Unprecedented High Long Term Frequency Stability with a Macroscopic Resonator Oscillator
Serge Grop, Wolfgang Schäfer, Pierre-Yves Bourgeois, Nicolas Bazin, Yann Kersalé, Mark Oxborrow, Enrico Rubiola, Vincent Giordano
aa r X i v : . [ phy s i c s . i n s - d e t ] N ov Unprecedented High Long Term Frequency Stability with a Macroscopic ResonatorOscillator
S. Grop, W. Schäfer, P.Y. Bourgeois, N. Bazin, Y. Kersalé, M. Oxborrow, E. Rubiola, and V. Giordano FEMTO–ST Institute, Time and Frequency Dpt., UMR 6174 CNRS-UFC-ENSMM,32 av. de l’Observatoire, 25044 Besançon Cedex, France TimeTech GmbH, Curiestrasse 2, D-70563 Stuttgart, Germany National Physical Laboratory, Queens Road, Teddington, Middlesex, TW11 0LW,UK (Dated: 13 October 2018)
This article reports on the long-term frequency stabilty characterisation of a new type ofcryogenic sapphire oscillator using an autonomous pulse-tube cryocooler as its cold source.This new design enables a relative frequency stability of better than 4 . × − over oneday of integration. This represents to our knowledge the best long-term frequency stabilityever obtained with a signal source based on a macroscopic resonator.1n oscillator consists of a resonator in closed loop with a sustaining amplifier that compen-sates for losses. The frequency stability is limited by the noise of the amplifier through the Leesoneffect and by the fluctuation of the resonator’s natural frequency. It turns out that the stabilityof the resonator is by far the most important parameter that determines the long-term stability,while the noise of the sustaining amplifier affects only the phase-noise and the short-term stability.When the very-long-term stability is the most important parameter, as in timekeeping and in ra-dionavigation systems, atomic resonances are the only viable frequency references. In this case, aflywheel oscillator is frequency locked to the atomic resonance. On the other hand, macroscopic-cavity resonators show several advantages versus the atomic resonators because of their simplicity,reliability and power-handling capability. Higher power results in higher signal-to-noise ratio, andultimately in low phase noise and high short-term stability. Ultimate stability in the range of1 − s measurement time is of paramount importance in physical experiments involving longaveraging, and of course in radioastronomy.In this paper we demonstrate for the first time a microwave oscillator based on a macroscopicresonator with a frequency stability at long integration times that is competitive with those ofclassical microwave atomic clocks.Microwave Cryogenic Sapphire Oscillators (CSO) exhibits the higest short-term stability, at-taining parts in 10 − near 10 s integration time . A CSO incorporates a cryogenic whisperinggallery mode resonator made in sapphire which provides a Q-factor as high as 1 × at 4 . and for fundamentalphysical experiments as Local Lorentz Invariance tests . It is also planned to implement such os-cillators in Deep Space Network ground stations to improve the tracking of space vehicules and inVLBI observatory for better data correlation. For these last applications, the use of liquid heliumis inconvenient and a change of technology is needed. We recently validated in the frame of aEuropean Space Agency research contract, an new instrument: ELISA based on a CSO operatingin a specially designed cryocooler. The detailed design and preliminary characterisations can befound in . This CSO is associated with a frequency synthesis delivering round frequencies, i.e.10 GHz, 100 MHz and 5 MHz. The ELISA’s relative frequency stablity is better than 3 × − ≤ t ≤ , × − over one day without any clearly observed drift.The resonator consists of a Crystal System HEMEX grade single-crystal sapphire, 54.2 mm di-ameter and 30 mm thickness with a 10 mm diameter spindle allowing a stable mechnical clampingin the center of a gold plated copper cavity. This assembly as schematised in figure 1 is fixed onthe experimental cold plate of a pulse-tube cryocooler. A special soft thermal link and a thermalballast were designed in order to filter the vibrations and the temperature modulation at 1 . Thermal shieldandVacuum can SapphireresonatorThermal sensorMicrowave cable Cold source mechanicaldampingcavityCopper 54.2 mm mm HeaterThermal and
FIG. 1.
Scheme of the synthesis used to generate the 10GHz, 100 MHz and 5 MHz signals
Using a mechanical model, the g-sensitivity of the frequency of the resonator’s operating modewas determined to be 3 . × − / g . Phase noise measurements about the pulse-tube’s coolerfrequency of reciprocation ( 1 Hz), thereupon demonstrated that the residual displacement of theresonator is less than 2 µ m at the cryocooler cycle frequency . The resonator temperature isstabilized at 6.1 K with overal temperature rms fluctuations of ± . × − K − . The CSO is completed by an external sustaining circuit and two servos tostabilize the power injected into the resonator and the phase lag along the sustaining loop.3he mechanical tolerances in the resonator machining induce an uncertainty in the actualresonator frequency of ± . W GH , , whispering gallery mode at 9 .
99 GHz. The intentional 10 MHz frequency offset from the 10 GHzround frequency was chosen to permit to compensate for the resonator frequency uncertainty byusing a low noise Direct Digital Synthesizer (DDS). The actual resonator frequency measured at6.1 K is 9.989,121 GHz. The anatomy of the frequency synthesis chain is shown in the figure 2.
100 MHz LP x4 BP /4 /10/10 LP /10 LP
100 MHzoutputs5 MHzoutputs10 GHzoutputsDirectoutput
CSO9.99 GHzinput
DDS
250 MHz wordDDS control
10 GHz LP FIG. 2.
Scheme of the synthesis used to generate the 10GHz, 100 MHz and 5 MHz signals
A 2.5 GHz Dielectric Resonator Oscillator (DRO) choosen for its low phase noise is frequencymultiplied by 4 and mixed with the CSO’s signal. The resultant 11 MHz beatnote is compared tothe signal coming from a DDS. The resulting error signal is used to phase lock the DRO to theCSO. Frequency dividers complete the system to generate the 100 MHz and 5 MHz frequenciesfrom the 10 GHz signal.To evaluate the Elisa frequency stability on a large integration times range, two other frequencyreferences have been used: i) we implemented a second CSO: Alizée but cooled in a liquid-helium dewar and equipped with the same frequency synthesis. The Elisa and Alizée resonatorsare almost identical and were machined from the same sapphire boule. Alizée’s resonator is placed4n a vacuum can immersed in a 100 litre liquid-helium dewar. ii) An hydrogen maser which doesnot include an automated cavity tuning. The latter instrument was placed in the same room asthe two CSOs. This room is not temperature controlled. The results of the two comparisons aresummarized in the figure 3:
Integration Time (s) −16−14−13−15−12 y s ( t ) FIG. 3.
Relative frequency stability as measured by beating ELISA with another CSO ( (cid:3) ) and the hydrogenmaser ( • ). The broken line represents a conservative ELISA’s frequency stability estimation from1s to more than 1 day. The short term frequency stability of the synthesized signals has been evaluated at 10 GHz bybeating the Elisa’s and Alizée’s 10 GHz outputs. The Alizée output was intentionally frequencyshifted by acting on the DDS command in order to get a 200 kHz beatnote. This beatnote wasdirectly counted with a gate time t = s L ( t ) which slightly differs fromthe true Allan deviation s y ( t ) . Nevertheless for the integration times we consider here, itgives an overestimated relative frequency deviation with respect to s y ( t ) . Moreover no data post-processing has been done and we did not divide the result by √
2: a pratice which is generallyadopted when comparating two almost equivalent oscillators. The results presented here are thusconservative.The short-term frequency stability is limited by a white frequency noise process s L ( t ) ≈ × − t − / , which we attribute to the noise of the Pound servo used to stabilize the phase along5he sustaining loop. At long term a random walk or a frequency drift alters the frequency stability.The implementation of Elisa was finalized in October 2009 and since it has been continuously run-ning apart from two short periods of time, firstly for implementing an optimised rotary valve forthe cryocooler and secondly after a general electrical breakdown arrising in our laboratory. Aftereach stop, Elisa was simply switched on and recovered its optimal temperature in about 8 hours.Conversely, Alizée was stopped a number of times because of limited supplies in liquid helium.Moreover, for a long measurement compaign the dewar needs to be refilled every 10 days. Duringthis 6-months period, a number of measurements were realised, demonstrating that the long-termbehavior of the beatnote depends substantially on the status of Alizee and on the environmentalperturbations. As an example, figure 4 shows the correlation between the beatnote frequency andthe local atmospheric pressure. The liquid helium temperature of evaporation depends on theatmospheric pressure with a sensitivity equals to 1mK/mbar near 4.2 K. Temperature exchangeby radiation between the vacuum can and the Alizée resonator takes place and perturbs the modefrequency leading to long term instability. A t m o s ph e r i c p r e ss u r e ( h P a ) −0.00100.00000.00100.0020 0 50000 100000 150000 200000 996 998 1000 1002 1004 1006Time (s) b ea t − no t e fr e qu e n c y − , . H z −0.0020 FIG. 4.
Beatnote frequency (red curve) and atmospheric pressure (blue curve) as a function of time
The long-term stability has been evaluated at 100 MHz by using the hydrogen maser as refer-ence. The relative frequency stability has been computed from the phase difference data averagedover a sampling periode of 1s. The data were taken continuously during more than 5 days and the6llan deviation was computed. The result is shown in figure 3 (black bullets). The maser short-term instability limits the measurement for t ≤
500 s, but for longer integration times, it is obviousthat Elisa is far better than Alizée. The maximum frequency instability, i.e. 4 . × − arisesnear 1 day. It is likely that the hydrogen maser itself significantly contributes to this frequencyinstability. Indeed, its residual sensitivity has been measured to be 1 . × − / K which is farfrom negligible given that the daily variation of the temperature in the laboratory was typically afew degrees Celsius.Elisa presents the highest frequency stability over one day ever obtained with an oscillatorbased on a macroscopic resonator. To illustrate this point the figure 5 compares the previous Elisarelative frequency stability to the best ever published ultra-stable oscillator performances.
Integration Time (s) −15−16−13−12 s ( t ) y −14 X−tal Cavity
ELISA
10 cryocooled CSO10 Optical 1 10 100 1000 10000 100000 0.1 UWA1010 LHe−CSO10
FIG. 5. • : Estimated ELISA’s relative frequency stability compared to some other frequency standardsbased on macroscopic resonator. △ : 5 MHz quartz oscillator ; ◦ : Laser stabilized on an ultra-stable op-tical cavity ; (cid:4) : UWA cryocooled CSO ; (cid:3) : UWA liquid-helium cooled CSO . NB: To be consistent withour own procedure to evaluate the frequency stability, the published results for which the two-equivalent-oscillators hypothesis has been assumed have been multiplied by a factor √ . Acknowledgements : This work was supported by the European Space Agency (ESA).7
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