Philippe Abbé

Extremely Low Loss Phonon-Trapping Cryogenic Acoustic Cavities for Future Physical Experiments

Low loss Bulk Acoustic Wave devices are considered from the point of view of the solid state approach as phonon-confining cavities. We demonstrate effective design of such acoustic cavities with phonon-trapping techniques exhibiting extremely high quality factors for trapped longitudinally-polarized phonons of various wavelengths. Quality factors of observed modes exceed 1 billion, with a maximum Q-factor of 8 billion and Q × f product of 1.6 · 1018 at liquid helium temperatures. Such high sensitivities allow analysis of intrinsic material losses in resonant phonon systems. Various mechanisms of phonon losses are discussed and estimated.

Losses in high quality quartz crystal resonators at cryogenic temperatures

Measurement of the mechanical losses of quartz crystal is a topic of interest for communities dealing with the gravitational wave detectors and also the time and frequency domain. About the latter, the authors describe Q-factor measurements of quartz crystal resonators at cryogenic temperatures under 10 K, thanks to a cryocooler-based experimental set-up. A Q-factor of 325 millions at 4 K, on the fifth overtone of the quasilongitudinal mode at 15.9 MHz, has been recorded. As shown, the acoustic wave trapping is suspected to limit the Landau–Rumer regime below 6 K [Landau and Rumer, Phys. Z. Sowjetunion 11, 18 (1937)].

Quartz resonator instabilities under cryogenic conditions

The phase noise of a quartz crystal resonator working at liquid helium temperatures is studied. Measurement methods and the device environment are explained. The phase noise is measured for different resonance modes, excitation levels, amount of operating time, device orientations in relation to the cryocooler vibration axis, and temperatures. Stability limits of a frequency source based on such devices are evaluated in the present measurement conditions. The sources of phase flicker and white noises are identified. Finally, the results are compared with previous works.

Recent investigations on BAW resonators at cryogenic temperatures

This work presents the results of investigations on different aspects of cryogenic operation of BAW resonators. For the quartz crystal resonators the losses mechanisms, the temperature sensitivity, the amplitude-frequency effect are described for liquid helium temperatures. The corresponding problems are discussed. To overcome some of these problems, the possible solution of operation at higher modes is considered. Some of these higher modes exhibit outstanding quality factors. The highest (for BAW resonators) quality factor value and quality factor-frequency product are measured for the 11th and 13th overtones respectively. In addition, two LGT resonators have been characterized in a wide temperature range. Finally, some preliminary results on utilization of cryogenic quartz resonators as a part of a frequency stabilization closed loop system are given.

Advances in development of quartz crystal oscillators at liquid helium temperatures

Abstract This work presents some recent results in the field of liquid helium bulk acoustic wave oscillators. The discussion covers the whole development procedure starting from component selection and characterisation and concluding with actual phase noise measurements. The associated problems and limitations are discussed. The unique features of obtained phase noise power spectral densities are explained with a proposed extension of the Leeson effect.

Thermal characterization of crystal ovens used in phase noise measurement system

In this paper, the thermal stability characterization of crystal ovens used in a phase noise measurement system of ultra-low noise crystal resonators is proposed. This bench is dedicated to test 5 MHz and 10 MHz crystal devices packaged in HC40 enclosures. New double ovens have been designed to improve the ultimate noise floor of our carrier suppression bench. A brief description of the temperature environment and processing are given. In addition, experiments to measure the thermal stability of the oven control are given. These new crystal ovens present an Allan standard deviation of about 2-10-15 at 1 s in terms of relative frequency fluctuations

Laser light routing in an elongated micromachined vapor cell with diffraction gratings for atomic clock applications.

This paper reports on an original architecture of microfabricated alkali vapor cell designed for miniature atomic clocks. The cell combines diffraction gratings with anisotropically etched single-crystalline silicon sidewalls to route a normally-incident beam in a cavity oriented along the substrate plane. Gratings have been specifically designed to diffract circularly polarized light in the first order, the latter having an angle of diffraction matching the (111) sidewalls orientation. Then, the length of the cavity where light interacts with alkali atoms can be extended. We demonstrate that a longer cell allows to reduce the beam diameter, while preserving the clock performances. As the cavity depth and the beam diameter are reduced, collimation can be performed in a tighter space. This solution relaxes the constraints on the device packaging and is suitable for wafer-level assembly. Several cells have been fabricated and characterized in a clock setup using coherent population trapping spectroscopy. The measured signals exhibit null power linewidths down to 2.23 kHz and high transmission contrasts up to 17%. A high contrast-to-linewidth ratio is found at a linewidth of 4.17 kHz and a contrast of 5.2% in a 7-mm-long cell despite a beam diameter reduced to 600 μm.

Development of a 10 MHz oscillator working with an LGT crystal resonator: Preliminary results

Presently, to our knowledge, measurement of the noise of langatate (LGT) crystal oscillators has not previously been reported. First results of such a measurement are given in this paper. They have been obtained from 10 MHz resonator prototypes tested with a dedicated electronics. The main steps of the resonator manufacturing are described in this paper. Good quality factors, close to 1.4 106, have already been achieved on the 5th overtone of the thickness shear mode of LGT Y cuts, even if the energy trapping should still be optimized. The motional parameters of these resonator prototypes are quite different from those of usual quartz crystal resonators. As a consequence, dedicated sustaining electronics have been designed. The explored options are reported to justify the implemented one. Moreover, the high thermal sensitivity of LGT crystal resonators (parabolic f-T curve) requires that particular attention be paid to the oven thermal stability. This important feature is also pointed out in the paper. The preliminary version of the resulting system exhibits a relative frequency stability of 6 10-2.

Quality Factor Measurements of Various Types of Quartz Crystal Resonators Operating Near 4 K

Quartz crystal resonators can exhibit huge quality factors (in excess of 1 billion) at liquid-helium temperature. However, they must satisfy a set of conditions to meet this high level of performance. With the help of experimentation, the main conditions are identified, such as the material quality, the energy trapping due to the vibrational mode structure, as well as the corresponding influence of the support mechanism and the effects of the electrodes.

Theoretical and experimental investigations of 1/f noise in quartz crystal resonators

Fluctuation dissipation theorem allows to recover a 1/f noise spectral density at low frequency. The level of this 1/f noise is governed by a single fitting parameter that can be connected to the onset frequency of this 1/f regime. It constitutes the fundamental intrinsic limit of quartz crystal. Some preliminary considerations on the physical origin of this parameter in terms of microscopic processes in the crystal are given. Experimentally, quartz crystal resonators have been cut from a quartz crystal block supplied specifically for this study on 1/f noise. The short-term stabilities of several resonators have been measured to be lower than 8-10-1. A comparison of these resonators is given and the results are discussed according to the position of the resonators inside the crystal block.