High Resolution Flicker-Noise-Free Frequency Measurements of Weak Microwave Signals

Amplification is usually necessary when measuring the frequency instability of microwave signals. In this work, we develop a flicker noise free frequency measurement system based on a common or shared amplifier. First, we show that correlated flicker phase noise can be cancelled in such a system. Then we compare the new system with the conventional by simultaneously measuring the beat frequency from two cryogenic sapphire oscillators with parts in 10^15 fractional frequency instability. We determine for low power, below -80 dBm, the measurements were not limited by correlated noise processes but by thermal noise of the readout amplifier. In this regime, we show that the new readout system performs as expected and at the same level as the standard system but with only half the number of amplifiers. We also show that, using a standard readout system, the next generation of cryogenic sapphire oscillators could be flicker phase noise limited when instability reaches parts in 10^16 or betterComment: Accepted for publication in IEEE Transactions on Microwave Theory & Technique

Controlling the Frequency-Temperature Sensitivity of a Cryogenic Sapphire Maser Frequency Standard by Manipulating Fe3+ Spins in the Sapphire Lattice

To create a stable signal from a cryogenic sapphire maser frequency standard, the frequency-temperature dependence of the supporting Whispering Gallery mode must be annulled. We report the ability to control this dependence by manipulating the paramagnetic susceptibility of Fe3+ ions in the sapphire lattice. We show that the maser signal depends on other Whispering Gallery modes tuned to the pump signal near 31 GHz, and the annulment point can be controlled to exist between 5 to 10 K depending on the Fe3+ ion concentration and the frequency of the pump. This level of control has not been achieved previously, and will allow improvements in the stability of such devices.Comment: 17 pages, 10 figure

ELISA: a cryocooled 10 GHz oscillator with 10-15 frequency stability

This article reports the design, the breadboarding and the validation of an ultra-stable Cryogenic Sapphire Oscillator operated in an autonomous cryocooler. The objective of this project was to demonstrate the feasibility of a frequency stability of 3x10-15 between 1 s and 1,000 s for the European Space Agency deep space stations. This represents the lowest fractional frequency instability ever achieved with cryocoolers. The preliminary results presented in this paper validate the design we adopted for the sapphire resonator, the cold source and the oscillator loop.Comment: 13 pages, 10 figure

Ultra-low vibration pulse-tube cryocooler stabilized cryogenic sapphire oscillator with 10^-16 fractional frequency stability

A low maintenance long-term operational cryogenic sapphire oscillator has been implemented at 11.2 GHz using an ultra-low-vibration cryostat and pulse-tube cryocooler. It is currently the world's most stable microwave oscillator employing a cryocooler. Its performance is explained in terms of temperature and frequency stability. The phase noise and the Allan deviation of frequency fluctuations have been evaluated by comparing it to an ultra-stable liquid-helium cooled cryogenic sapphire oscillator in the same laboratory. Assuming both contribute equally, the Allan deviation evaluated for the cryocooled oscillator is sigma_y = 1 x 10^-15 tau^-1/2 for integration times 1 < tau < 10 s with a minimum sigma_y = 3.9 x 10^-16 at tau = 20 s. The long term frequency drift is less than 5 x 10^-14/day. From the measured power spectral density of phase fluctuations the single side band phase noise can be represented by L_phi(f) = 10^-14.0/f^4+10^-11.6/f^3+10^-10.0/f^2+10^-10.2/f+ 10^-11.0 for Fourier frequencies 10^-3<f<10^3 Hz in the single oscillator. As a result L_phi approx -97.5 dBc/Hz at 1 Hz offset from the carrier.Comment: 8 pages, 10 figures, presented at European Frequency and Time Forum, ESTEC, Noordwijk, Netherland, April 11-16th 2010 accepted in IEEE Trans. on Micro. Theory & Technique

Thermometry based on Whispering Gallery Mode resonators

Whispering gallery (WG) mode resonators were studied since 1980s for precision clock oscillators and for cavity quantum electrodynamics studies. They are a kind of stable, high Q, microwave resonators where a symmetric dielectric medium, such as a cylinder or a disk, is suspended in the centre of a metal cavity. A coaxial cable or a waveguide are used to couple the EM field in the microwave region and thus to excite the system resonant frequencies. WG modes are resonant modes of higher-order azimuthal number (m) having most of the EM energy concentrated on the dielectric surface. Within the temperature range of -196 °C to 500 °C the most commonly used industrial thermometer is platinum resistance thermometer (PRT) with the uncertainties of 10 mK. The PRT offers high accuracy, low drift, a wide operating range; however, it is very sensitive to mechanical shock in handing and shipping. Besides, an AC resistance bridge which is typically required as a readout device for PRT is very expensive. Accordingly, there is a great need for a stability-improved, resistant to mechanical shock, potential lower uncertainty and cost-effective industrial thermometer. WGMR thermometer (WGMRT) is a new kind of thermometer which offers greater vibration immunity, improved stability, smaller uncertainty in temperature measurement and potential lower cost than platinum resistance thermometry. An innovative sapphire whispering gallery thermometer (SWGT) was first explored at the National Institute of Standards and Technology (NIST) in 2007 by Strouse [1] with the uncertainty less than 10 mK. Five WGMs with nominal resonant frequencies ranging from 14.4 GHz to 19.1 GHz and with Q-factors, respectively, ranging from 20,000 to 90,000 were measured within the temperature range of 0 °C to 100 °C. The accuracies of his WGMTs were in the range of ± 0.02 °C and ice point repeatability was better than 2 mK. The thesis reports the tests performed on several WGMR thermometers which have different shapes of crystals to evaluate their stability, resolution and repeatability in the temperature range of -40 °C to 85°C. Thermal cycle experimental results IV showed a Q in excess of 100000 for the mode with the highest azimuthal number, making it possible to achieve a potential temperature resolution of 0.1 mK. Besides, different specimens of crystals with the same nominal specification and reassemble for the same specimen were both tested to check the reproducibility of the thermometer. The birefringence of the sapphire was also studied to make an innovative thermometer. The ratios of two doublet frequencies are sensitive to the temperature-dependent birefringence of the crystal and relatively insensitive to surface contamination and changes in the shape of the cavity. Besides, it can have an external shape that closely approximates the shape of conventional platinum resistance thermometer

Design of a next-generation modern Michelson-Morley experiment

Ein Fortschritt im Verständnis der Naturgesetzte wäre eine quantenphysikalische Beschreibung der Gravitation. Eine gültige Theorie der Quantengravitation (QG) existiert derzeit wegen des fehlenden experimentellen Zugangs des Planck-Skalen-Bereichs nicht. Dennoch können Experimente Hinweise für die Suche nach einer QG liefern. Die Standardmodellerweiterung (SME) bspw. beschreibt mögliche QG-induzierte beobachtbare niederenergetische Planck-Skalen-Effekte. Diesem Ansatz folgend wurde ein modernes Michelson-Morley-Experiment der nächsten Generation entwickelt, das es erstmalig erlaubt, simultan Obergrenzen für niederenergetische Planck-Skalen-Effekte in den Bewegungsgleichungen von Photonen und Fermionen zu bestimmen. Das zugrundeliegende theoretische Modell innerhalb der SME wurde neu betrachtet und Unstimmigkeiten korrigiert. Der Aufbau besteht aus ultra-stabilen kryogenen optischen Resonatoren (COREs) und Mikrowellenresonatoren, die gemeinsam im Raum rotieren. Die durch thermisches Rauschen limitierte vorhergesagte relative Frequenzinstabilität der entwickelten COREs liegt bei Temperaturen von flüssigem Helium im Bereich von 10^-17. Die Mikrowellenresonatoren können eine relative Frequenzinstabilität von 10^-16 erreichen. Um Störeinflüsse zu reduzieren, wurde zudem ein rauscharmer Niedrigtemperatur- sowie Drehtischaufbau konzipiert. Parallel wurde mit den Mikrowellenresonatoren ein einjähriges modernes Michelson-Morley-Experiment mit einer Sensitivität im Bereich von 10^-18 durchgeführt und erstmalig vollständig entkoppelte Obergrenzen für niederenergetische Planck-Skalen-Effekte im Bereich von 10^-17 bestimmt. Für den Aufbau der nächsten Generation lässt sich basierend auf der Frequenzinstabilität der COREs und der Mikrowellenresonatoren eine Sensitivität für niederenergetische Planck-Skalen-Effekte im Bereich von 10^-20 abschätzen. Zum ersten Mal kann somit der hypothetische Planck-unterdrückte-Bereich mit elektromagnetischen Resonatoren erkundet werden.The next big leap in understanding the working principles of nature can be expected from a quantum physical description of gravity. None of the quantum gravity (QG) candidate theories can be verified, since observations at the Planck regime have currently been impossible. Still, experiments can help to give insights. For example, standard model extension (SME) describes potential observable low-energy remnant Planck scale effects. With this in mind, a design for a next-generation modern Michelson-Morley experiment has been developed that allows extracting upper bounds on potentially observable remnant Planck scale effects in the equations of motion of photons and fermions simultaneously. The corresponding theoretical model within the framework of the SME has been revisited and discrepancies have been corrected. The experimental setup consists of co-rotating ultra-stable cryogenic optical resonators (COREs) and ultra-stable sapphire loaded cryogenic microwave whispering-gallery resonators. The developed COREs have a theoretical thermal noise limited fractional frequency instability on the order of 10^-17 at liquid helium temperatures. The cryogenic microwave resonators allow in principle a performance on the order of 10^-16. For noise reduction, a suitable low noise cryogenic as well as turntable system has been designed. In parallel, a one-year modern Michelson-Morley measurement campaign with a sensitivity on the order of 10^-18 was carried out using the cryogenic microwave resonators. The experiment has allowed to set new stringent disentangled upper bounds on remnant Planck scale effects on the order of 10^-17. With the frequency performance of the COREs and cryogenic microwave resonators of the next-generation experimental setup, a sensitivity for remnant Planck scale effects on the order of 10^-20 can be estimated. Thus, the designed setup has the potential to explore the hypothetical Planck suppressed regime using electromagnetic resonators for the first time

Nonlinear and Quantum Optics with Whispering Gallery Resonators

Optical Whispering Gallery Modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago. This phenomenon has a rather general nature, equally applicable to sound and all other waves. It enables resonators of unique properties attractive both in science and engineering. Very high quality factors of optical WGM resonators persisting in a wide wavelength range spanning from radio frequencies to ultraviolet light, their small mode volume, and tunable in- and out- coupling make them exceptionally efficient for nonlinear optical applications. Nonlinear optics facilitates interaction of photons with each other and with other physical systems, and is of prime importance in quantum optics. In this paper we review numerous applications of WGM resonators in nonlinear and quantum optics. We outline the current areas of interest, summarize progress, highlight difficulties, and discuss possible future development trends in these areas.Comment: This is a review paper with 615 references, submitted to J. Op

A Low Power Cryogenic Sapphire Oscillator with better than 10-15 short term frequency stability

International audienceIn the field of Time and Frequency metrology, the most stable frequency source is based on a microwave whispering gallery mode sapphire resonator cooled near 6 K. Provided the resonator environment is sufficiently free of vibration and temperature fluctuation, the Cryogenic Sapphire Oscillator (CSO) presents a short term fractional frequency stability of better than 1 x 10-15. The recent demonstration of a low maintenance CSO based on a pulse-tube cryocooler paves the way for its deployment in real field applications. The main drawback which limits the deployment of the CSO technology is the large electrical consumption (three-phase 8 kW peak / 6 kW stable operation) of the current system. In this paper, we describe an optimized cryostat designed to operate with a low consumption cryocooler requiring only 3 kW single phase of input power to cool down to 4 K a sapphire resonator.We demonstrate that the proposed design is compatible with reaching a state-of-the-art frequency stabilit