1 A Cryogenic Sapphire Resonator Oscillator with 1016mid-term fractional frequency stability

2025-04-27 1 0 273.67KB 4 页 10玖币

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A Cryogenic Sapphire Resonator Oscillator with

10−16 mid-term fractional frequency stability

Christophe Fluhr∇, Benoˆ

ıt Dubois∇, Claudio E. Calosso[, Franc¸ois Vernotte], Enrico Rubiola] [ and Vincent

Giordano]

Abstract—We report in this letter the outstanding frequency

stability performances of an autonomous cryogenique sapphire

oscillator presenting a ﬂicker frequency noise ﬂoor below

2×10−16 near 1,000sof integration time and a long term

Allan Deviation (ADEV) limited by a random walk process of

∼1×10−18√τ. The frequency stability qualiﬁcation at this

level called for the implementation of sophisticated instrumen-

tation associated with ultra-stable frequency references and ad

hoq averaging and correlation methods.

Index Terms—Time and frequency metrology, ultra-stable

oscillators, frequency stability.

I. INTRODUCTION

TESTS of fundamental physic [1], [2], [3], [4],

radioastronomy [5], [6] or fundamental and applied

metrology [7], [8] make an extensive use of ultra-stable

frequency sources, for which there is a constant demand for

improved frequency stability performance for measurement

time ranging from 1to 106s. Atomic frequency standards are

of course preferred when accuracy and long-term frequency

stability are required. But even in this case, an ultra-stable

signal source based on a high Q-factor macroscopic resonator

is needed to reach the ultimate frequency stability of the

atomic clock [9], [10], [11]. These secondary references,

means that are not based on the observation of an atomic

resonance, are built around an ultrasonic quartz resonator for

the RF or VHF band, a dielectric resonator for microwave, or

a Fabry-Perrot cavity for optics. The macroscopic resonator

can be integrated directly in the loop of a self-sustained

oscillator, or used as a passive reference on which a ﬂywheel

oscillator is stabilized. The high Q-factor and the power-

handling capability of the macroscopic resonator guarantee

a high short term frequency stability. However, at mid

and long term, i.e. for integration times ranging to say

from 10 s to few days, the oscillator frequency stability is

degraded by the ﬂuctuations of the resonator natural frequency.

The design of a signal source with the highest frequency

stability in the widest integration time range is challenging.

Indeed, we have to manage a great number of perturbation

Manuscript created August, 2022

∇France Comt´

e Innov, Besanc¸on, France.

]FEMTO-ST Institute, Dept. of Time and Frequency, Universit´

e de Bour-

gogne and Franche-Compt´

e (UBFC), and Centre National de la Recherche

Scientiﬁque(CNRS), E-mail: giordano@femto-st.fr, Address: ENSMM, 26

Rue de l’Epitaphe, 25000 Besanc¸on, France.

[Physics Metrology Division, Istituto Nazionale di Ricerca Metrologica

INRiM, Torino, Italy.

sources impacting the frequency stability at different

integration times. The means of overcoming all these

disturbances are often contradictory between them, and thus

tradeoffs have to be found. For example, increasing the

signal power increases the signal to noise ratio and thus

is favourable for the short term frequency stability. But it

can also induce a resonator non-linearity, which makes the

resonant frequency sensitive to the signal amplitude [12],

[13], [14], as thus will impact the long term frequency stability.

The metrological aspect is also very challenging when

we have to optimize and qualify a new type of ultra-stable

source. If a better reference is not available, two almost

identical units have to be implemented and compared. As it

is impossible to ensure that each signal source contributes

equally to the observed frequency ﬂuctuations, the measured

result gives only an overestimated ADEV. If an improvement

is made to one unit, its impact on the measurement result

can be hidden by ﬂuctuations of the other source. A more

efﬁcient way to get the intrinsic frequency stability of the

oscillator to be qualiﬁed, is to apply the three-cornered-hat

(TCH) method or other equivalent Covariance method [15].

The price to be payed is the need of two other signal

sources with comparable performances. These methods have

actually been used for several types of ultra-stable oscillators

[16], [17], [18], providing a better understanding of the

main frequency stability limitations. However, the TCH or

Covariance methods fall when correlations exist between

two of the signal sources that are comparated, giving non

realistic variances. One of the major issue comes from mid-

or long term environment ﬂuctuations that could induce such

correlations.

The Cryogenic Sapphire Oscillator (CSO) is an autonmous

microwave oscillator able to meet the requirements for many

very demanding applications. The ﬁrst CSO generation

incorporating a 6 or 8 kW cryocooler as the cold

source, demonstrated an ADEV σy(τ)<1×10−15 for

1s≤τ≤10,000 s with <1×10−14/day drift [19], [20]. A

second CSO generation, code-named ULISS-2G, consuming

only 3kW single phase is now commercially available. For

these instruments the conservative ADEV speciﬁcation is:

σy(τ)≤3×10−15 for 1s≤τ≤10,000 s and better than

1×10−14 over one day [21], [22]. We already build, validated

and delivered ﬁve ULISS-2G CSOs to different international

metrological Institutes [23]. The sixth unit has been operating

for the ﬁrst time in March 2022 and, at the time of writing, is

arXiv:2210.06059v1 [physics.ins-det] 12 Oct 2022

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1ACryogenicSapphireResonatorOscillatorwith1016mid-termfractionalfrequencystabilityChristopheFluhrr,BenotDuboisr,ClaudioE.Calosso[,Franc¸oisVernotte],EnricoRubiola][andVincentGiordano]AbstractWereportinthislettertheoutstandingfrequencystabilityperformancesofanautonomouscryogeniquesapphireoscillato...

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1 A Cryogenic Sapphire Resonator Oscillator with 1016mid-term fractional frequency stability

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