Clayton R. Locke

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.

Test of Lorentz Invariance in Electrodynamics Using Rotating Cryogenic Sapphire Microwave Oscillators

We present the first results from a rotating Michelson-Morley experiment that uses two orthogonally orientated cryogenic sapphire resonator oscillators operating in whispering gallery modes near 10 GHz. The experiment is used to test for violations of Lorentz invariance in the framework of the photon sector of the standard model extension (SME), as well as the isotropy term of the Robertson-Mansouri-Sexl (RMS) framework. In the SME we set a new bound on the previously unmeasured kappa(ZZ)(e-) component of 2.1(5.7) x 10(-14), and set more stringent bounds by up to a factor of 7 on seven other components. In the RMS a more stringent bound of -0.9(2.0) x 10(-10) on the isotropy parameter, P(MM) = delta-beta + 1 / 2 is set, which is more than a factor of 7 improvement.

Cryogenic sapphire oscillator with exceptionally high long-term frequency stability

The authors report on the development of a sapphire cryogenic microwave resonator oscillator with long-term fractional frequency stability of 2×10−17√τ for integration times τ>103s and a negative drift of about 2.2×10−15∕day. The short-term frequency instability of the oscillator is highly reproducible and also state of the art: 5.6×10−16 for an integration time of τ≈20s.

Improved test of Lorentz invariance in electrodynamics using rotating cryogenic sapphire oscillators

We present new results from our test of Lorentz invariance, which compares two orthogonal cryogenic sapphire microwave oscillators rotating in the lab. We have now acquired over 1 year of data, allowing us to avoid the short data set approximation (less than 1 year) that assumes no cancellation occurs between the {kappa}-tilde{sub e-} and {kappa}-tilde{sub o+} parameters from the photon sector of the standard model extension. Thus, we are able to place independent limits on all eight {kappa}-tilde{sub e-} and {kappa}-tilde{sub o+} parameters. Our result represents up to a factor of 10 improvement over previous nonrotating measurements (which independently constrained seven parameters) and is a slight improvement (except for {kappa}-tilde{sub e-}{sup ZZ}) over results from previous rotating experiments that assumed the short data set approximation. Also, an analysis in the Robertson-Mansouri-Sexl framework allows us to place a new limit on the isotropy parameter P{sub MM}={delta}-{beta}+(1/2) of 9.4(8.1)x10{sup -11}, an improvement of a factor of 2.

Short Term Frequency Stability Tests of Two Cryogenic Sapphire Oscillators

Ultra-high short-term frequency stability has been realized in microwave oscillators based on liquid helium cooled sapphire resonators which operate on the same Whispering Gallery mode. Two cryogenic sapphire oscillators were built to evaluate their stability at short averaging times. These oscillators exhibited a fractional frequency stability of 1.1×10-15 at an averaging time of 1 s, which is more than 100 times better than that of a hydrogen maser. For averaging times between 2 and 640 s the measured oscillator fractional frequency instability was below 10-15 with a minimum of 5.5×10-16 at an averaging time of 20 s. The noise floors of the control servos which contribute to the short-term frequency stability are also discussed.

Long-term operation and performance of cryogenic sapphire oscillators

Cryogenic sapphire oscillators (CSO) developed at the University of Western Australia (UWA) have now been in operation around the world continuously for many years. Such oscillators, due to their excellent spectral purity are essential for interrogating atomic frequency standards at the limit of quantum projection noise; otherwise aliasing effects will dominate the frequency stability due to the periodic sampling between successive interrogations of the atomic transition. Other applications, which have attracted attention in recent years, include tests on fundamental principles of physics, such as tests of Lorentz invariance. This paper reports on the long-term operation and performance of such oscillators. We compare the long-term drift of some different CSOs. The drift rates turn out to be linear over many years and in the same direction. However, the magnitude seems to vary by more than one order of magnitude between the oscillators, ranging from 1014 per day to a few parts in 1013 per day

Laser frequency comb techniques for precise astronomical spectroscopy

ABSTRACT Precise astronomical spectroscopic analyses routinely assume that individual pixels in charge-coupled devices (CCDs) have uniform sensitivity to photons. Intra-pixel sensitivity (IPS) vari-ations may already cause small systematic errors in, for example, studies of extra-solar planetsvia stellar radial velocities and cosmological variability in fundamental constants via quasarspectroscopy, but future experiments requiring velocity precisions approaching ˘1cms 1 willbe more strongly a ected. Laser frequency combs have been shown to provide highly precisewavelength calibration for astronomical spectrographs, but here we show that they can also beused to measure IPS variations in astronomical CCDs in situ. We successfully tested a laserfrequency comb system on the Ultra-High Resolution Facility spectrograph at the Anglo-Australian Telescope. By modelling the 2-dimensional comb signal recorded in a single CCDexposure, we find that the average IPS deviates by <8per cent if it is assumed to vary sym-metrically about the pixel centre. We also demonstrate that series of comb exposures withabsolutely known o sets between them can yield tighter constraints on symmetric IPS varia-tions from ˘100 pixels. We discuss measurement of asymmetric IPS variations and absolutewavelength calibration of astronomical spectrographs and CCDs using frequency combs.Key words: instrumentation: spectrographs – instrumentation: detectors – methods: labora-tory – techniques: spectroscopic

A simple technique for accurate and complete characterisation of a Fabry-Perot cavity

It has become a significant challenge to accurately characterise the properties of recently developed very high finesse optical resonators (F > 10(6)). A similar challenge is encountered when trying to measure the properties of cavities in which either the probing laser or the cavity length is intrinsically unstable. We demonstrate in this article the means by which the finesse, mode-matching, free spectral range, mirror transmissions and dispersion may be measured easily and accurately even when the laser or cavity has a relatively poor intrinsic frequency stability.

Rotating Resonator-Oscillator Experiments to Test Lorentz Invariance in Electrodynamics

The Einstein Equivalence Principle (EEP) is a founding principle of relativity [1]. One of the constituent elements of EEP is Local Lorentz Invariance (LLI), which postulates that the outcome of a local experiment is independent of the velocity and orientation of the apparatus. The central importance of this postulate has motivated tremendous work to experimentally test LLI. Also, a number of unification theories suggest a violation of LLI at some level. However, to test for violations it is necessary to have an alternative theory to allow interpretation of experiments [1], and many have been developed [2–7]. The kinematical frameworks (RMS) [2,3] postulate a simple parameterization of the Lorentz transformations with experiments setting limits on the deviation of those parameters from their values in special relativity (SR). Because of their simplicity they have been widely used to interpret many experiments [8–11]. More recently, a general Lorentz violating extension of the standard model of particle physics (SME) has been developed [6] whose Lagrangian includes all parameterized Lorentz violating terms that can be formed from known fields. This work analyses rotating laboratory Lorentz invariance experiments that compare precisely the resonant frequencies of two high-Q factor (or high finesse) cavity resonators. High stability electromagnetic oscillatory fields are generated by implementing state of the art frequency stabilization systems with the narrow line width of the resonators. Previous non-rotating experiments [10,12,13] relied on the rotation of the Earth to modulate putative Lorentz violating effects. This is not optimal for two reasons. Firstly, the sensitivity to Lorentz violations is proportional to the noise of the oscillators at the modulation frequency, typically best for periods between 10 and 100 seconds. Secondly, the sensitivity is proportional to the square root of the number of periods of the modulation signal, therefore taking a relatively long time to acquire sufficient data. Thus, by

PARAMETRIC INTERACTION OF THE ELECTRIC AND ACOUSTIC FIELDS IN A SAPPHIRE MONOCRYSTAL TRANSDUCER WITH A MICROWAVE READOUT

A sapphire monocrystal configured with a parametric microwave readout can potentially monitor the motion of its internal acoustic resonances at the precision governed by quantum mechanical fluctuations. The mechanism of transductance is due to parametric interaction between the electric and acoustic field within the crystal. This mechanism has been tested for the first time, and the theory has been verified by observing the pump frequency dependence of the acoustic quality factor. Because of the extremely low acoustic losses (Q>107) and electrical losses (Q>104), measurements were sensitive enough to attain positive verification at room temperature.