Michael E. Tobar

Complex permittivity of some ultralow loss dielectric crystals at cryogenic temperatures

Whispering gallery modes were used for very accurate permittivity and dielectric loss measurements of ultralow loss isotropic and uniaxially anisotropic single crystals. Several materials including sapphire, YAG, quartz, and SrLaAlO4 were measured. The total absolute uncertainty in the real part of permittivity tensor components was estimated to be ±0.1%, limited principally by the uncertainty in sample dimensions. Imaginary parts of permittivities were measured with uncertainties of about 10%, limited by the accuracy of Q-factor measurements of whispering gallery modes. It has been observed that, for most crystals, dielectric losses can be approximated by a power function of absolute temperature only in limited temperature ranges. At temperatures between 4-50 K, losses are often affected by impurities, which are always present in real crystals.

Use of whispering-gallery modes for complex permittivity determinations of ultra-low-loss dielectric materials

Whispering-gallery modes are used for very accurate permittivity, dielectric loss, and temperature coefficient of permittivity measurements for both isotropic and uniaxially anisotropic dielectric materials. The relationship between resonant frequencies, dimensions of the resonant structure, and permittivity of the sample under test is calculated with a radial mode-matching technique. The relative accuracy of these computations is better then 10/sup -4/. The influence of conductor losses on dielectric loss tangent determination is treated for both whispering-gallery-mode and TE/sub 01/spl delta//-mode dielectric-resonator techniques. Two permittivity tensor components of sapphire and their temperature dependence were measured from 4.2 to 300 K. The total uncertainty in permittivity when use is made of whispering-gallery modes was estimated to be less than 0.05%. The uncertainty was limited principally by uncertainty in sample dimensions. Experimental and calculated resonant frequencies of several whispering-gallery modes differed by no more than 0.01%. The dielectric loss tangent of sapphire parallel and perpendicular to its anisotropy axis was calculated to be less than 10/sup -9/ at 4.2 K. The permittivity and dielectric loss tangent of a commercially available low-loss high-permittivity ceramic material has also been measured at S- and C-band frequencies using a large number of whispering-gallery modes.

Lithium tantalate - a high permittivity dielectric material for microwave communication systems

Lithium tantalate single crystal is characterized by very low thermal expansion and exhibits excellent electro-optical, piezoelectric and pyroelectric properties. We have studied the real part of relative permittivity (/spl epsi//sub r/) perpendicular to the crystal axis and the loss tangent of LiTaO/sub 3/ over the temperature range from 15 K to room temperature at a frequency of 11.4 GHz. The /spl epsi//sub r/ and tan/spl delta/ were determined by measurements of the resonance frequency and the unloaded Q-factor of a TE/sub 011/ mode cylindrical cavity containing the sample under test. The permittivity of LiTaO/sub 3/ was found to change from 38.9 to 41.1 and the loss tangent increased from 1.1 /spl times/ 10/sub -4/ to 6.5 /spl times/ 10/sub -4/ over the temperature range from 15 K to 295 K. Due to the low losses and high permittivity this material can be used in many microwave applications.

Resonant frequencies of higher order modes in cylindrical anisotropic dielectric resonators

A method that calculates the frequency of the lowest order mode in a cylindrical isotropic dielectric is extended to higher order modes in a anisotropic crystal. Four different axial match equations are derived depending on whether they are quasi TE or quasi TM, and have an odd or even axial mode number. A general radial match equation is also derived. Combining it with the relevant axial equation forms a set of two coupled transcendental equations that can be solved numerically. The theory is confirmed by room temperature measurements in two sapphire crystals of different aspect ratios, and in cryogenic sapphire resonators used in high stability fixed and tunable oscillators. The sensitivity of mode frequency to dimensional and permittivity perturbations is analyzed. >

Cold atom clocks and applications

This paper describes advances in microwave frequency standards using laser-cooled atoms at BNM-SYRTE. First, recent improvements of the 133Cs and 87Rb atomic fountains are described. Thanks to the routine use of a cryogenic sapphire oscillator as an ultra-stable local frequency reference, a fountain frequency instability of 1.6 × 10−14 τ−1/2 where τ is the measurement time in seconds is measured. The second advance is a powerful method to control the frequency shift due to cold collisions. These two advances lead to a frequency stability of 2 × 10−16 at 50 000 s for the first time for primary standards. In addition, these clocks realize the SI second with an accuracy of 7 × 10−16, one order of magnitude below that of uncooled devices. In a second part, we describe tests of possible variations of fundamental constants using 87Rb and 133Cs fountains. Finally we give an update on the cold atom space clock PHARAO developed in collaboration with CNES. This clock is one of the main instruments of the ACES/ESA mission which is scheduled to fly on board the International Space Station in 2008, enabling a new generation of relativity tests.

Tests of Lorentz invariance using a microwave resonator.

The frequencies of a cryogenic sapphire oscillator and a hydrogen maser are compared to set new constraints on a possible violation of Lorentz invariance. We determine the variation of the oscillator frequency as a function of its orientation (Michelson-Morley test) and of its velocity (Kennedy-Thorndike test) with respect to a preferred frame candidate. We constrain the corresponding parameters of the Mansouri and Sexl test theory to delta-beta + 1/2 = (1.5+/-4.2) x 10(-9) and beta-alpha - 1= (-3.1+/-6.9) x 10(-7) which is of the same order as the best previous result for the former and represents a 30-fold improvement for the latter.

Ultralow noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock

We demonstrate the use of a fiber-based femtosecond laser locked onto an ultrastable optical cavity to generate a low-noise microwave reference signal. Comparison with both a cryogenic sapphire oscillator (CSO) and a titanium-sapphire-based optical frequency comb system exhibit a stability of about 3×10−15 between 1 and 10 s. The microwave signal from the fiber system is used to perform Ramsey spectroscopy in a state-of-the-art cesium fountain clock. The resulting clock is compared to the CSO and exhibits a stability of 3.5×10−14τ−1/2.

Anisotropic complex permittivity measurements of mono-crystalline rutile between 10 and 300 K

The dielectric properties of a single crystal rutile (TiO2) resonator have been measured using whispering gallery modes. Q factors and resonant frequencies were measured from 300 to 10 K. Q factors as high as 104, 105, and 107 were obtained at 300, 80, and 10 K, respectively. Using the whispering gallery mode technique we have determined accurately the loss tangent and dielectric constant of monocrystalline rutile and obtained much more sensitive measurements than previously reported. We show that rutile exhibits anisotropy in both the loss tangent and permittivity over the range from 10 to 300 K.

Applications of interferometric signal processing to phase-noise reduction in microwave oscillators

To enhance the sensitivity of oscillator phase-noise measurements, an interferometric frequency-discriminator system may be implemented. Such systems consist of a microwave interferometer, incorporating a high-Q resonator and a phase-sensitive microwave readout. Suppressing the carrier at the output of the interferometer enables the microwave readout to operate in the small-signal regime with an effective noise temperature close to its physical temperature, When used as a sensor of a frequency-control system to lock the oscillator to a selected resonant mode of a high-Q resonator, the interferometric frequency discriminator has enabled more than two orders of magnitude improvement in oscillator phase-noise performance as compared with the state-of-the-art. Thus, the phase noise of an S-band oscillator was reduced to -150 dBc/Hz at 1-kHz Fourier frequency without the use of cryogenics, and was limited by the thermal noise in the microwave interferometer. To facilitate tuning and locking, an automatically balanced microwave frequency discriminator was developed using voltage-controlled attenuators and phase shifters. Rapid frequency tuning of the oscillator was achieved by varying the interferometer phase mismatch and automatically controlling the carrier suppression without tuning the high-Q resonator.

Invited Article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators

We review the techniques used in the design and construction of cryogenic sapphire oscillators at the University of Western Australia over the 18 year history of the project. We describe the project from its beginnings when sapphire oscillators were first developed as low-noise transducers for gravitational wave detection. Specifically, we describe the techniques that were applied to the construction of an interrogation oscillator for the PHARAO Cs atomic clock in CNES, in Toulouse France, and to the 2006 construction of four high performance oscillators for use at NMIJ and NICT, in Japan, as well as a permanent secondary frequency standard for the laboratory at UWA. Fractional-frequency fluctuations below 6 x 10(-16) at integration times between 10 and 200 s have been repeatedly achieved.