Cryogenic Sapphire Oscillator using a low-vibration design pulse-tube cryocooler: First results

A Cryogenic Sapphire Oscillator has been implemented at 11.2 GHz using a low-vibration design pulse-tube cryocooler. Compared with a state-of-the-art liquid helium cooled CSO in the same laboratory, the square root Allan variance of their combined fractional frequency instability is $\sigma_y = 1.4 \times 10^{-15}\tau^{-1/2}$ for integration times $1 < \tau < 10$ s, dominated by white frequency noise. The minimum $\sigma_y = 5.3 \times 10^{-16}$ for the two oscillators was reached at $\tau = 20$ s. Assuming equal contributions from both CSOs, the single oscillator phase noise $S_{\phi} \approx -96 \; dB \; rad^2/Hz$ at 1 Hz offset from the carrier.Comment: 5 pages, 5 figures, accepted in IEEE Trans on Ultrasonics, Ferroelectrics and Frequency Contro

Single Crystal Sapphire at milli-Kelvin Temperatures: Observation of Electromagnetically Induced Thermal Bistability in High Q-factor Whispering Gallery Modes

Resonance modes in single crystal sapphire ($\alpha$-Al$_2$O$_3$) exhibit extremely high electrical and mechanical Q-factors ($\approx 10^9$ at 4K), which are important characteristics for electromechanical experiments at the quantum limit. We report the first cooldown of a bulk sapphire sample below superfluid liquid helium temperature (1.6K) to as low as 25mK. The electromagnetic properties were characterised at microwave frequencies, and we report the first observation of electromagnetically induced thermal bistability in whispering gallery modes due to the material $T^3$ dependence on thermal conductivity and the ultra-low dielectric loss tangent. We identify "magic temperatures" between 80 to 2100 mK, the lowest ever measured, at which the onset of bistability is suppressed and the frequency-temperature dependence is annulled. These phenomena at low temperatures make sapphire suitable for quantum metrology and ultra-stable clock applications, including the possible realization of the first quantum limited sapphire clock.Comment: 5 pages, 4 figure

Discovery of Bragg confined hybrid modes with high Q-factor in a hollow dielectric resonator

The authors report on observation of Bragg confined mode in a hollow cylindrical dielectric cavity. A resonance was observed at 13.4 $GHz$ with an unloaded Q-factor of order $2\times10^5$, which is more than a factor of 6 above the dielectric loss limit. Previously such modes have only been realized from pure Transverse Electric modes with no azimuthal variations and only the $E_{\phi}$ component. From rigorous numeric simulations it is shown that the mode is a hybrid mode with non-zero azimuthal variations and with dominant $E_r$ and $E_{\phi}$ electric field components and $H_z$ magnetic field component.Comment: Accepted to be published in Applied Physics Letter

Detrapping and retrapping of free carriers in nominally pure single crystal GaP, GaAs and 4H-SiC semiconductors under light illumination at cryogenic temperatures

We report on extremely sensitive measurements of changes in the microwave properties of high purity non-intentionally-doped single-crystal semiconductor samples of gallium phosphide, gallium arsenide and 4H-silicon carbide when illuminated with light of different wavelengths at cryogenic temperatures. Whispering gallery modes were excited in the semiconductors whilst they were cooled on the coldfinger of a single-stage cryocooler and their frequencies and Q-factors measured under light and dark conditions. With these materials, the whispering gallery mode technique is able to resolve changes of a few parts per million in the permittivity and the microwave losses as compared with those measured in darkness. A phenomenological model is proposed to explain the observed changes, which result not from direct valence to conduction band transitions but from detrapping and retrapping of carriers from impurity/defect sites with ionization energies that lay in the semiconductor band gap. Detrapping and retrapping relaxation times have been evaluated from comparison with measured data.Comment: 7 pages, 6 figure

Hyperparametric effects in a whispering-gallery mode rutile dielectric resonator at liquid helium temperatures

We report the first observation of low power drive level sensitivity, hyperparametric amplification, and single-mode hyperparametric oscillations in a dielectric rutile whispering-gallery mode resonator at 4.2 K. The latter gives rise to a comb of sidebands at 19.756 GHz. Whereas, most frequency combs in the literature have been observed in optical systems using an ensemble of equally spaced modes in microresonators or fibers, the present work represents generation of a frequency comb using only a single-mode. The experimental observations are explained by an additional 1/2 degree-of-freedom originating from an intrinsic material nonlinearity at optical frequencies, which affects the microwave properties due to the extremely low loss of rutile. Using a model based on lumped circuits, we demonstrate that the resonance between the photonic and material 1/2 degree-of-freedom, is responsible for the hyperparametric energy transfer in the system.Comment: 9 pages, 10 figure

Low-loss Materials for high Q-factor Bragg Reflector Resonators

A Bragg resonator uses dielectric plates within a metallic cavity to confine the energy within a central free space region. The importance of the permittivity is shown with a better Q-factor possible using higher permittivity materials of larger intrinsic dielectric losses. This is because the electric energy in the reflectors decreases proportionally to the square root of permittivity and the coupling to the metallic losses decrease linearly. In a sapphire resonator with a single reflector pair a Q-factor of 2.34x10^5 is obtained, which may be improved on by up to a factor of 2 using higher permittivity materials