Cryogenic Sapphire Oscillator Research Articles

A cryogenic sapphire resonator oscillator with 10−16 mid-term fractional frequency stability

We report in this Letter the outstanding frequency stability performance of an autonomous cryogenic sapphire oscillator (CSO) presenting a flicker frequency noise floor below 2×10−16 near 1000 s of integration time and a long-term Allan deviation limited by a random walk process of ∼1×10−18τ. The frequency stability qualification at this level called for the implementation of sophisticated instrumentation associated with ultra-stable frequency references. This result is technologically sound as it demonstrates the potentiality of the CSO technology. From the physical point of view, it sets an upper limit to the ultimate noise floor of the cryogenic microwave resonator that is competitive to that of the ultra-stable optical Fabry–Pérot cavities.

Reliability and Reproducibility of the Cryogenic Sapphire Oscillator Technology

The cryogenic sapphire oscillator (CSO) is a highly specialized machine, which delivers a microwave reference signal exhibiting the lowest frequency fluctuations (Allan deviation σy(τ)) for the integration time τ between 1 s and 104 s, indeed 4 decades. In such interval, good units feature σy(τ) < 10-15, with < 10-14 drift in one day. The oscillator is based on a sapphire monocrystal resonating at 10 GHz in a whisperinggallery mode, cooled at ≈ 6 K for zero thermal coefficient and optimal quality factor Q.We report on the progress accomplished implementing eleven CSOs in about 10 years since the first sample delivered to the Malargüe station of the European Space Agency (ESA) in Argentina. Short-term stability is improved by a factor of 3.10, depending on τ, and the refrigerator’s electric power is reduced to 3 kW single-phase line. Frequency stability and overall performances are reproducible, with unattended operation between scheduled maintenance every two years. The CSO is now a semicommercial product suitable to scientific applications requiring extreme frequency stability with reliable unattended long-term operation, like the flywheel for primary frequency standards, the ground segment of Global Navigation Satellite System (GNSS), astrometry, Very Long Baseline Interferometry, and radio astronomy stations.

First uncertainty evaluation of the cesium fountain primary frequency standard NMIJ-F2

We report the first uncertainty evaluation of NMIJ-F2, the second atomic fountain primary frequency standard at the National Metrology Institute of Japan. To improve the frequency stability, we increase the number of detected atoms to 9 × 105 using high-power cooling laser beams for vapor-loaded optical molasses and optical pumping into the Zeeman sublevel m F = 0. We also employ an ultra-stable cryogenic sapphire oscillator as a local oscillator to prevent the degradation of frequency stability due to the Dick effect. After correcting the collisional frequency shift by alternating atom densities, the frequency stability typically reaches 2.5 × 10−13(τ/s)−1/2. Its value is 1.9 × 10−16 after 20 days of measurement. Type B uncertainty is typically evaluated at 4.7 × 10−16; the largest contribution is from a distributed cavity phase shift, followed by a microwave leakage shift. In long-term comparison, the frequency of NMIJ-F2 is found to be consistent with that of the other primary and secondary frequency standards within the uncertainty.

Simple thermal model to characterize dry and wet pulsed-tube cryocoolers

Cryogenic sapphire oscillators are unique three-dimensional structures that provide the highest performance local oscillators at short-term integration times. To further understand this device whose highest weakness is its sensitivity to temperature and reach its ultimate limit, we undertake a rigorous analysis of the properties of the cryocoolers with a simple thermal model. We show that the separation of variables is possible, as the cryocooler structure transfers heat from top to bottom and side to center independently. Comparisons between the modeling and experiments are consistent, and we illustrate where predictions using the established lumped element model work well with a test-set of valid conditions. With the aid of published data, we provide fittings of the thermophysical properties of air for temperatures less than 300K and pressures less than 1 atm.

Searching for Scalar Dark Matter via Coupling to Fundamental Constants with Photonic, Atomic, and Mechanical Oscillators.

We present a way to search for light scalar dark matter (DM), seeking to exploit putative coupling between dark matter scalar fields and fundamental constants, by searching for frequency modulations in direct comparisons between frequency stable oscillators. Specifically we compare a cryogenic sapphire oscillator (CSO), hydrogen maser (HM) atomic oscillator, and a bulk acoustic wave quartz oscillator (OCXO). This work includes the first calculation of the dependence of acoustic oscillators on variations of the fundamental constants, and demonstration that they can be a sensitive tool for scalar DM experiments. Results are presented based on 16days of data in comparisons between the HM and OCXO, and 2days of comparison between the OCXO and CSO. No evidence of oscillating fundamental constants consistent with a coupling to scalar dark matter is found, and instead limits on the strength of these couplings as a function of the dark matter mass are determined. We constrain the dimensionless coupling constant d_{e} and combination |d_{m_{e}}-d_{g}| across the mass band 4.4×10^{-19}≲m_{φ}≲6.8×10^{-14} eV c^{-2}, with most sensitive limits d_{e}≳1.59×10^{-1}, |d_{m_{e}}-dg|≳6.97×10^{-1}. Notably, these limits do not rely on maximum reach analysis (MRA), instead employing the more general coefficient separation technique. This experiment paves the way for future, highly sensitive experiments based on state-of-the-art acoustic oscillators, and we show that these limits can be competitive with the best current MRA-based exclusion limits.

Physics of the sapphire whispering-gallery-mode solid-state MASER oscillator

The Cryogenic Sapphire Oscillator (CSO) is currently the best available technology that can provide a relative frequency stability better than 10−15 with integration times between 1 s and 10,000 s. But, the CSO remains a complex instrument that requires multiple loop controls to achieve the best frequency stability. The possibility to use the sapphire resonator in a self-sustained MASER oscillator presents an elegant alternative to the CSO. Here, sustaining the amplification is achieved through the interaction between a high-Q factor whispering gallery mode and the paramagnetic Fe3+ ions, which are present in small concentration in the sapphire crystal. The Fe3+ ion exhibits three energy states enabling to realize a self-sustaining solid-state maser. Although, this principle has been already experimentally demonstrated few years ago, its development as a truly usable ultra-stable source has not yet been completed, mainly due to the lack of control of the complex physical phenomena involved. This paper complements the previous theoretical work based on the rate equations model. Here we derive the full quantum equations describing the evolution of the Fe3+ ions inside the sapphire lattice and submitted to a pump and a maser signal. The influence of the ions concentration and spin-spin relaxation time will be pointed out.

Magnetic sensitivity of the microwave cryogenic sapphire oscillator

The Cryogenic Sapphire Oscillator (CSO) is today recognized for its unprecedented frequency stability, mainly coming from the exceptional physical properties of its resonator made in a high-quality sapphire crystal. With these instruments, the fractional frequency measurement resolution, currently of the order of 10−16, is such that it is possible to detect very small phenomena such as residual resonator environmental sensitivities. Thus, we highlighted an unexpected magnetic sensitivity of the CSO at low magnetic fields. The fractional frequency sensitivity has been preliminarily evaluated to be 10−13/G, making this phenomenon a potential cause of frequency stability limitations. In this paper, we report the experimental data related to the magnetic sensitivity of the quasi-transverse magnetic Whispering Gallery (WGH) modes excited in sapphire crystals differing from their paramagnetic contaminant concentration. The magnetic behavior of the WGH modes does not follow the expected theory combining the Curie law and the Zeeman effect affecting the electron spin resonance of the paramagnetic ions present in the crystal.

Frequency Stability Measurement of Cryogenic Sapphire Oscillators With a Multichannel Tracking DDS and the Two-Sample Covariance.

This paper shows the first measurement of three 100-MHz signals exhibiting fluctuations from 2×10-16 to parts in 10-15 for an integration time τ between 1 s and 1 day. Such stable signals are provided by three cryogenic sapphire oscillators (CSOs) operating at about 10 GHz, also delivering the 100-MHz output via a dedicated synthesizer. The measurement is made possible by a six-channel tracking direct digital synthesizer (TDDS) and the two-sample covariance tool, used to estimate the Allan variance. The use of two TDDS channels per CSO enables high rejection of the instrument background noise. The covariance outperforms the three-cornered hat (TCH) method in that the background converges to zero "out of the box," with no need of the hypothesis that the instrument channels are equally noisy, nor of more sophisticated techniques to estimate the background noise of each channel. Thanks to correlation and averaging, the instrument background (AVAR) rolls off with a slope 1/√m , the number of measurements, down to 10-18 at τ = 104 s. For consistency check, we compare the results to the traditional TCH method beating the 10-GHz outputs down to the megahertz region. Given the flexibility of the TDDS, our methods find an immediate application to the measurement of the 250-MHz output of the femtosecond combs.

Drifts and Environmental Disturbances in Atomic Clock Subsystems: Quantifying Local Oscillator, Control Loop, and Ion Resonance Interactions.

Linear ion trap frequency standards are among the most stable continuously operating frequency references and clocks. Depending on the application, they have been operated with a variety of local oscillators (LOs), including quartz ultrastable oscillators, hydrogen-masers, and cryogenic sapphire oscillators. The short-, intermediate-, and long-term stability of the frequency output is a complicated function of the fundamental performances, the time dependence of environmental disturbances, the atomic interrogation algorithm, the implemented control loop, and the environmental sensitivity of the LO and the atomic system components. For applications that require moving these references out of controlled lab spaces and into less stable environments, such as fieldwork or spaceflight, a deeper understanding is needed of how disturbances at different timescales impact the various subsystems of the clock and ultimately the output stability. In this paper, we analyze which perturbations have an impact and to what degree. We also report on a computational model of a control loop, which keeps the microwave source locked to the ion resonance. This model is shown to agree with laboratory measurements of how well the feedback removes various disturbances and also with a useful analytic approach we developed for predicting these impacts.

The Autonomous Cryocooled Sapphire Oscillator: A Reference for Frequency Stability and Phase Noise Measurements

The Cryogenic Sapphire Oscillator (CSO) is the microwave oscillator which feature the highest short-term stability. Our best units exhibit Allan deviation σy(τ) of 4.5x10-16 at 1s, ≈ 1.5x10-16 at 100 s ≤ t ≤ 5,000 s (floor), and ≤ 5x10-15 at one day. The use of a Pulse-Tube cryocooler enables full two year operation with virtually no maintenance.Starting with a short history of the CSO in our lab, we go through the architecture and we provide more details about the resonator, the cryostat, the oscillator loop, and the servo electronics.We implemented three similar oscillators, which enable the evaluation of each with the three- cornered hat method, and provide the potential for Allan deviation measurements at parts of 10-17 level. One of our CSOs (ULISS) is transportable, and goes with a small customized truck. The unique feature of ULISS is that its σy (τ) can be validated at destination by measuring before and after the roundtrip. To this extent, ULISS can be regarded as a traveling standard of frequency stability.The CSOs are a part of the Oscillator IMP project, a platform dedicated to the measurement of noise and short-term stability of oscillators and devices in the whole radio spectrum (from MHz to THz), including microwave photonics. The scope spans from routine measurements to the research on new oscillators, components, and measurement methods.

Operation of NIM5 fountain with 1.5x10-15 uncertainty and design of new NIM6 in NIM

The cesium fountain primary frequency standard NIM5 started to operate since 2008 and started to report to BIPM since 2014. The major constrains of NIM5 is a relatively large background signal at the detection and microwave leakages due to the Ramsey cavity. A new fountain clock NIM6 is under construction. Besides some improvements on the vacuum system, a new Ramsey cavity and a microwave synthesizer are made to reduce the Type B uncertainty. Another feature of NIM6 is collecting atoms from a MOT loading optical molasses to get more atoms with a more uniform density distribution. With a new frequency synthesizer based on cryogenic sapphire oscillator (CSO), NIM6 is aiming to reach the quantum projection noise, thus leading to a reduced Type A uncertainty compared with NIM5.

High Stability Comparison of Atomic Fountains using two Different Cryogenic Oscillators.

We present a detailed characterization of two atomic clock interrogation systems based on two different cryogenic sapphire oscillators operated simultaneously. We use them as references for two accurate fountain clock frequency standards participating in international atomic time and operating both at the quantum projection noise frequency limit. The two fountain comparison down to a few 10􀀀16 over 28 days demonstrates the potential of a cryocooled oscillator to replace a He refilled cryogenic oscillator.

Characterization of the Individual Short-Term Frequency Stability of Cryogenic Sapphire Oscillators at the 10(-16) Level.

We present the characterization of three cryogenic sapphire oscillators (CSOs)using the three-cornered-hat method. Easily implemented with commercial components and instruments, this method reveals itself very useful to analyze the fractional frequency stability limitations of these state-of-the-art ultrastable oscillators. The best unit presents a fractional frequency stability better than 5 ×10(-16) at 1s and below 2 ×10(-16) for [Formula: see text].

Drift-Compensated Low-Noise Frequency Synthesis Based on a cryoCSO for the KRISS-F1

In this paper, we report on the implementation and stability analysis of a drift-compensated frequency synthesizer from a cryogenic sapphire oscillator (CSO) designed for a Cs/Rb atomic fountain clock. The synthesizer has two microwave outputs of 7 and 9 GHz for Rb and Cs atom interrogation, respectively. The short-term stability of these microwave signals, measured using an optical frequency comb locked to an ultrastable laser, is better than $5 \times 10^{-15}$ at an averaging time of 1 s. We demonstrate that the short-term stability of the synthesizer is lower than the quantum projection noise limit of the Cs fountain clock, KRISS-F1(Cs) by measuring the short-term stability of the fountain with varying trapped atom number. The stability of the atomic fountain at 1 s averaging time reaches $2.5 \times 10^{-14}$ at the highest atom number in the experiment when the synthesizer is used as an interrogation oscillator of the fountain. In order to compensate the frequency drift of the CSO, the output frequency of a waveform generator, in the synthesis chain, is ramped linearly. By doing this, the frequency stability of the synthesizer at an average time of one hour reaches a level of $10^{-16}$ , which is measured with the fountain clock.

Tests of Sapphire Crystals Manufactured With Different Growth Processes for Ultra-Stable Microwave Oscillators

We present the characterization of 8-12 GHz whispering gallery mode resonators machined in high-quality sapphire crystals elaborated with different growth techniques. These microwave resonators are intended to constitute the reference frequency of ultra-stable Cryogenic Sapphire Oscillators. We conducted systematic tests near 4 K on these crystals to determine the unloaded Q-factor and the turnover temperature for whispering gallery modes in the 8-12 GHz frequency range. These characterizations show that high quality sapphire crystals elaborated with the Heat Exchange or the Kyropoulos growth technique are both suitable to meet a fractional frequency stability better than 1x10-15 for 1 s to 10.000 s integration times.

Atomic fountain clock with very high frequency stability employing a pulse-tube-cryocooled sapphire oscillator.

The frequency stability of an atomic fountain clock was significantly improved by employing an ultra-stable local oscillator and increasing the number of atoms detected after the Ramsey interrogation, resulting in a measured Allan deviation of 8.3 × 10(-14)τ(-1/2)). A cryogenic sapphire oscillator using an ultra-low-vibration pulse-tube cryocooler and cryostat, without the need for refilling with liquid helium, was applied as a local oscillator and a frequency reference. High atom number was achieved by the high power of the cooling laser beams and optical pumping to the Zeeman sublevel m(F) = 0 employed for a frequency measurement, although vapor-loaded optical molasses with the simple (001) configuration was used for the atomic fountain clock. The resulting stability is not limited by the Dick effect as it is when a BVA quartz oscillator is used as the local oscillator. The stability reached the quantum projection noise limit to within 11%. Using a combination of a cryocooled sapphire oscillator and techniques to enhance the atom number, the frequency stability of any atomic fountain clock, already established as primary frequency standard, may be improved without opening its vacuum chamber.

Influence of the electron spin resonance saturation on the power sensitivity of cryogenic sapphire resonators

Here, we study the paramagnetic ions behavior in presence of a strong microwave electromagnetic field sustained inside a cryogenic sapphire whispering gallery mode resonator. The high frequency measurement resolution that can be now achieved by comparing two Cryogenic Sapphire Oscillators (CSOs) permit to observe clearly the non-linearity of the resonator power sensitivity. These observations that, in turn, allow us to optimize the CSO operation are well explained by the electron spin resonance saturation of the paramagnetic impurities contained in the sapphire crystal.

Cs-based optical frequency measurement using cross-linked optical and microwave oscillators

We describe a measurement of the frequency of the 2S1/2(F = 0) - 2D3/2(F' = 2) transition of 171Yb+ at the wavelength 436 nm (frequency 688 THz), using a single Yb+ ion confined in a Paul trap and two caesium fountains as references. In one of the fountains, the frequency of the microwave oscillator that interrogates the caesium atoms is stabilized by the laser that excites the Yb+ reference transition with a linewidth in the hertz range. The stability is transferred to the microwave oscillator with the use of a fiber laser based optical frequency comb generator that also provides the frequency conversion for the absolute frequency measurement. The frequency comb generator is configured as a transfer oscillator so that fluctuations of the pulse repetition rate and of the carrier offset frequency do not degrade the stability of the frequency conversion. The phase noise level of the generated ultrastable microwave signal is comparable to that of a cryogenic sapphire oscillator. For fountain operation with optical molasses loaded from a laser cooled atomic beam source, we obtain a stability corresponding to a fractional Allan deviation of $4.1\times 10^{-14}\ (\tau/\text{s})^{-1/2}$. With the molasses loaded from thermal vapor and an averaging time of 65 h, we measure the frequency of the Yb+ transition with a relative statistical uncertainty of $2.8\times10^{-16}$ and a systematic uncertainty of $5.9\times10^{-16}$. The frequency was also simultaneously measured with the second fountain that uses a quartz-based interrogation oscillator. The unperturbed frequency of the Yb+ transition is realized with an uncertainty of $1.1\times10^{-16}$ that mainly results from the uncertainty of the blackbody shift at the operating temperature near 300 K. The transition frequency of 688 358 979 309 307.82(36) Hz, measured with the two fountains, is in good agreement with previous results.

Radio frequency signals synthesised from independent cryogenic sapphire oscillators

The phase noise and frequency stability measurements of 1 GHz, 100 MHz and 10 MHz signals are presented which have been synthesised from the 11.2 GHz outputs of two nominally identical independent cryogenic microwave sapphire oscillators.

Resonator power to frequency conversion in a cryogenic sapphire oscillator

We report on the measurement and characterization of power to frequency conversion in the resonant mode of a cryogenic sapphire loaded cavity resonator, which is used as the frequency discriminating element of a loop oscillator circuit. Fluctuations of power incident on the resonator lead to changes in radiation pressure and temperature in the sapphire dielectric, both of which contribute to a shift in the resonance frequency. We measure a modulation and temperature independent radiation pressure induced power to frequency sensitivity of −0.15 Hz/mW and find that this is the primary factor limiting the stability of the resonator frequency.