Ultra-stable Resonators Research Articles

Carrier suppression system to measure phase noise of acoustic resonators with low motional resistance

A carrier suppression system is implemented in order to measure the phase noise of acoustic resonators that have a low motional resistance. A special adapters' system using transformers is proposed to improve the loaded quality factor of the resonators. With this developed device and described protocol, the inherent noise of resonators can be obtained without the usual electronical oscillator conditioning that could take part in the results. The loaded quality factor is improved from about 10% to 60% of the intrinsic quality factor. As an example, the system is used to study Langatate crystal resonators vibrating at 10 MHz. Langatate crystals can be an alternative to substitute for the quartz crystal resonators for frequency and time applications. Their coupling coefficient and the product quality factor-frequency are normally higher than those in quartz crystal resonators. For ultrastable resonators, the motional resistance obtained with Langatate crystals is about five times lower than that for the quartz crystal; it can reach typically few ohms. These resonators have been characterized in terms of impedance, Q-factors, turnover temperature, amplitude-frequency effect, and phase noise. The short-term stability of these resonators is given in terms of Allan standard deviation. The influence of the driving power is presented.

Characterizations of the nonlinear optical properties for (010) and (2¯01) beta-phase gallium oxide.

We report, for the first time, the characterizations on optical nonlinearities of beta-phase gallium oxide (β-Ga2O3), where both (010) β-Ga2O3 and (2¯01) β-Ga2O3 were examined for two-photon absorption coefficient, Kerr nonlinear refractive index, and their polarization dependence. The wavelength dependence of two-photo absorption coefficient and Kerr nonlinear refractive index were also estimated by a widely used analytical model. β-Ga2O3 exhibits a two photon absorption (TPA) coefficient of 1.2 cm/GW for (010) β-Ga2O3 and 0.6 cm/GW for (2¯01) β-Ga2O3. The Kerr nonlinear refractive index is -2.1 × 10-15 cm2/W for (010) β-Ga2O3 and -2.9 × 10-15 cm2/W for (2¯01) β-Ga2O3. In addition, β-Ga2O3 shows stronger in-plane nonlinear optical anisotropy on (2¯01) plane than on (010) plane. Compared with GaN, TPA coefficient of β-Ga2O3 is 20 times smaller, and the Kerr nonlinear refractive index of β-Ga2O3 is also found to be 4-5 times smaller. These results indicate that β-Ga2O3 have the potential for ultra-low loss waveguides and ultra-stable resonators and integrated photonics, especially in UV and visible wavelength spectral range.

Reply to the Comment on: The quantum vacuum as the origin of the speed of light

We reply to the comment by Schiller on our paper “The quantum vacuum as the origin of the speed of light” [M. Urban et al., Eur. Phys. J. D 67, 58 (2013)]. We further detail our model and explain why the limits provided by ultra-stable optical cavities on the amplitude of fluctuations of the light speed do not apply to the predictions on group velocity that we gave in [M. Urban et al., Eur. Phys. J. D 67, 58 (2013)]. We then estimate the magnitude of phase velocity fluctuations expected in our model, showing that they are much smaller than those of the group velocity, and hence, well below the best present limits obtained either with ultra-stable resonators or large interferometers.

Frequency stability measurements of ultrastable BVA resonators and oscillators

The performances of instruments developed for the measurement of 5 MHz ultra-stable resonators, before and after being integrated in an oscillator, are presented. The chosen resonator has an estimated stability of several 10 -14 . The intrinsic noise floor of these benches are about 7 to 9.5 10 -15 .