Rare Events Detected with a Bulk Acoustic Wave High Frequency Gravitational Wave Antenna.

This work describes the operation of a high frequency gravitational wave detector based on a cryogenic bulk acoustic wave cavity and reports observation of rare events during 153 days of operation over two separate experimental runs (run 1 and run 2). In both run 1 and run 2, two modes were simultaneously monitored. Across both runs, the third overtone of the fast shear mode (3B) operating at 5.506 MHz was monitored; whereas in run 1, the second mode was chosen to be the fifth overtone of the slow shear mode (5C) operating at 8.392 MHz. However, in run 2, the second mode was selected to be closer in frequency to the first mode; and it was chosen to be the third overtone of the slow shear mode (3C) operating at 4.993 MHz. Two strong events were observed as transients responding to energy deposition within acoustic modes of the cavity. The first event occurred during run 1 on 12 May 2019 (UTC), and it was observed in the 5.506 MHz mode; whereas the second mode at 8.392 MHz observed no event. During run 2, a second event occurred on 27 November 2019 (UTC) and was observed by both modes. Timings of the events were checked against available environmental observations as well as data from other detectors. Various possibilities explaining the origins of the events are discussed.

Measurement of the refractive index at cryogenic temperature of absorptive silver thin films used as reflectors in a Fabry-Perot cavity.

Data on the refractive index of silver thin films are scarce in the literature, and largely dependent on both the deposition method and thickness. We measure the refractive index of silver films at cryogenic temperature with a technique that takes advantage of the absorption of the films and the corresponding peculiar properties of Fabry-Perot cavities: a frequency shift between the reflection and transmission peaks, together with a modified cavity bandwidth. We demonstrate a decrease in the real value of the refractive index, together with a decrease in its imaginary value at 4 K.

Influence of flicker noise and nonlinearity on the frequency spectrum of spin torque nano-oscillators.

The correlation of phase fluctuations in any type of oscillator fundamentally defines its spectral shape. However, in nonlinear oscillators, such as spin torque nano-oscillators, the frequency spectrum can become particularly complex. This is specifically true when not only considering thermal but also colored 1/f flicker noise processes, which are crucial in the context of the oscillator's long term stability. In this study, we address the frequency spectrum of spin torque oscillators in the regime of large-amplitude steady oscillations experimentally and as well theoretically. We particularly take both thermal and flicker noise into account. We perform a series of measurements of the phase noise and the spectrum on spin torque vortex oscillators, notably varying the measurement time duration. Furthermore, we develop the modelling of thermal and flicker noise in Thiele equation based simulations. We also derive the complete phase variance in the framework of the nonlinear auto-oscillator theory and deduce the actual frequency spectrum. We investigate its dependence on the measurement time duration and compare with the experimental results. Long term stability is important in several of the recent applicative developments of spin torque oscillators. This study brings some insights on how to better address this issue.

Mitigation of Temperature-Induced Light-Shift Effects in Miniaturized Atomic Clocks.

The demonstration of miniature atomic clocks (MACs) based on coherent population trapping (CPT) with improved mid- and long-term frequency stability benefits from the implementation of additional stabilization loops to reduce temperature-induced light-shift effects. In this article, we report and highlight the individual and combined benefits of such servo loops on the frequency stability of a CPT-based MAC. The first loop stabilizes the actual temperature of the vertical-cavity surface-emitting laser (VCSEL) chip using a compensation method in which the reading of external temperature variations is derived from the atomic vapor output signal. The second loop maintains the total microwave power absorbed by the laser to a value that maximizes the optical absorption and significantly reduces the laser power dependence of the clock frequency. Experimental tests are performed onto a miniaturized CPT-clock physics package using a chip-VCSEL tuned on the Cs D1 line ( λ = 895 nm). The VCSEL temperature compensation technique improves, by a factor of 4, the Allan deviation of the clock at 104 s. The simultaneous operation of both servo loops improves, by a factor of 7, the clock fractional frequency stability at 104 s. The clock demonstrates a fractional frequency stability of 7.5×10 -11 at 1 s and better than 2×10-11 at 1 day.

Frequency-Temperature Compensated Cuts of Crystalline-Quartz Acoustic Cavity Within the Cryogenic Range [4 K, 15 K].

New temperature coefficients of quartz elastic coefficients particularly relevant at liquid-helium temperature have been reported recently. Based on this result, frequency-temperature compensated cuts are predicted by calculation and then demonstrated by experiment. Such compensated cuts can definitely fix the issue of remaining temperature sensitivity of crystalline-quartz acoustic cavities unbeatable for their extremely low mechanical loss, as low as $10^{-9}$ , when operated at liquid-He temperature.

A new method of probing mechanical losses of coatings at cryogenic temperatures.

A new method of probing mechanical losses and comparing the corresponding deposition processes of metallic and dielectric coatings in 1-100 MHz frequency range and cryogenic temperatures is presented. The method is based on the use of high-quality quartz acoustic cavities whose internal losses are orders of magnitude lower than any available coating nowadays. The approach is demonstrated for chromium, chromium/gold, and multilayer tantala/silica coatings. The Ta2O5/SiO2 coating has been found to exhibit a loss angle lower than 1.6 × 10-5 near 30 MHz at 4 K. The results are compared to the previous measurements.

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.

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.

Observation of Rayleigh phonon scattering through excitation of extremely high overtones in low-loss cryogenic acoustic cavities for hybrid quantum systems.

The confinement of high frequency phonons approaching 1 GHz is demonstrated in phonon-trapping acoustic cavities at cryogenic temperatures using a low-coupled network approach. The frequency range is extended by nearly an order of magnitude, with excitation at greater than the 200th overtone achieved for the first time. Such a high frequency operation reveals Rayleigh-type phonon scattering losses due to highly diluted lattice impurities and corresponding glasslike behavior, with a maximum Q(L)×f product of 8.6×10(17) at 3.8 K and 4×10(17) at 15 mK. This suggests a limit on the Q×f product due to unavoidable crystal disorder. Operation at 15 mK is high enough in frequency that the average phonon occupation number is less than unity, with a loaded quality factor above half a billion. This work represents significant progress towards the utilization of such acoustic cavities for hybrid quantum systems.

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 · 10(18) 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.

Computation method for the short-term stability of quartz crystal resonators obtained from passive phase noise measures.

The amplitude-frequency effect is a well-known phenomenon in quartz crystal resonators. It can distort the results of short-term stability measurements. In our case, results are computed from phase noise measurements in passive bridge systems. This article presents a method to correct computation of short-term stability from passive measurements.

A high-performance frequency stability compact CPT clock based on a Cs-Ne microcell.

This paper reports on a compact table-top Cs clock based on coherent population trapping (CPT) with advanced frequency stability performance. The heart of the clock is a single buffer gas Cs-Ne microfabricated cell. Using a distributed feedback (DFB) laser resonant with the Cs D1 line, the contrast of the CPT signal is found to be maximized around 80°C, a value for which the temperature dependence of the Cs clock frequency is canceled. Advanced techniques are implemented to actively stabilize the clock operation on a zero-light-shift point. The clock frequency stability is measured to be 3.8 × 10(-11) at 1 s and well below 10(-11) until 50,000 s. These results demonstrate the possibility to develop high-performance chip-scale atomic clocks using vapor cells containing a single buffer gas.

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.

Oscillator frequency stability improvement by means of negative feedback.

A novel, simple method is proposed to increase the frequency stability of an oscillator. An additional negative feedback is used in combination with the positive loop of the harmonic oscillator to decrease the phase sensitivity to fluctuations of parameters other than the resonator. The main advantage of the proposed correction approach is that it does not require expensive external elements such as mixers or resonators. The validity of the method is theoretically demonstrated on a Colpitts oscillator using the control system theory approach and numerical simulations, and is experimentally verified with phase noise measurements of an actual oscillator-mockup. It is shown that the medium-term frequency stability can be easily improved by a factor of ten.

Parametric model of the BAW resonator phase-noise.

Excepted for the very short terms the frequency stability of ultra-stable oscillators is mainly limited by the resonator noise. In this work we proposed a parametric model of the bulk acoustic wave (BAW) resonator phase noise based on an equivalent circuit. This model explains phase noise generated by a BAW crystal from a point of view of parametric fluctuations and proves the f(-1) dependences of the crystal noise. The model performance is verified with simulation. Simulation results are compared to experimental data and discussed. Comparison of three existing models is made.

Precision close-to-carrier phase noise simulation of BAW oscillators.

Based on a commercial simulation tool, the influence of BAW resonator noise on the resulting oscillator phase noise is revisited. The parametric model of the resonator uses experimental data, and includes an f(-2) noise not often considered in measurements, in addition to its flicker noise.

Investigations on LGS and LGT crystals to realize BAW resonators.

The LGS family are promising materials for the design of high quality bulk acoustic wave resonators. We have manufactured many plano-convex 10 MHz 5th overtone Y-cut resonators using langasite (LGS, La(3)Ga(5)SiO(14)) and langatate (LGT, La(3)Ga(5.5)Ta(0.5)O(14)) crystals. We observed that the quality factor strongly depends on the polishing method, the supplier of the material, and on the energy trapping. For quartz crystals, we have found that resulting IR spectra exhibit absorption peaks more or less deep, linked to defects. These predominant criteria are not surprising, but they have to be defined in manner similar to that used for quartz crystal. A satisfying machining and polishing method has been first applied to elaborate high Q resonators, and a comparison between samples of LGS and LGT materials from different suppliers is established. In addition, LGT resonators are characterized by their motional parameters and frequency-temperature curves. Nevertheless, one of the main results is that the measured Q x f product is not the expected one. We present results of Q-factor versus radius of curvature: it appears that an optimization should be performed and that this last one cannot be directly transposed from that of quartz crystal resonator. Currently, the best resonator that we have made has a Q x f product of 1.4 x 10(13) on its 5th overtone (1.7 x 10(13) on its 9th overtone). This result is slightly higher than the similar parameter obtained on a state-of-the-art SC-cut quartz crystal resonator working at the same frequency.

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 10(6), 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(-12).

Predicting phase noise in crystal oscillators.

In order to predict the phase noise in crystal oscillators an enhanced phase-noise model has been built. With this model, the power spectral densities of phase fluctuations can be computed in different points of the oscillator loop. They are calculated from their correlation functions. The resonator-caused noise as well as the amplifier-caused noise are taken into account and distinguished. To validate this enhanced model, the behavior of a batch of 10 MHz quartz crystal oscillators is observed and analyzed. The tested batch has been chosen in a facility production. Their associated resonators have been selected according to the value of their resonant frequency and their motional resistance. Open-loop and closed-loop measurements are given. The phase noise of the overall oscillator working in closed loop is provided by the usual active method. Theoretical and experimental results are compared and discussed.

New phase-noise model for crystal oscillators: application to the Clapp oscillator.

Leeson's is the basic model for predicting oscillator noise. A mathematical analysis of this "heuristic" model has been proposed. Both models do not detail the relative importance of the amplifier transfer function associated to its own noise with regard to that of the resonator. In this paper, an improved version of those previous models is presented. The phase noise generated by the amplifier and the one generated by the resonator are differentiated without considering their origins, such as the conversion of amplitude modulation noise into phase modulation noise. The power spectral densities of phase noise at various points of the oscillator loop are calculated from their respective correlation functions. As a consequence, the influence of the inner amplifier and resonator noises on the resulting oscillator noise is predictable. The model is especially attractive to the makers of widely used quartz oscillators. The resulting oscillator noise is easily obtained from the oscillator open-loop noise. An example of the phase-noise modeling of the Clapp quartz crystal oscillator is simulated and discussed.