabling deterministic routing through spin-momentum locking. Our system exploits [Formula: see text] symmetry, which supports degenerate [Formula: see text]-type and [Formula: see text]-type orbital modes at the [Formula: see text] point serving as pseudospin degrees of freedom. When a single harmonic force is applied, it projects onto both pseudospin channels, yielding bidirectional propagation. By contrast, a quadrature phased force pair on neighboring inclusions generates a rotating displacement field whose coupling to one pseudospin state identically vanishes, locking propagation to a single direction. Swapping the force positions reverses the routing direction, and this reversal is spatially invariant across the interface, providing evidence of spin-momentum locking. By varying only the source configuration, the same interface operates as a bidirectional waveguide, unidirectional isolator, or selective router. These results demonstrate how spin-momentum locking can serve as an efficient mechanism for directional selectivity of topological interface states in monolithic structures, with relevance to on-chip acoustic signal routing and frequency-selective wave filtering.

Consumer demand for next-generation telecommunication devices with increasing performance and miniaturization imposes strong constraints on radio-frequency (RF) surface-acoustic-wave (SAW) devices, such as low cost, low insertion loss, and a small footprint. We use COMSOL MULTIPHYSICS to investigate the properties of realistic RF SAW devices with a thin film located along the delay line between the source and detector interdigitated transducers on a 128 degrees Y-cut lithium niobate (LN) substrate. In these simulations, a chalcogenide phase-change material, germanium antimony telluride, is chosen for the thin film material that could be converted to desired superlattices (SLs) constituted of crystalline and amorphous segments. Two types of SL configuration, with crystalline to amorphous segment ratios of 1:1 and 1:2, are investigated, and corresponding frequency responses are discussed. The primary outcome of this work is the demonstration of a SL RF duplexer and a topological acoustic narrow-band resonator in a SAW device that otherwise acts as a broadband filter. This work shows that a SL with thickness amounting to one tenth of the wavelength of the SAW can drastically affect the transmission of the composite device through mode hybridization between Bloch waves in the SL and the SAW in the LN substrate.

Vibration responses from nonlinear mechanical systems exhibit rich dynamical structure that can be utilized for information encoding and processing. We demonstrate that such structures can be used to encode and manipulate information in a manner analogous to multi-qubit systems. By using a coupled mass and conical spring oscillator, we reveal that distinct harmonic segments of the nonlinear response can be projected onto modal eigenstates to form two-level elastic-bit subsystems, which are analogous to qubits. These bits arise from measurable amplitudes and phase relationships across the Fourier spectrum and evolve deterministically under steady-state excitation. By combining multiple spectral segments within a single oscillator, we achieve two-bit and three-bit states that occupy four- and eight-dimensional Hilbert spaces, respectively. The time dependence of the complex modal coefficients yields intrinsic transformations that act as phase and rotation type gates. The temporal evolution of the complex modal coefficients results in phase accumulation and a rotation-like evolution within this state space. To characterize how the system moves between experimentally observed logical states at different times, we derive a Householder reflection that yields the exact Hermitian and unitary operator connecting these states. This unitary transformation is subsequently decomposed into sequences of analogous quantum gates, providing a representation of the observed modal evolution in terms of familiar multi-qubit logic primitives. This spectral-encoding approach enables scalable state construction within a single mechanical platform, establishing a pathway toward room-temperature mechanical computation based on deterministic nonlinear dynamics.

This work extends the Cahn–Larché thermodynamic framework to binary alloys in which two coherent solid phases coexist with an incoherent liquid and investigates how coherency strain energy modifies classical eutectic and peritectic equilibria. We derive equilibrium conditions for three-phase coexistence that include an elastic energy term dependent on the molar fractions of the solid phases and apply them to model binary eutectic and peritectic systems. We find that coherency stress transforms the eutectic point into a finite three-phase equilibrium field spanning a continuous range of compositions and temperatures. In contrast, coherency stress in peritectic systems progressively destabilizes the two-solid equilibrium without generating a stable three-phase field and can suppress the peritectic reaction entirely. This asymmetry is governed by the geometric relationship between the stress-free compositions of the phases: when the liquid composition lies between those of the two solids (eutectic configuration), the liquid serves as a thermodynamic buffer against the coherency penalty on the solid–solid pair; when it lies outside (peritectic configuration), no such mechanism is available. These results demonstrate that coherency stress can fundamentally alter three-phase equilibria involving a liquid and suggest that such effects may be significant in systems with large coherent misfits.

Quantum algorithms motivate alternative approaches to computation, and classical physical systems that generate correlations can enable parallelism. Here we present a framework for quantum-inspired computing based on phase bits (phibits), which represent logical units through the phases of nonlinear topological acoustic waves. We define two theoretical tools: the phase cache, which dynamically tracks the evolution of geometric phases, and the operator spectra shift, which enables consistent mapping between physical manipulations and computational operations. Using this framework, we implement the period finding core of Shor's algorithm and demonstrate the factorization of composite integers 15 and 35. The experimental probability distributions for the measured outcomes show good agreement with theoretical predictions, validating the accuracy of the phibit implementation and the robustness of the nonlinear acoustic platform. These results show the potential of phibits as an approach to performing complex computational tasks.

Classical systems that emulate quantum behaviors provide an effective means of exploring information processing without relying on fragile quantum hardware. In this work, we introduce a validated theoretical framework for phi-bits—nonlinear, phase-dependent modes serving as classical analogues of qubits—in a system consisting of three coupled finite-length acoustic waveguides. Using a discrete mass-spring model, we reproduce the experimentally observed continuous phase evolution of low-order combination modes under dual-frequency excitation. The model integrates nonlinearities at the end springs, damping effects, and boundary conditions, capturing the evolution of phi-bit phases as a function of the driving frequency. For spectrally isolated, high-SNR modes, the phase responses predicted by linear combinations of the driver phases are in qualitative agreement with experimental observations. Additionally, we investigate the role of higher-order nonlinearities, which extend the range of phi-bit behaviors but can disturb the linear relationship unless spring coefficients are recalibrated via nondimensional scaling. This framework provides a set of design criteria for selecting stable phi-bits, tuning sweep protocols, and adapting models to different geometries and materials. Our results demonstrate that classical nonlinear lattices can replicate key aspects of quantum information flow, offering a versatile and tunable platform for phase-encoded logic and quantum-inspired acoustic computation.

The future integration of topological acoustic materials into technology requires a better understanding of composites of topological systems. We consider two coupled Su–Schrieffer–Heeger chains and analytically find conditions governing the topology of the composite system. The conditions show that coupling two topologically trivial chains can give rise to a topologically non-trivial system. Furthermore, two topologically non-trivial chains can couple to form a topologically trivial system. We can even tune the coupling spring constant to go from trivial to non-trivial topology and vice versa. Trivial topology can be visualized as the parallel transport of a vector along a Moebius strip-type manifold having an even number of twists, whereas, in case of non-trivial topology, the manifold will have an odd number of twists. Each contribution of π to the Berry phase corresponds to a twist in the manifold. Our model serves as a prototype for composite topological acoustic structures that can be translated into practical technology.

We present a quantum-inspired computational method in which information is encoded and processed in the relative geometric phases of acoustic fields. The method is implemented in a nonlinear topological acoustic metamaterial structure and uses phase bits (phibits), where logical states correspond to phase relationships between spectrally defined nonlinear mixing components. To enable reliable multistep computation, we introduce two tools: a phase cache that dynamically tracks phase updates across a computation, and an operator spectra shift that provides a consistent mapping between experimentally applied physical manipulations and the intended computational operations. Using this framework, we realize the period-finding core of Shor's integer factorization algorithm and experimentally demonstrate factoring of the composite integers 15 and 35. Measured probability distributions are benchmarked against theoretical predictions and show strong agreement, indicating robustness of the nonlinear acoustic implementation. The results establish phase-encoded phibit computation as a practical way for implementing quantum-inspired algorithms on an acoustic wave platform at room temperature. [Work supported by the Science and Technology Center New Frontiers of Sound (NewFoS) through the U.S. National Science Foundation (NSF) Cooperative Agreement No. 2242925.]

The human brain performs complex, high-dimensional (HD) computations, such as causal reasoning, counterfactual thinking, and abstraction, with ~10 11 neurons while consuming ~20 watts of power. Neuromorphic computing seeks similar efficiency, but current devices face bottlenecks in bandwidth, energy, wiring, footprint, and reliability that limit scalability. Here, we introduce the topological acoustic synapse (TAS), an acoustic-wave neuromorphic device that circumvents these limits by mapping information in multivariate state spaces. A single TAS generates and manipulates numerous computing channels that operate independently and in parallel. The TAS leverages nonlinear interactions to emulate biorealistic neuromorphic functionalities, including reconfigurable synaptic plasticity, neuromodulation, and hybrid analog-digital control. In classification tasks, a TAS handles multiple inputs simultaneously and generates various outputs, converging 20% faster while using 60% fewer parameters and at least an order of magnitude less power than state-of-the-art electrical devices. This work establishes the first acoustic synapse with parallel HD computing capabilities, presenting a scalable paradigm for neuromorphic hardware with high computational density.

This work presents the theory and experimental demonstrations of frequency-controlled energy absorption in parametric mixing circuits which may find applications in the design of tunable notch filters and frequency-selective surfaces. A time-varying capacitance model is used to describe the energy exchange among the pump, signal, and idler frequencies in parametric mixing circuits. Analytical derivations reveal that under specific frequency ordering, the system exhibits a positive conductance at the signal frequency that is correlated with the pump frequency, leading to measurable energy absorption. A fabricated on-chip circuit operating between 1.3 and 2.3 GHz serves as a physical representation of the theoretical model, experimentally validating the predicted energy transfer behavior. The results establish a unified framework linking circuit-level phenomena to the fundamental physics of energy redistribution in parametric systems.

The dynamical equations of motion of a discrete one-dimensional harmonic chain with side restoring forces is analogous to the relativistic Klein-Gordon equation. Dirac factorization of that discrete Klein-Gordon equation introduces two equations with time reversal (T) and parity (P) symmetry breaking conditions. The Dirac-factored equations enable the exploration of the properties of the solutions of the dynamical equations under P and T symmetry breaking conditions. The spinor solutions of the Dirac factored equations describe two types of acoustic waves, one with a conventional topology (Berry phase equal to 0) and the other one with a non-conventional topology (Berry phase of π). In this latter case, the acoustic wave is isomorphic to the quantum spin of an electron, also known as an acoustic pseudospin, which requires a closed path corresponding to two Brillouin zones to recover the original spinor. The interface between topologically conventional and non-conventional chains supports topological surface states. The Dirac-factored equations of motions of the one-dimensional harmonic chain with side springs can serve as a model for the investigation of the properties of acoustic topological insulators. [Work supported by NSF Award No. 2242925.]

Defect localization in homogeneous structures using ultrasonic waves is relatively easy to implement. However, locating defects in heterogeneous structures made of different materials can be challenging. This is because complicated reflections, refractions and scatterings occur when ultrasonic waves pass through the interfaces between two dissimilar materials of the heterogeneous structures. To address this issue, a localization methodology based on geometric phase change - index (GPC-I), derived from topological acoustic (TA) sensing, is proposed to adapt to the complicated scenarios when defects are present in heterogeneous plate structures. The GPC-I is adopted as the damage index (DI) to present the possibility of defects appearing on different acoustic sensing paths. A maximum peak value-dependent threshold in GPC-I plots (GPC-I vs. sensor sites) is defined to filter out unreliable sensing paths resulting from the heterogeneity. Different sensing modes (I and II) are combined to comprehensively provide a more reliable and accurate localization framework. Numerical modeling carried out by Abaqus/CAE software verifies the proposed GPC-I based localization technique. Comparison results among GPC-I and other two commonly used acoustic parameters-wave velocity differences (VD) and amplitude ratio (AR) (or wave attenuation) show that the GPC-I has superiority with higher sensitivity and stability for defect localization. This work can provide promising guidance for localizing defects in complex heterogeneous plate structures used in real-world engineering applications.

We leverage ambient seismic noise to implement a novel geometric phase sensing method for investigating the effects of environmental conditions on near-surface ground properties. The geometric phase, derived from topological acoustics, characterizes the geometry of a wavefield by incorporating cross-correlation information between seismic sensors. Changes in geometric phase, , are expressed as changes in vectorial orientation, describing the wavefield evolution over time. To demonstrate the method, we designed an end-to-end workflow by applying an open access temporal high-resolution data from a seismic array in southwest Iceland and measured over a 2-year period. We observe that the seasonal fluctuations of are highly correlated with surface air temperature, reflecting changes in ground properties during the freeze-thaw cycle. We assess the seasonal stability of the noise source distribution and conduct a numerical test to verify that the seasonal pattern in is minimally affected by shifts in noise source direction. Several advantages of geometric phase measurements, including the elimination of lag window selection and reduced computational costs, suggest their strong effectiveness in monitoring changes in ground properties with time. We suggest that the geometric phase can play a significant role in the future of environmental monitoring.

Defect localization in homogeneous plate structures is relatively easy with various well-established acoustics-based techniques. However, localizing defects in heterogeneous structures can be challenging due to complicated reflection, refraction and scattering patterns arising from heterogeneous boundaries during wave propagations. This work introduces a topological acoustic (TA) sensing technique for localizing defects in heterogeneous plate structures. The geometric phase change index (GPC-I) derived from TA sensing is used to detect perturbations caused by defects along the sensing paths between transmitters and receivers. The proposed method identifies the largest GPC-I values for various sensing paths. A higher GPC-I value on a sensing path implies a higher probability of having a defect on that path. A maximum peak value dependent threshold in GPC-I plots (GPC-I vs.sensor sites) is defined to identify and filter out those unreliable sensing paths in the proposed localization method. Finite element based numerical analysis in Abaqus/CAE software verifies the effectiveness of the proposed method.The commonly used methods using velocity differences (VD) and amplitude ratios (AR) are also tried out for defect localization for comparison.The performance comparison of the localization results using GPC-I, VD, and AR reveal that the GPC-I based technique is the most effective technique for defect localization

Traditional structural damage detection methods in aerospace applications face challenges in accuracy and sensitivity, often necessitating multiple sensors to evaluate various measurement paths between the reference and defective states. However, the recently developed topological acoustic (TA) sensing technique can capture shifts in the geometric phase of an acoustic field, enabling the detection of even minor perturbations in the supporting medium. In this study, a diagnostic imaging method for damage detection in plate structures based on the TA sensing technique is presented. The method extracts the geometric phase shift index (GPS-I) from the Lamb wave response signals to indicate the location of the damage. Using Abaqus/CAE, a finite element model of the plate was established to simulate the Lamb wave response signals, which were then used to validate the feasibility of the proposed method. The results indicate that this technique enables rapid and precise identification of damage and its location within the plate structure, requiring response signals from only a few points on the damaged plate, and it is reference-free.

Nonlinear mechanical oscillators can emulate qubit analogue algebra by leveraging multiple harmonics of large‑amplitude vibrations. We realize a logical elastic bit—a room temperature mechanical analogue of a qubit—in a two‑mass oscillator joined by a conical spring whose graded stiffness generates a robust sequence of phase‑coherent harmonics. From time‑series velocity measurements, a Fourier–projection maps the response onto the complete space of in‑phase and out‑of‑phase eigenvectors. The resulting complex coefficients define a Bloch‑sphere representation in which classical superpositions are directly controllable. Moreover, we gain more control over the coefficients by pairing the Fourier harmonics in different orders. When the paired Fourier components share a frequency, the coefficients are independent of time, producing tunable states that can serve as phase-defined memory. Pairing distinct harmonics introduces a beat frequency that drives deterministic precession of the Bloch vector, realizing single‑bit rotations (e.g., Pauli‑X and Hadamard analogues) without the need of additional external input, with time as the gate clock. By splitting the spectrum into blocks, a single resonator can host several elastic bits at once. The Hilbert space grows with the number of blocks while the hardware stays the same, allowing scalable architectures that show classical non-separable correlations. A linear mass-spring model yields closed‑form eigenfrequencies and Bloch‑angle formulas that overlay measured trajectories across resonance and provide design rules for state initialization and gate timing. All operations occur at ambient conditions and require no feedback or cryogenics, establishing a simple, reproducible route to quantum‑inspired logic in macroscopic mechanics.

This study demonstrates a novel nondestructive evaluation (NDE) method that combines geometric phase sensing with cross-correlation processed acoustical responses, enabling the detection of structural anomalies even when the acoustic excitation is stochastic and the source characteristics are variable. Traditional ultrasonic techniques, which depend on impulse responses from known source locations to capture wave transmission behavior, often fail under stochastic excitations due to incoherent phase alignment and unpredictable wave paths. The proposed method applies cross-correlation between a fixed reference site and other sensor locations to refine the acoustic field representation, enabling physically meaningful geometric phase extraction through the dot product of two state vectors representative of the acoustic field in a high-dimensional complex Hilbert space. This allows detection of both excitation-induced field asymmetries and subtle nonlinearities. Experimental validation using laser Doppler vibrometry on a circular IN625 plate demonstrates that this approach preserves excitation-induced field asymmetries while remaining sensitive to structural perturbations such as mass defects. The cross-correlation geometric phase change (CC-Delta phi) spectra reveal modal differences across excitation conditions, even under white noise, where geometric phase without cross-correlation (Delta phi) remains centered near 90 deg, obscuring structural insights. The method also detects mass-induced effects, showing increased average CC-Delta phi compared to the no-mass case under the same excitation condition. These results establish a foundation for a robust, non-contact, source-independent NDE technique, suitable for operation under variable and uncontrolled excitation scenarios.

Commonly used methods for defect localization in structures are based on velocity differences (VD) or amplitude ratio (AR) (or attenuation due to scattering) measured along different sensing paths between a reference system and a defective system. A high value on a sensing path indicates a higher probability of the presence of defect on that path. We introduce an alternative approach based on the newly developed topological acoustic (TA) sensing technique for localizing defects in plate structures using Lamb waves. TA sensing exploits changes in geometric phase of acoustic waves to detect perturbations in the supporting medium. This approach uses a geometric phase change - index (GPC-I), a measure of the geometry of the acoustic field averaged over a spectral domain, as detection metric in lieu of VD or AR. Calculations based on the finite element method (FEM) in Abaqus/CAE software verifies the effectiveness of the proposed GPC-I-based defect localization method. Randomly located defects on the surface of a plate are localized with higher sensitivity and accuracy, by the GPC-I method in comparison to VD or AR-based methods.

We present both the theoretical framework and experimental implementation of permutation gates using logical phi-bits, classical acoustic analogs of qubits. Logical phi-bits are nonlinear acoustic modes supported by externally driven acoustic metamaterials. Using a tensor product of modified Bloch sphere representations, we realize all possible two logical phi-bit permutations including SWAP and C-NOT. We also illustrate the scalability of a permutation for any number of logical phi-bits. Experimental demonstrations of these permutations require a single physical action on the driving conditions of the acoustic metamaterial. All logical phi-bits exist in the same physical system. We compare the phi-bit system with its quantum counterpart using Qiskit simulations, which illustrate the complexity of realizing these permutations in a quantum context.

We demonstrate an integrated non-destructive inspection methodology that employs the nonlinear ultrasonics-based sideband peak counting (SPC) technique in conjunction with topological acoustics (TA) sensing to comprehensively characterize the acoustic response of steel plates that contain differing levels of damage. By combining the SPC technique and TA, increased sensitivity to defect/damage detection as well as the ability to spatially resolve the presence of defects was successfully established. Towards this end, using a Rockwell hardness indenter, steel plates were subject to one, three and five centrally located indentations respectively. The acoustic response of the plate as a function of number of indentations was examined at a frequency range between 50 kHz and 800 kHz, from which the change in a global geometric phase was evaluated. Here, geometric phase is a measure of the topological acoustic field response to the spatial locations of the indentations within the steel plates. The global geometric phase unambiguously showed an increase with increasing number of indentations. In addition, spatial variations in a 'local' geometric phase as well as spatial variations in the SPC-index (SPC-I) were also determined. Spatial variations in both the local geometric phase as well as the SPC-I were particularly significant across the indentations for frequencies below 300 kHz, and by combining the respective spatial variations in the SPC-I and geometric phase, the locations of the indentations were accurately identified. The developed SPC-TA nondestructive method represents a promising technique for detecting and evaluating defects in structural materials.