Quartz Bulk Acoustic Wave Resonators Research Articles

The multi-mode acoustic gravitational wave experiment: MAGE

The Multi-mode Acoustic Gravitational wave Experiment (MAGE) is a high frequency gravitational wave detection experiment. In its first stage, the experiment features two near-identical quartz bulk acoustic wave resonators that act as strain antennas with spectral sensitivity as low as 6.6 × 10−21 [strain]/Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\ ext {Hz}}$$\\end{document} in multiple narrow bands across MHz frequencies. MAGE is the successor to the initial path-finding experiments; GEN 1 and GEN 2. These precursor runs demonstrated the successful use of the technology, employing a single quartz gravitational wave detector that found significantly strong and rare transient features. As the next step to this initial experiment, MAGE will employ further systematic rejection strategies by adding an additional quartz detector such that localised strains incident on just a single detector can be identified. The primary goals of MAGE will be to target signatures arising from objects and/or particles beyond that of the standard model, as well as identifying the source of the rare events seen in the predecessor experiment. The experimental set-up, current status and future directions for MAGE are discussed. Calibration procedures of the detector and signal amplification chain are presented. The sensitivity of MAGE to gravitational waves is estimated from knowledge of the quartz resonators. Finally, MAGE is assembled and tested in order to determine the thermal state of its new components.

Electro-mechanical tuning of high-Q bulk acoustic phonon modes at cryogenic temperatures

We investigate the electromechanical properties of quartz bulk acoustic wave resonators at extreme cryogenic temperatures. By applying a DC bias voltage, we demonstrate broad frequency tuning of high-Q phonon modes in a quartz bulk acoustic wave cavity at cryogenic temperatures of 4 K and 20 mK. More than 100 line-widths of tuning of the resonance peak without any degradation in loaded quality factor, which are as high as 1.73×109, is seen for high order overtone modes. For all modes and temperatures, the observed coefficient of frequency tuning is ≈ 3.5 mHz/V per overtone number n corresponding to a maximum of 255.5 mHz/V for the n = 73 overtone mode. No degradation in the quality factor is observed for any value of an applied biasing field.

Generation of coherent phonons via a cavity enhanced photonic lambda scheme

We demonstrate the generation of coherent phonons in a quartz bulk acoustic wave (BAW) resonator through the photoelastic properties of the crystal, via coupling to a microwave cavity enhanced by a photonic lambda scheme. This is achieved by imbedding a single crystal BAW resonator between the post and the adjacent wall of a microwave re-entrant cavity resonator. This 3D photonic lumped LC resonator at the same time acts as the electrode of a BAW phonon resonator and allows the direct readout of coherent phonons via the linear piezoelectric response of the quartz. A microwave pump, ωp, is tuned to the cavity resonance ω0, while a probe frequency, ωprobe, is detuned and varied around the red and blue detuned values with respect to the BAW phonon frequency, Ωm. The pump and probe power dependence of the generated phonons unequivocally determines the process to be electrostrictive, with the phonons produced at the difference frequency between the pump and the probe, with no back action effects involved. Thus, the phonons are created without threshold and can be considered analogous to a passive coherent population trapped maser scheme.

Observation of low-temperature magnetomechanic effects in crystalline resonant phonon cavities

We observe magnetic effects in ultra-high quality factor crystalline quartz Bulk Acoustic Wave resonators at milli-Kelvin temperature. The study reveals existence of hysteresis loops, jumps and memory effects of acoustical resonance frequencies. These loops arise as a response to the external magnetic field and span over few Hertz range for modes with linewidths of about $25$mHz, which constitute a frequency shift of order 60 linewidths. The effects are broadband but get stronger towards higher frequencies where both nonlinear effects and losses are limited by two level systems. This suggests that the observed effects are due to ferromagnet-like phase of a spin ensemble coupled to mechanical modes. The observed coupling between mechanical and spin degrees of freedom in the ultra low loss regime brings new possibilities for the emerging class of quantum hybrid systems.

Piezo-optomechanical coupling of a 3D microwave resonator to a bulk acoustic wave crystalline resonator

We report the observation of coupling between a 3D microwave cavity mode and a bulk mechanical resonator mediated by piezoelectric and radiation pressure effects. The system is composed of a quartz bulk acoustic wave resonator placed inside a microwave re-entrant cavity, which is designed to act as both the electrodes for piezoelectric actuation and a 3D resonator. The cavity electromagnetic mode is modulated by a 5 MHz bulk acoustic wave shear mode, which is modeled and experimentally verified using the input-output formalism. Through finite element method simulations, we calculate the various contributions to the electromechanical coupling and discuss the potential of the system to reach high cooperativities as well as suitable applications.

Testing the generalized uncertainty principle with macroscopic mechanical oscillators and pendulums

Recent progress in observing and manipulating mechanical oscillators at quantum regime provides new opportunities of studying fundamental physics, for example, to search for low energy signatures of quantum gravity. For example, it was recently proposed that such devices can be used to test quantum gravity effects, by detecting the change in the [x,p] commutation relation that could result from quantum gravity corrections. We show that such a correction results in a dependence of a resonant frequency of a mechanical oscillator on its amplitude, which is known as amplitude-frequency effect. By implementing this new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q sapphire split-bar mechanical resonator and for 10 mg quartz bulk acoustic wave resonator. Our experiments with sapphire resonator have established the upper limit on quantum gravity correction constant for $\beta_0<5 \times10^6$ which is a factor of 6 better than previously detected. The reasonable estimates of $\beta_0$ from experiments with quartz resonators yield an even more stringent limit of $4\times10^4$. The data sets of 1936 measurement of physical pendulum period by Atkinson results in significantly stronger limitations on $\beta_0 \ll 1$. Yet, due to the lack of proper pendulum frequency stability measurement in these experiments, the exact upper bound on $\beta_0$ can not be reliably established. Moreover, pendulum based systems only allow testing a specific form of the modified commutator that depends on the mean value of momentum. The electro-mechanical oscillators to the contrary enable testing of any form of generalized uncertainty principle directly due to much higher stability and a higher degree of control.

Experimental Studies in Micromachined AT-Cut Quartz-Based Differential Vacuum Gauges

In this paper, a micromachined differential pressure sensor based on force frequency effect in AT-cut quartz bulk acoustic wave resonators for vacuum measurements is presented. The frequency shift arising from the stresses generated in the quartz due to force application is known as the force frequency effect. Pressure is sensed by monitoring the shifts in the thickness shear mode resonance frequency of AT-cut quartz resonator due to the application of differential pressure across the micromachined quartz diaphragm. The sensors exhibit a large dynamic range of 1 mTorr–100 Torr with a resolution of ~1 mTorr (in the medium vacuum regime). A parametric study has also been carried out to study the effect of resonator thickness and diameter on sensitivity. It was found that the sensor’s response to pressure is extremely sensitive to mechanical boundary conditions, which results in performance characteristics such as dependence on the direction of the applied pressure and unexpected scaling with the diaphragm radius.

Inducing Strong Non-Linearities in a Phonon Trapping Quartz Bulk Acoustic Wave Resonator Coupled to a Superconducting Quantum Interference Device

A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10 18 Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID) amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime.

Hybrid quantum systems with trapped charged particles

We study theoretically the possibilities of coupling the quantum mechanical motion of a trapped charged particle (e.g. ion or electron) to quantum degrees of freedom of superconducting devices, nano-mechanical resonators and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e. the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples, using parameters that are experimentally attainable in the foreseeable future. We conclude that those hybrid quantum system considered involving an atomic ion are unfavorable, compared to using an electron, since the coupling rates between the charged particle and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates which significantly exceed decoherence rates. Moreover it might have appealing properties such as fast entangling gates, long coherence and flexible electron interconnectivity topology. Realizing such a system, however, is technologically challenging, since it requires accommodating both trapping technology and superconducting circuitry in a compatible manner. We review some of the challenges involved, such as the required trap parameters, electron sources, electrical circuitry and cooling schemes in order to promote further investigations towards the realization of such a hybrid system.

Extremely low-loss acoustic phonons in a quartz bulk acoustic wave resonator at millikelvin temperature

Low-loss, high frequency acoustic resonators cooled to millikelvin temperatures are a topic of great interest for application to hybrid quantum systems. When cooled to 20 mK, we show that resonant acoustic phonon modes in a bulk acoustic wave quartz resonator demonstrate exceptionally low loss (with Q-factors of order billions) at frequencies of 15.6 and 65.4 MHz, with a maximum f · Q product of 7.8 × 1016 Hz. Given this result, we show that the Q-factor in such devices near the quantum ground state can be four orders of magnitude better than previously attained. Such resonators possess the low losses crucial for electromagnetic cooling to the phonon ground state, and the possibility of long coherence and interaction times of a few seconds, allowing multiple quantum gate operations.

Study of Adsorption of Globular Proteins on Hydrophobic Surfaces

In this paper, we use micromachined, high-frequency, quartz bulk acoustic wave resonators to systematically study the physical and viscoelastic properties of spontaneously adsorbed globular protein films with molecular weights (MWs) spanning three decades on hydrophobic surfaces. Specifically, changes in the frequency and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -factor of the micromachined resonator array were studied as a function of concentration for five proteins, namely human serum albumin (HSA), immunoglobulin G (IgG), human fibrinogen (Fib), alpha-2-macroglobulin (AMG), and immunoglobulin M (IgM) at the fundamental and third resonance modes. The results obtained were interpreted using equivalent electrical impedance models for the multilayer stack on the quartz crystal microbalances surface. Discrete changes in the protein adsorption and the viscoelastic behavior with solution concentration were observed for all the five protein films. The spherical core-shell protein model is used to provide a simple explanation of the results. The work presents the first systematic and quantitative evaluation of the density, thickness, viscosity, and elastic modulus of adsorbed globular protein films and demonstrates the advantages of using micromachined high-frequency bulk acoustic wave resonators for obtaining these types of data.

Systematic studies on globular proteins using micromachined high frequency bulk acoustic wave resonators

In this paper we use micromachined, high-frequency, quartz bulk acoustic wave resonator arrays to evaluate the physical and viscoelastic properties of adsorbed globular protein films with molecular weights spanning two orders of magnitude. Specifically, changes in the frequency and the Q-factor of the micromachined resonator array were studied as a function of concentration for three proteins, namely Human Serum Albumin (HSA), Immunoglobulin G (IgG) and Human Fibrinogen (Fib) at the fundamental and third resonance modes. The results obtained are interpreted using continuum mechanics approach for multilayer stack on the QCM surface. Discrete changes in the protein adsorption rate constant and the viscoelastic behavior was observed for all the three protein films. The thickness, density, elastic modulus and viscosity of protein layer were successfully obtained through this analysis.

1/f frequency fluctuations in quartz acoustic resonators

The level of 1/f frequency fluctuations has been measured on numerous quartz surface acoustic wave resonators. When these results are combined with existing data for quartz bulk acoustic wave resonators it becomes clear that the 1/f process is essentially the same in both types of devices. Furthermore, the power spectral density of frequency fluctuations shows a clear power law dependence that is very close to 1/Q4u , where Qu is the unloaded Q. However, the observed dependence on loaded Q is weak.