Phononic Crystal Cavity Research Articles

Studying phonon coherence with a quantum sensor

Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size (n¯≃1−10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{n}\\simeq 1-10$$\\end{document} phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble (N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime.

Acoustic analog-to-digital converter based on solid–solid phononic crystal cavity

Acoustic analog-to-digital converter based on solid–solid phononic crystal cavity

The Design and Analysis of Topological Phononic Crystals with Cavity

The topological phononic crystal is composed of two topologically distinct structures. The topological phononic crystal resonant cavity based are proposed and the acoustic wave propagate characteristics are also presented. The topological cavity with defects will change the resonance frequency and quality factor is also discussed. The advantages of the topological cavity are the better quality factors and the concentrated sound pressure larger than general defect cavity.

Imaging phonon eigenstates and elucidating the energy storage characteristics of a honeycomb-lattice phononic crystal cavity

We extend gigahertz time-domain imaging to a wideband investigation of the eigenstates of a phononic crystal cavity. Using omnidirectionally excited phonon wave vectors, we implement an ultrafast technique to experimentally probe the two-dimensional acoustic field inside and outside a hexagonal cavity in a honeycomb-lattice phononic crystal formed in a microscopic crystalline silicon slab, thereby revealing the confinement and mode volumes of phonon eigenstates—some of which are clearly hexapole in character—lying both inside and outside the phononic-crystal band gap. This allows us to obtain a quantitative measure of the spatial acoustic energy storage characteristics of a phononic crystal cavity. We also introduce a numerical approach involving toneburst excitation and the monitoring of the acoustic energy decay together with the integral of the Poynting vector to calculate the Q factor of the principal in-gap eigenmode, showing it to be limited by ultrasonic attenuation rather than by phonon leakage to the surrounding region.

Optomechanical Generation of Coherent GHz Vibrations in a Phononic Waveguide.

Nanophononics has the potential for information transfer, in an analogous manner to its photonic and electronic counterparts. The adoption of phononic systems has been limited, due to difficulties associated with the generation, manipulation, and detection of phonons, especially at GHz frequencies. Existing techniques often require piezoelectric materials with an external radiofrequency excitation that are not readily integrated into existing CMOS infrastructures, while nonpiezoelectric demonstrations have been inefficient. In this Letter, we explore the optomechanical generation of coherent phonons in a suspended 2D silicon phononic crystal cavity with a guided mode around 6.8GHz. By incorporating an air-slot into this cavity, we turn the phononic waveguide into an optomechanical platform that exploits localized photonic modes resulting from inherent fabrication imperfections for the transduction of mechanics. Such a platform exhibits very fine control of phonons using light, and is capable of coherent self-sustained phonon generation around 6.8GHz, operating at room temperature. The ability to generate high frequency coherent mechanical vibrations within such a simple 2D CMOS-compatible system could be a first step towards the development of sources in phononic circuitry and the coherent manipulation of other solid-state properties.

Dissipation-induced acoustic nonreciprocity

Linear acoustic transmission through a stationary elastic medium possesses Rayleigh reciprocal symmetry with respect to pressure produced by a source at point A(B) and measured at point B(A), pA(rB) = pB(rA). In ideal (inviscid) fluids, pressure plays the role of the scalar potential for velocity, v∼∇p. The Rayleigh reciprocity theorem is formulated for velocity potentials but not for their gradients. Any function of the absolute value of velocity, v(r), lacks reciprocal symmetry. In particular, acoustic intencity I = pv is not symmetric, IA(rB) ≠ IB(rA). Dynamics of ideal fluid is time-reversible, and lack of reciprocal symmetry is attributed to asymmetry in scattering. However, in a viscous environment dissipation breaks T symmetry making fluid dynamics irreversible. We report that acoustic transmission is not only irreversible but also becomes nonreciprocal due to different amount of dissipated energy for forward and backward propagation, provided that mirror symmetry (P symmetry) is broken. Since dissipation occurs within a narrow viscous layer at solid–fluid interface, the amount of nonreciprocity in transmission strongly depends on the quality of the surface of scatterers. Experiments performed with scatterers of different surface quality show how surface roughness affects the level of nonreciprocity. In a series of experiments with asymmetric phononic crystal, Tesla valve, and acoustic cavity, we demonstrate dissipation-induced nonreciprocity in transmission. [This work is supported by the NSF under EFRI Grant No. 1741677.]

Energy trapping in a phononic crystal cavity enhanced by nonreciprocal acoustic wave transmission

Defect mode induced energy trapping at the bandgap frequency of a phononic crystal has been widely explored. Unlike this extensively used mechanism, this work reports the use of nonreciprocity in the transmission band to trap energy inside a phononic crystal cavity. Passive nonreciprocity is due to natural viscosity of the background liquid (water) and asymmetry of aluminum scatterers. The level of non-resonant energy trapping was compared for three cavities with different symmetry. Enhancement of energy trapping at a frequency of 624 kHz was observed experimentally for the cavity where nonreciprocity suppresses acoustic radiation into environment. Experimental results were further investigated and confirmed using finite element numerical analysis.

Theoretical design of phononic crystal cavity sensor for simple and efficient detection of low concentrations of heavy metals in water

Theoretical design of phononic crystal cavity sensor for simple and efficient detection of low concentrations of heavy metals in water

Enhanced energy trapping in a nonreciprocal phononic crystal cavity

Acoustic energy trapping using defect modes in the band gap frequencies of acoustic metamaterials has been widely explored. Unlike this extensively used mechanism, the present work demonstrates the use of non-reciprocity in the transmission band to trap energy inside a phononic crystal cavity. A phononic crystal with broken parity and time reversal symmetry can be used to generate linear nonreciprocal transmission of the ultrasound waves. A gradient induced differential dissipation (GIDD) based passive non-reciprocal phononic crystal with asymmetric scatterers was employed to create three configurations of cavities. The parity of the present system is broken by the asymmetric shape of the scatterers, and the time reversal symmetry is naturally broken by viscous dissipation. The cavity configurations were based on the orientations of the asymmetric scatterers in part of the crystal that allowed utilization of non-reciprocity involved in only one of the cavities' configurations. Enhancement of energy trapping at a frequency of 622.5 kHz was observed experimentally for the cavity utilizing nonreciprocity compared to other cavity configurations. Experimental results were further confirmed and comprehended using finite element method based computational outcome. This energy trapping device is linear, robust, and allows sound energy trapping without an external energy source.

Phononic crystal locally-resonant cavity for sensing metallic oxides nano-powders

In this paper, the goal is to specify the type of metallic oxides including Fe2O3, Fe3O4, ZnO, Al2O3, MgO, TiO2, and NiO, provided as nano-powders. The phononic directional coupler is firstly employed and investigated to detect the materials. Subsequently, a novel locally-resonant structure based on the solid-solid phononic crystal is proposed to be used as a mass sensor. This structure consists of the PMMA background with tungsten inclusions and three resonant cavities for increasing the quality factor. There are two hollow cylinders inside the middle cavity filled with the materials whose type should be determined. Filling these cylinders with different target materials results in different resonant frequencies. To specify these frequencies, the transmission spectrum of the structure is obtained via the 3-dimensional finite element simulation method.

Mode-sensitive magnetoelastic coupling in phononic-crystal magnomechanics

The acoustically driven spin-wave resonance in a phononic-crystal cavity is numerically investigated. The designed cavity enables confinement of gigahertz vibrations in a wavelength-scale point-defect structure and sustains a variety of resonance modes. Inhomogeneous strain distributions in the modes modify the magnetostrictive coupling and the spin-wave excitation susceptible to an external-field orientation. In particular, a monopole-like mode in the cavity having a near-symmetrical pattern shows a subwavelength-scale mode volume and can provide a versatile acoustic excitation scheme independent of the field-angle variation. Thus, the phononic-crystal platform offers an alternative approach to acoustically control the spin-wave dynamics with ultrasmall and inhomogeneous mode structures, which will be a key technology to integrate and operate large-scale magnomechanical circuits.

Extreme quantum nonlinearity in superfluid thin-film surface waves

We show that highly confined superfluid films are extremely nonlinear mechanical resonators, offering the prospect to realize a mechanical qubit. Specifically, we consider third-sound surface waves, with nonlinearities introduced by the van der Waals interaction with the substrate. Confining these waves to a disk, we derive analytic expressions for the cubic and quartic nonlinearities and determine the resonance frequency shifts they introduce. We predict single-phonon shifts that are three orders of magnitude larger than in current state-of-the-art nonlinear resonators. Combined with the exquisitely low intrinsic dissipation of superfluid helium and the strongly suppressed acoustic radiation loss in phononic crystal cavities, we predict that this could allow blockade interactions between phonons as well as two-level-system-like behavior. Our work provides a pathway towards extreme mechanical nonlinearities, and towards quantum devices that use mechanical resonators as qubits.

Modeling of phononic crystal cavity for sensing different biodiesel fuels with high sensitivity

The biodiesel production process requires accurate information about its physical properties for monitoring the production process. This work introduced a one-dimensional ternary phononic crystal (1D-TPnC) sensor capable of discriminating and sensing between the acoustic properties of different biodiesel fuels in the ultrasonic range. The sensor structure combines a liquid-filled defect layer into a perfect TPnC. The liquid-filled defect layer restores some of the incident acoustic energy and excites a transmitted resonant dip inside the reflection spectrum. The reflection spectrum of the layered TPnC structure is calculated based on the transfer matrix method (TMM). The simulations showed that the proposed sensor has the feature of being ultra-highly sensitive and selective between the Extra-virgin olive, Tesco sunflower, Methyl Oleate, and Soybean biofuels.The numerical results revealed that Soybean oil has the highest sensitivity (76589 m−1) and Q-factor (267) compared with the other three oils. For Methyl Oleate, the sensitivity and quality factor of the sensor reached the values of about 12680 m−1 and 204, respectively. With increasing the temperature from 30 ∘C to 50 ∘C, the sensitivity increased from 33853Hz/ °C to 36096 Hz/ ∘C for Soybean oil while it decreased from 4064 Hz/ ∘C to 37243 Hz/ ∘C for Methyl Oleate oil. This is because the Soybean oil has a higher speed of sound than Methyl Oleate. The proposed sensor has higher performance than many previously reported PnC sensors. Also, it can be used to determine different types of biodiesel fuels.

Acoustic diamond resonators with ultrasmall mode volumes

Quantum acoustodynamics (QAD) is a rapidly developing field of research, offering possibilities to realize and study macroscopic quantum-mechanical systems in a new range of frequencies, and implement transducers and new types of memories for hybrid quantum devices. Here we propose a novel design for a versatile diamond QAD cavity operating at GHz frequencies, exhibiting effective mode volumes of about $10^{-4}\lambda^3$. Our phononic crystal waveguide cavity implements a non-resonant analogue of the optical lightning-rod effect to localize the energy of an acoustic mode into a deeply-subwavelength volume. We demonstrate that this confinement can readily enhance the orbit-strain interaction with embedded nitrogen-vacancy (NV) centres towards the high-cooperativity regime, and enable efficient resonant cooling of the acoustic vibrations towards the ground state using a single NV. This architecture can be readily translated towards setup with multiple cavities in one- or two-dimensional phononic crystals, and the underlying non-resonant localization mechanism will pave the way to further enhance optoacoustic coupling in phoxonic crystal cavities.

Evaluation of second order optomechanical coupling strength in photonic crystal cavities including the case of degenerated modes

This paper presents the potentialities of the perturbation method to provide physical interpretations of optomechanical coupling in a simultaneous photonic and phononic crystal cavity. The classical perturbation method as applied to photonic modes is recalled. The method is then extended to the degenerated modes including second order perturbation. The method ends with semi-analytical expressions for the first and second order correction terms. These semi-analytical expressions enable, on the basis of symmetry criteria, to analyze and/or predict the modulation behaviors and ultimately lead to design rules. Special attention is given to the case of degenerated optical modes and the event of degeneracy lifting is also analyzed. In order to illustrate this method, we use the simplest example of an L1 cavity: a missing hole in a square lattice. This structure displays a miscellaneous situation exhibiting interesting behaviors that may be exploited to clearly highlight the versatility of the perturbation method. We select two cases: one where the first order is dominant and practically hides the second order behavior whatever the modes are degenerated or not; the other where the first order correction vanishes in the case of non-degenerate modes, resulting in a second order behavior, but in the case of degenerate modes, both first and second orders express themselves.

Superconducting circuit quantum computing with nanomechanical resonators as storage

We analyze the quantum information processing capability of a superconducting transmon circuit used to mediate interactions between quantum information stored in a collection of phononic crystal cavity resonators. Having only a single processing element to be controlled externally makes this approach significantly less hardware-intensive than traditional architectures with individual control of each qubit. Moreover, when compared with the commonly considered alternative approach using coplanar waveguide or 3d cavity microwave resonators for storage, the nanomechanical resonators offer both very long lifetime and small size—two conflicting requirements for microwave resonators. A detailed gate error analysis leads to an optimal value for the qubit-resonator coupling rate as a function of the number of mechanical resonators in the system. For a given set of system parameters, a specific amount of coupling and number of resonators is found to optimize the quantum volume, an approximate measure for the computational capacity of a system. We see this volume is higher in the proposed hybrid nanomechanical architecture than in the competing on-chip electromagnetic approach.

Coupling a Superconducting Quantum Circuit to a Phononic Crystal Defect Cavity

Connecting nanoscale mechanical resonators to microwave quantum circuits opens new avenues for storing, processing, and transmitting quantum information. In this work, we couple a phononic crystal cavity to a tunable superconducting quantum circuit. By fabricating a one-dimensional periodic pattern in a thin film of lithium niobate and introducing a defect in this artificial lattice, we localize a 6 gigahertz acoustic resonance to a wavelength-scale volume of less than one cubic micron. The strong piezoelectricity of lithium niobate efficiently couples the localized vibrations to the electric field of a widely tunable high-impedance Josephson junction array resonator. We measure a direct phonon-photon coupling rate $g/2\pi \approx 1.6 \, \mathrm{MHz}$ and a mechanical quality factor $Q_\mathrm{m} \approx 3 \times 10^4$ leading to a cooperativity $C\sim 4$ when the two modes are tuned into resonance. Our work has direct application to engineering hybrid quantum systems for microwave-to-optical conversion as well as emerging architectures for quantum information processing.

Enhanced directional acoustic sensing with phononic crystal cavity resonance

This letter reports a phononic crystal (PnC) cavity resonance device to realize an enhanced directional acoustic sensing. The acoustic cavity in the PnC device is designed with a line defect produced by replacing a line array from a perfect PnC. The line-defect PnC will make a defect band related to the cavity resonance within the perfect PnC band gap range. The design enhances the input sound wave at the resonance frequency of the acoustic cavity under the normal incidence, which produces an enhanced direction-sensitive response. The proposed device shows desirable directional acoustic sensing property, and the sensing frequency can be decreased by enlarging the effective refractive index of the acoustic cavity. The PnC cavity resonance devices present broad application prospects in weak signal detection and sound source localization.

Enhanced photoelastic modulation in silica phononic crystal cavities

The enhanced photoelastic modulation in quasi-one-dimensional (1D) phononic crystal (PnC) cavities made of fused silica is experimentally demonstrated. A confined acoustic wave in the cavity can induce a large birefringence through the photoelastic effect and enable larger optical modulation amplitude at the same acoustic power. We observe a phase retardation of ∼26 mrad of light passing through the cavity when the exciting acoustic frequency is tuned to the cavity mode resonance of ∼500 kHz at 2.5 V. In the present experiment, a 16-fold enhancement of retardation in the PnC cavity is demonstrated compared with that in a bar-shaped silica structure. Spatially resolved optical retardation measurement reveals that the large retardation is realized only around the cavity reflecting the localized nature of the acoustic cavity mode. The enhanced interactions between acoustic waves and light can be utilized to improve the performance of acousto-optic devices such as photoelastic modulators.

Miniature disposable phononic crystal biosensors

We introduce concept and first realizations of a disposable phononic crystal sensor, dedicated to point-of-care applications. Home tests, screening at a physician’s office or decentralized hospital tests require a disposable element filled with liquid analytes like blood or urine. The application of ultrasound leads to the advantage that speed of sound is sensitive to molecular shape, hydration or type of interaction potentials between mixture components. This provides reliable access to sensor specificity. The deviations however are rather small and require measurement at high resolution. The phononic crystal sensor concept applies the idea of liquid cavity resonance which can be realized with planar or cylindrical 2D or fully 3D phononic crystals containing the analyte in at least one element. High-Q resonance virtually extends the interaction path of the probing acoustic signal with the analyte. The specific challenge of a miniature disposable phononic crystal liquid cavity resonator is two-fold: First to find designs with high concentration of acoustic energy of a longitudinal mode in the cavity, and second to utilize a fabrication technology which meets the requirements in terms of materials, geometry, and prize. We use numerical models for design optimization and investigate high-resolution 3D printing as rapid, low-cost fabrication method.