Temperature coefficients of crystalline-quartz elastic constants over the cryogenic range [4 K, 15 K]

This paper brings out results of a measurement campaign aiming to determine the temperature coefficients of synthetic quartz elastic constants at liquid helium temperature. The method is based on the relationship between the resonance frequencies of a quartz acoustic cavity and the elastic constants of the material. The temperature coefficients of the elastic constants are extracted from experimental frequency-temperature data collected from a set of resonators of various cut angles, because of the anisotropy of quartz, measured on the very useful cryogenic range [4 K - 15 K]. The knowledge of these temperature coefficients would allow to further design either quartz temperature sensors or conversely frequency-temperature compensated quartz cuts. With extremely low losses, lower than $10^{-9}$ for the best ones, key applications of such devices are ultra-low loss mechanical systems used in many research areas including frequency control and fundamental measurements. The Eulerian formalism is used in this study to identify the temperature coefficients.Comment: 6 pages,4 figure

Observation of Low Temperature Magneto-Mechanic 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

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 a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic $Q$-factors at low temperature, with $Q\times f$ products of order $10^{18}$ Hz. In this work we couple such a resonator to a 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

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 (BAW) 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$\times10^{16}$ 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

A very high speed method to simulate quartz crystal oscillator

International audienceIn this paper, we present the SHA method, a Symbolic Harmonic Analysis method to simulate the behaviour of ultrastable quartz crystal oscillators. This nonlinear method is aimed to compute very quickly the steady state as well as amplitude and frequency transients. The ultimate goal is to see instantaneously the influence of a parameter change on the oscillator's features thank to the computation speed. The method proposed here is a mixing of the nonlinear dipolar method previouly developed in our team and the harmonic method. It allows to replace the set of algebro-differential equation of the circuit by a nonlinear system of the Fourier coefficients of the circuit unknowns

Advanced bridge instrument for the measurement of the phase noise and of the short-term frequency stability of ultra-stable quartz resonators

High-stability quartz oscillators are needed in a number of space applications. A short-term stability of parts in 10^{-14} [Allan deviation σy(τ) ] is sometimes required, for integration time τ of approximately 1-10 s. The Centre National d'Etudes Spatiales (CNES) and the FEMTO-ST Institute (formerly LPMO and LCEP), have been collaborating for many years in this domain, aiming at measuring and at understanding the oscillator noise. The highest stability has been observed on 5 MHz and 10 MHz bulk acoustic-wave resonators. Yet this stability is still not sufficient, or the the manufacturing method is not reproducible. Recently, the analysis of a few premium-stability oscillators has demonstrated that the oscillator frequency instability is due to the fluctuation of the resonator natural frequency, rather than to the noise of the sustaining amplifier via the Leeson effect. It is therefore natural to give attention to the measurement of the resonator fluctuations

Bruit des oscillateurs et des résonateurs à quartz

Un des problèmes qui se posent au concepteur des oscillateurs à quartz de haute stabilité est le bruit propre des résonateurs. Nous effectuons tout d'abord une brève description des principaux mécanismes susceptibles d'affecter la stabilité des oscillateurs et des résonateurs à quartz. Ensuite sont explicitées les grandeurs mises en jeu dans la métrologie des fréquences : la densité spectrale de bruit de phase dans le domaine spectral et la variance d'Allan dans le domaine temporel. Enfin nous présentons l'instrumentation utilisée et développée pour la mesure du bruit des oscillateurs en général et des résonateurs en particulier

Operation of graphene-on-quartz acoustic cavity at cryogenic temperatures

This paper presents observation of mechanical effects of a graphene monolayer deposited on a quartz substrate designed to operate as an extremely low-loss acoustic cavity standard at liquid-helium temperature. Resonances of this state-of-the-art cavity are used to probe the mechanical loss of the graphene film, assessed to be about $80 \: 10^{-4}$ at 4K. Significant frequency shifts of positive and negative sign have been observed for many overtones of three modes of vibration. These shifts cannot be predicted by the mass-loading model widely used in the Quartz Microbalance community. Although thermo-mechanical stresses are expected in such a graphene-on-quartz composite device at low temperature due to a mismatch of expansion coefficients of both materials, it cannot fully recover the mismatch of the mass loading effect. Based on a force-frequency theory applied to the three thickness modes, to reconcile the experimental results, the mean stresses in the graphene monolayer should be of the order of 140 GPa, likely close to its tensile strength.Comment: Corrected typos. New Fig. Text improve

A Program to Analyse the Origin of Noise in Ultra- Stable Quartz Crystal Resonators

International audienceIn the mid 90s the quartz crystal oscillator attained a stability in the upper 10–14 (flicker floor of the Allan deviation σy(τ), which occurs at τ =1..10 s). As a matter of fact, the highest stability was obtained with bulk-acoustic-wave quartz crystal resonators at 5 MHz and at 10 MHz. Since, the research for higher stability seems to be at a standstill, while space applications are more and more demanding. Recently, the analysis of a few premium-stability oscillators has shown that the oscillator frequency instability is due to the fluctuation of the resonator natural frequency, rather than to the noise of the sustaining amplifier via the Leeson effect. It is therefore natural to give attention to the measurement of the resonator fluctuations. The Centre National d'Etudes Spatiales (CNES) and FEMTO-ST Institute have started a research program on the origin of noise in 5 MHz and 10 MHz quartz crystal resonators. Several European manufacturers of high-stability resonators and oscillators participate. This article reports on the present status and on the future plans of this program. The first part consists in the analysis of the sensitivity of selected resonators to various externally-controlled parameters, like temperature, drive power, load impedance, series capacitance. The second part, planned, consists of listing the possible causes of noise, and of modeling their effects on frequency stability. Tests and measurements are mainly performed on an advanced phase noise measurement system, recently set up for this program. Of course, this program is a unique opportunity to test various batches of 5 MHz and 10 MHz resonators provided by the industrial partners