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Accuracy evaluation of ITCsF2: a nitrogen cooled caesium fountain

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2014 Metrologia 51 270

(http://iopscience.iop.org/0026-1394/51/3/270)

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| Bureau International des Poids et Mesures Metrologia

Metrologia 51 (2014) 270–284 doi:10.1088/0026-1394/51/3/270

Accuracy evaluation of ITCsF2: a nitrogencooled caesium fountainFilippo Levi1, Davide Calonico1, Claudio E Calosso1, Aldo Godone1,Salvatore Micalizio1 and Giovanni A Costanzo2

1 INRIM-Str. Delle Cacce 91, 10135 Torino, Italy2 Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

E-mail: f.levi@inrim.it

Received 12 December 2013, revised 4 April 2014Accepted for publication 4 April 2014Published 28 May 2014

AbstractFor almost two decades, caesium fountain primary frequency standards (PFS) haverepresented the best realization of the definition of the second in the International System ofunits. Their accuracy has progressively improved with time, reaching a few parts in 1016. Inthis paper, we present the accuracy evaluation of ITCsF2, the new Cs fountain PFS developedat the Italian National Metrological Institute, designed to be operated at cryogenic temperatureto reduce the blackbody radiation shift. The short-term stability of the ITCsF2 fountain is2 × 10−13τ−1/2 when operated at high atomic density, and the relative inaccuracy reaches2.3 × 10−16. We also report four calibrations of International Atomic Time with a relativefrequency agreement of (−1.7 ± 3.2) × 10−16, between ITCsF2 and the average of the otherfountains operated in the world during the reference periods.

Keywords: primary frequency standards, TAI, Cs fountain

(Some figures may appear in colour only in the online journal)

1. Introduction

Since its discovery in the early 1980s, laser cooling of neutralatoms has attracted the attention of the time and frequencycommunity for its possible application to the development ofa new generation of Cs primary frequency standards. Indeed,the first Cs fountain [1] immediately demonstrated a betteraccuracy than thermal beam standards. In the following years,new fountains were developed in many different metrologicallaboratories worldwide, improving by more than one orderof magnitude the accuracy in the realization of the SIsecond [1–11].

After the first report of a fountain to the BureauInternational des Poids et Mesures (BIPM) in 1995, regularfountain evaluations have been reported since 1999, increasingprogressively their weight in International Atomic Time(TAI) calibration [12], rapidly becoming the fundamentalelement for time and frequency accuracy worldwide; elevenfountains have reported frequency accuracy evaluations toBIPM until today. Among other institutes, the Italian NationalMetrological Institute (INRIM) has contributed to this processsince 2003, operating the Cs fountain ITCsF1 with a typicaluncertainty of ≈1 × 10−15 in the realization of the SIsecond [6].

A remarkable work [12] has shown a substantial statisticalagreement among all the fountains that have reported data toBIPM to steer TAI.

A significant amount of theoretical and experimental workprogressively improved the accuracy of the Cs fountains,properly evaluating the frequency biases in the pulsed regime,typical of these primary frequency standards. In particular,specific tests have been developed to produce a strong leverageeffect in the assessment of several biases: magnifying the bias,those tests allowed better evaluations and reduced uncertainties[13–19]. As a result, many of the biases affecting a fountain cannow be evaluated with a relative uncertainty in the 10−17 range.

In this paper, we present and discuss the accuracyevaluation of the new INRIM Cs fountain ITCsF2 [20]. Oneof its most important peculiarities is the strong reductionof the blackbody radiation shift, achieved by maintainingthe interaction region of the standard near the liquidnitrogen temperature (89.4 K). ITCsF2 was operated almostcontinuously in the last two years, allowing a completeand repeatable accuracy budget. Several informal accuracyevaluations were performed against TAI, confirming theaccuracy of the standard.

In the first part of this paper, a detailed description of theITCsF2 apparatus is given; in the second, the analysis of the

0026-1394/14/030270+15$33.00 270 © 2014 BIPM & IOP Publishing Ltd Printed in the UK

Metrologia 51 (2014) 270 F Levi et al

Figure 1. Schematic drawing of the ITCsF2 physical package.

frequency biases affecting the standard is presented, togetherwith their measurement methods and uncertainty; the last partis devoted to the frequency comparisons between ITCsF2 andTAI realized so far.

ITCsF2 has been realized in tight collaboration with NISTtime and frequency division (Boulder, CO), where the physicalpackage of the fountain was designed and realized. A twinsystem, NIST-F2, cooled with liquid nitrogen as well, isoperated there.

2. Description of the standard

2.1. Physical package

The main features of the ITCsF2 design are related to thecryogenic temperature operation, achieved with liquid nitrogencooling. The physical structure is composed of two parts, onekept at room temperature and the other in thermal contact witha liquid nitrogen cryostat. Figure 1 shows a schematic drawingof the 230 cm tall fountain apparatus.

The cryostat is thermally insulated through a mid-vacuum(MV) chamber containing the cryostat itself, the C-fieldsolenoid, the magnetic shields and the cavity feeding coaxialcables. The second part is an ordinary ultra-high vacuum(UHV) chamber where all the atomic manipulations andinteractions are performed.

The UHV volume consists of a lower chamber, whichhosts the atom trapping and the detection regions, and anupper region that includes the state selection and the Ramseycavities and the drift tube. The lower chamber is kept at roomtemperature, whilst the upper part is cold. The temperaturedifference between the two parts is maintained with stainlesssteel vacuum bellows, specifically designed also to electricallyinsulate the two zones, avoiding thermoelectric current flow.

The trapping and the detection chamber is provided withsix recesses for the collimators of the molasses beams orientedaccording to the (1,1,1) geometry.

The Cs oven consists of a simple copper tube, where aCs ampoule is located. After the bake-out of the system theampoule is broken, and the caesium vapour released. The

oven temperature is controlled with Peltier elements and it isset around 23 ◦C.

A steel plate separates the lower part of the trappingchamber from the upper detection region. Graphite getters areplaced in the trapping zone to reduce the Cs vapour diffusioninto the detection region.

Similarly to the design of ITCsF1 [21] the detection zoneis twofold, allowing for spatially well-separated detection ofatoms in 6S1/2 F = 3 and 6S1/2 F = 4 ground states. Twoindependent photodetectors are used, one for each detectionstage. Four ribbon shaped beams (15 mm horizontal and 2 mmvertical) are aligned for this purpose two by two. In theirdownward trajectory the atoms first see a standing wave laserbeam, resonant on the cycling transition F = 4 → F ′ = 5,that is used to detect the atoms into the F = 4 state; secondly,they see a travelling wave beam resonant on the same transitionthat blasts away the detected atoms. In the second detectionstage, they interact first with a pumping beam, which transfersF = 3 atoms into the F = 4 state, and finally with anotherstanding wave beam, resonant on the cycling transition F =4 → F ′ = 5, used to detect the atoms previously in theF = 3 state. The relative intensity of the two standing wavesis carefully adjusted to get the same detection efficiency. Thetwo time-of-flight (TOF) signals are used to directly calculatethe transition probability after the microwave interaction.

The Ramsey interaction region consists of microwavecavities and a metre tall drift tube; the whole structure isrealized in OFHC copper; just below it a second cavity,identical to the Ramsey one, is used for state selectionof the atoms in the m = 0 state. Thermal conductionwith the cryostat is achieved using an aluminium plate thattightly connects the bottom of the cryostat with the bodyof the cavities. On the cryostat’s top another aluminiumplate closes the interaction region, creating a closed low-temperature chamber. Despite this design, a few thermal flowchannels (such as microwave cables and wiring) affect theinsulation. Consequently, the temperature of the interactionregion is constantly several degrees above the liquid nitrogentemperature, with a temperature gradient of 1.5 K alongthe drift tube. The temperature of the interaction regionis monitored by three high-accuracy Pt-100 sensors placedbetween the state selection and the Ramsey cavities, at theatoms’ apogee and at the top of the drift tube.

Figure 2(a) shows the temperature of the interaction regionover 110 days: nitrogen refills occur three times a day. Thelarger peaks in figure 2(a) correspond to the substitution ofan empty Dewar that caused a skipped liquid nitrogen refill.Figure 2(b) shows the temperature stability of the Ramseycavity.

The Ramsey cavity design is quite similar to that ofITCsF1 and a detailed description can be found in [22]. Thecavity measures 60 mm in diameter and 21.8 mm in height.Four feeds are placed on its equatorial plane, each separatedby 90◦ from the other. The feeds are supplied two-by-twothrough a bent rectangular waveguide cavity matched on theexternal wall of the Ramsey cavity. The cavity loaded qualityfactor is QL = 17 000 at room temperature and QL = 42 000at 88 K, in agreement with the values of Cu losses reported

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Metrologia 51 (2014) 270 F Levi et al

56320 56340 56360 56380 56400 5642088

89

90

91T

empe

ratu

re /K

MJD

Cavity Apogee Top

1000 10000 100000 10000001E-3

0,01

0,1

Tem

pera

ture

Sta

bilit

y /K

Time/ s

(a) (b)

Figure 2. Temperatures of the interaction region (a) and temperature stability of the Ramsey cavity (b).

in the literature at the two temperatures [20]. Similar valueshave been measured for the state selection cavity, placed a fewcentimetres below the Ramsey one.

The Ramsey cavity was originally designed to be resonantwith the Cs clock transition at 80 K, but since the temperatureachieved by the cavity is higher than the expected temperature(∼88 K), the cavity is detuned by 1 MHz with respect to theCs transition in normal fountain operation. However, thisproblem does not result in a major limitation of the standardfinal accuracy.

The vacuum in the interaction region is maintained withan ion pump (20 l s−1) and a Ti sublimation pump; moreover,the cryogenic environment helps us to maintain the vacuumlevel, reducing the structure outgassing and condensing someresidual gases (cryo-pumping). The achieved vacuum levelis constantly below the sensitivity of our measurement gauge(<10−7 Pa).

Outside the drift tube, a 1 m long solenoid generates themagnetic C-field, typically 150 nT in ITCsF2. A long verticalcoil placed inside the C-field solenoid is used to excite a low-frequency magnetic field orthogonal to the atomic trajectory,driving Majorana transitions at 540 Hz between |F = 3, mF =0〉 and |F = 3, mF = ±1〉 states, as will be described insection 3.2. These transitions are exploited to map and monitorthe magnetic field. The interaction region is shielded by theexternal magnetic fields through three layers of µ-metal; thetwo innermost shields are located in the cold region (insidethe cryostat), the third is at room temperature (outside thecryostat). The uniformity and the stability of the magneticfield are discussed later, when the evaluation of the Zeemanshift is described.

The vertical alignment of the fountain is guaranteed bythe mechanical construction with respect to a reference planewith 0.05 mrad uncertainty. The reference plane alignment isthen set horizontal with a high quality level with 0.125 mradresolution.

2.2. Laser set-up

The complexity of the accuracy evaluation of a PFS needsa very reliable optical set-up to allow long measurementcampaigns.

The optical set-up was designed to control all the relevantparameters for optimal atomic manipulation, and to allow long-term operations without maintenance and optics realignment.The latter is aided by good temperature stabilization of thelaboratory hosting ITCsF2.

The optical set-up is based on a MOPA system consistingof a 150 mW DFB diode laser and a tapered amplifier:frequency stabilization is accomplished by locking the laser tothe Cs saturated absorption crossover dip between F = 4 →F ′ = X45, which is 125 MHz red detuned compared with thecycling transition F = 4 → F ′ = 5 used for Cs cooling.

The transition is observed with a modulation transfertechnique where the saturating beam is shifted by −80 MHzand the frequency shift key (FSK) is modulated with anacousto-optic modulator (AOM); in this way, the laserfrequency is 165 MHz red detuned compared with the cyclingtransition. The successive double-pass AOM stages, usedto realize the six molasses trapping beams, add +160 MHz,achieving a total red detuning of a few megahertz, as neededfor optimum Doppler cooling. A PC controlled digital looppermits very long-term reliable operation of the master laser.

The master laser power is split into two beams: the firstis used to generate the detection beams, the second to seed thetapered amplifier. The MOPA output is then coupled into a PMfibre to avoid a long air path across the optical table and to filterthe MOPA mode, which is far from being Gaussian. At the fibreoutput, 220 mW of laser light is split to feed six double-passAOM systems [23] corresponding to the six laser beams usedfor the molasses generation. Reshaping the laser beams afterthe fibre with Galilean telescopes allows for optimal couplingwith the AOMs attaining 70% efficiency in the double pass.The light is then injected into six polarization maintaining (PM)fibres and delivered to the collimators; the overall efficiency ofeach branch is ≈55%, resulting in an output power of 15 mWon each fibre.

A commercial extended cavity diode laser locked on theCs F = 3 → F ′ = 4 transition is used as repumping laser.

The optical bench design was conceived for a continuousactive control of the power of the six laser beams. In fact, for anaccuracy target in the low 10−16 region, a repeatable numberof loaded atoms is highly desirable for precise density shiftmeasurements. Six independent active servo systems (100 kHz

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Figure 3. Amplitude noise spectrum of a molasses laser beam, withand without the power servo system.

bandwidth) stabilize the laser beams’ power, and implementthe laser amplitude ramps during the post-cooling process aswell. Figure 3 shows the laser amplitude noise spectrum, withand without the servo system.

The spatial direction of each molasses beam is pre-alignedby the physical design of the trapping chamber. Given themechanical design, minimum tilt adjustment is required toproperly align the trapping beams. Micrometric screws allowa fine adjustment of the beams. The collimators, shown infigure 4, use the natural divergence of the fibre output, anda single plano-convex lens to generate a collimated Gaussianbeam of 25 mm diameter (at 1/e). Polarization optics are placedinside each collimator to improve the quality of the beamsand to reduce the cross-talk between each pair of counter-propagating beams in the power control system.

A first polarizing beam splitter cube converts thepolarization noise introduced by the PM fibre into AM noise.Then a pick-off optic sends a fraction of the beam to a largearea photodiode, which is used to stabilize and control thelaser power during the fountain cycle. A linear film polarizer(absorber) is placed along the beam to minimize the counter-propagating beam light impinging on the detector used in thelaser power control loop.

A fixed collimator is used to deliver the repumper lightinto the trapping chamber and no power servo is used in thiscase.

Figure 5 shows the relative stability of the detected TOF.The shot-to-shot atom number stability is better than 3% andin the long term better than 1%; to achieve this stability thedetection beam power is stabilized with an electronic servosystem similar to that of the trapping beams.

2.3. Operation of the primary frequency standard

ITCsF2 is operated with two distinct software packages: thefirst one drives the pattern generator and the direct digitalsynthesizer (DDS) parameters for the various AOMs, thesecond drives the fountain cycle, the TOF signal digitalization,the clock frequency lock loop and all the other clock

Figure 4. Schematic of the laser collimators.

1 10 100 1000 10000 100000 10000001E-3

0,01

0,1

Relative signal

Ove

rlapp

ing

Alla

n D

evia

tion

Time /s

Figure 5. Stability of the TOF signal from the detection.

configuration parameters (i.e. the pattern generator cycle,the microwave power, the amplitude ramp for post-cooling,the measurement time, the elapsed time among magneticfield sampling). This architecture allows high flexibilityin choosing the proper differential measurement sequences,permitting the concatenation of an arbitrary number of differentconfigurations in a recursive cycle.

Considering the hardware, a PC board is used as the mainboard for I/O signal, whilst a second home-built system [24]contains the pattern generator and six DDS modules, used todrive the trapping and the detection AOMs.

As a result, during the accuracy evaluations the frequencyof the H-maser (HM) reference has been measured sometimesfor more than 20 days, with a dead time of only a few hours.

The operation cycle of ITCsF2 is similar to that of otherfountains. A variable number of atoms is first captured in a(1,1,1) molasses for a loading time ranging from 150 ms to600 ms, and then transferred in a vertical moving frame, witha velocity of 4 m s−1 to 5 m s−1. In this new frame, atomsare further cooled with the Sisyphus cooling mechanism to atemperature of the order of 1 µK; atoms are then released fromthe molasses in the free flight trajectory. A microwave stateselection is implemented before entering the Ramsey cavity: amicrowave π pulse transfers the atoms from |F = 4, mF = 0〉to |F = 3, mF = 0〉. A subsequent light pulse removesfrom the cold atom cloud the remaining atoms in the F = 4manifold; all lasers are then switched off by the AOMs andthe mechanical shutters, before the Ramsey interaction begins.Atoms pass the Ramsey cavity with a speed of ≈2 m s−1 and

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0,030 0,032 0,034 0,036 0,038 0,040

0,0

0,5

1,0

1,5

2,0

2,5

200 ms 600ms TOF difference

Time /s

Det

ecte

d si

gnal

/a.u

.

0,0

0,1

0,2

0,3

0,4

0,5

TO

F d

iffer

ence

0,860 0,865 0,870 0,875 0,880 0,885 0,890

0,00

0,01

0,02

0,03

200 ms 600 ms TOF difference

Time /s

Det

ecte

d si

gnal

/a.

u.

0,000

0,005

0,010

TO

F d

iffer

ence

(a)(b)

Figure 6. TOF signals at high and low density on the way up (a) and on the way down (b). Once renormalized, the difference between thetwo signals is very small.

reach the apogee of the ballistic flight approximately 40 cmabove the Ramsey cavity; on the way down they pass again inthe Ramsey cavity for the second interaction before leaving thecold part of the fountain and entering the detection chamberwhere the transition probability is measured as previouslydescribed.

3. Accuracy evaluation

In this section of the paper, the accuracy budget is discussed,i.e. the measurement of the magnitude and the associateduncertainty of the different physical effects that limit thefrequency accuracy of the PFS.

3.1. Atomic density shift

As is well known, collisions between cold atoms produce arelevant shift on the clock transition and, if the time evolutionof the atomic cloud is independent of the initial density, thisshift is linearly proportional to the atomic density.

To evaluate this shift we vary the number of launchedatoms and accomplish a differential frequency measurementbetween two different states: high and low density [6]. Whenoperated at a high density the short-term stability of ITCsF2 istypically 2 × 10−13τ−1/2, whilst at a low density the stabilityis typically reduced by a factor of 2.

Among several possibilities, we chose to change thenumber of atoms by setting different loading times. The mostimportant advantage of this choice is the shorter clock cycletime in the low-density regime, allowing then a better stability.However, to ensure the linearity of the method, it is necessary toverify that the shape and the initial position of the molasses donot change between the two states. This is done by recordingthe TOF signal on the way up and on the way down for differentloading times. The high- and low-density TOFs taken onthe way down are statistically indistinguishable, while thoserecorded on the way up show a maximum difference below1%, indicating that the time evolution of the molasses doesnot change to a significant level between the two conditions.The recorded inhomogeneity causes a maximum uncertaintyin the evaluation of the density shift of 1 × 10−17, making itcompletely negligible with respect to the statistical uncertainty.Figure 6 shows the recorded TOFs and their differences.

51 52 53 540,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Pro

babi

lity

Frequency (-9192631770) /Hz

600 ms load 200 ms load

52,8 53,00,4

0,5

0,6

Figure 7. Details of the 30th fringe frequency recorded with thefountain operated at high and low densities. In the inset thefrequency displacement is magnified.

Also the position of the molasses slightly depends onthe loading time; using the high sensitivity of the Ramseyspectroscopy, this effect has been precisely measured. Figure 7shows the displacement of the 30th fringe corresponding to achange in the Ramsey time of 100 µs. Assuming the launchingvelocity to remain constant, the change in the initial positionof the molasses barycentre measures 0.1 mm. The increasein the loading time moves the barycentre of the molasses upslightly; however, this small change produces no significantnon-linearities in the density evaluation. Considering, forexample, the value of the Zeeman frequency shift due to thedifferent trajectories of the atoms in the magnetic field profile,the frequency shift among the two situations is less than 10−18.

Another effect that depends on the number of atoms isthe first-order cavity pulling [25]. However, this effect is alsolinear with the atom number and hence the extrapolation to‘zero density’ is accomplished together with the density shift.The theoretical magnitude of the cavity pulling (as shown lateron) is 10−17.

To obtain the best uncertainty, the zero density shiftextrapolation is evaluated with data collected over a whole TAIevaluation (typically 20 days), together with the historical data

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0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4-1,2x10-14

-8,0x10-15

-4,0x10-15

0,0

4,0x10-15

8,0x10-15

1,2x10-14

Rel

ativ

e F

requ

ency

TOF signal a.u.

Figure 8. Frequency measurement at high and low densities. Theatomic density is changed by setting the molasses loading timeeither at 200 ms or at 600 ms. The HM drift is removed.

collected during previous evaluations. In ITCsF2, we haveobserved that the detected TOF stability is better than 1% forextended periods of time, allowing a good coherence in thehistorical data set.

When the fountain is at a low density, the average densityshift relative to the caesium clock frequency νCs is typically

δνcoll

νCs= (−3.2 ± 1.3) × 10−16

whilst when the fountain is in the high-density regime the shiftis three time larger. In figure 8 we report the result of thefrequency measurement of one of our HMs, taken alternativelyat high and low densities for a period of 20 days. The driftof the maser is removed considering the low-density datasetalone; the red line is the result of a weighted linear fit. Theintercept uncertainty in the fit is 5 × 10−16; it is worth notingthat to improve the fountain accuracy high- and low-densityfrequency measurements are accumulated for longer times (upto 80 days of measurement).

3.2. Magnetic field

The Zeeman effect induced by the C-field is measured andcontrolled at the desired uncertainty level by a careful mappingof the C-field and by constant monitoring of its average value.

A shielding test has shown an attenuation of the externalmagnetic field of about 30 000 on the orthogonal direction ofthe C-field and of 2000 on the parallel axes.

Once the atomic sample is state selected, so that all theatoms are in the |F = 3, mF = 0〉 state, the magnetic field mapis obtained by exciting the low-frequency Majorana transitions|F = 3, mF = 0〉 → |F = 3, mF = ±1〉, figure 9(b). Thedetection of the transition probability is performed as usual,since during the second passage of the atoms in the stateselection cavity, only the atoms remaining in |F = 3, mF = 0〉are driven in the F = 4 state.

A short low-frequency pulse (100 ms) is applied when theatoms reach their apogee and the Rabi transition probabilityis measured. This measurement gives a local value of themagnetic field, since during the interaction time the atoms

sample a region of a few centimetres around the apogee. Byvarying the launch velocity, and with the proper timing of thelow-frequency pulse, it is possible to map the field along mostof the interaction region.

Once the map of the magnetic field is recorded, it is usedto predict the frequency of the central Ramsey fringe of themagnetically sensitive transition |F = 4, mF = 1〉 → |F =3, mF = 1〉 at arbitrary launching heights. This Ramseypattern is then recorded and the prediction given by the C-field map is used to identify unambiguously the central fringeof the |F = 4, mF = 1〉 → |F = 3, mF = 1〉 transition; itsfrequency is used to calibrate the Zeeman shift on the clocktransition.

The measured position of the Ramsey pattern centralfringe in the |F = 4, mF = 1〉 → |F = 3, mF =±1〉 transition agrees with the prediction at the level of200 mHz; the identification of the central fringe is thereforeunambiguous.

Since a first-order magnetically sensitive transition isused to determine the Zeeman shift in the clock transition,which instead has a second-order sensitivity, an additionalcontribution to the bias uncertainty is the difference �B

between the time average of the squared magnetic field B andthe square of the time-averaged field:

�B = 1

T

T∫0

B2(t) dt − 1

T

T∫0

B(t) dt

2

(1)

where T is the Ramsey time, as the time averaging of themagnetic field is performed on the atomic trajectory.

From the analysis of the recorded C-field map, shown infigure 9(a), the difference is �B ∼ 6.5 × 10−18 T2; usingthe sensitivity coefficient of the second-order Zeeman shift(427.45×108 Hz T−2), the contribution to the bias uncertaintyis <3 × 10−17.

This method is quite precise but requires several hoursof measurement time. Hence it can be used to monitorthe Zeeman shift from time to time, but it is not suitedto monitoring its value continuously, as is necessary duringfountain operation. In fact, we have seen slow fluctuationof the C-field as well as daily fluctuations and seldom moresignificant changes of the field that could possibly harm theaccuracy of the standard, resulting in a wrong assignment ofthe central fringe of the Ramsey pattern. To avoid this problemand to keep track of the magnetic field on a shorter time scale(typically a C-field measurement is performed every 2500 s),a low-frequency transition can be exploited.

Instead of a short pulse applied when the atoms areat apogee, the |F = 3, mF = 0〉 → |F = 3, mF =±1〉 transition can be excited continuously during the wholeballistic flight, so a good representation of the time-averagedvalue of the magnetic field is obtained. This method has thefundamental advantage that only one peak is present in thespectrum, avoiding any ambiguity of determining the centralfringe in the Ramsey pattern. However, this value cannotbe used directly to correct the bias, since the low-frequencyfield amplitude generated by the long vertical coil is nothomogeneous enough for a high-accuracy measurement.

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Metrologia 51 (2014) 270 F Levi et al

Figure 9. (a) Map of the C-field of ITCsF2, (b) plot of the low-frequency transition probability.

56200 56220 56240 56260154,0

154,5

155,0

155,5

156,0

Mag

netic

fiel

d /n

T

Time/ MJD

Figure 10. C-field amplitude measured with a Majorana transition,recorded over three months of ITCsF2 operation. The fastoscillations are observed on a daily period. Abrupt field changes ofunknown origin, like the one observed at MJD 56206, are wellmonitored with Majorana spectroscopy.

Nonetheless, for small fluctuations of the magnetic field,an excellent linearity was observed between the magneticfield value measured with Ramsey spectroscopy and theMajorana measurement; once calibrated, the latter allows oneto precisely track the field variations. The calibration betweenthe Majorana measurement and the Ramsey central fringevalue in the magnetically sensitive transition is periodicallyrepeated with a full map process.

Figure 10 shows the value of the central frequency ofthe Majorana transition, whilst figure 11 reports its frequencystability. In figure 10 a daily fluctuation of the average fieldwith a peak-to-peak amplitude of 100 pT is evident; moreover,rarely abrupt field variations occur, as large as 0.2 nT,uncorrelated with the recorded environmental parameters.

As said, the C-field is monitored with a period of 2500 s:at this measurement time, the stability of the magnetic field isaround 0.05 nT; considering a C-field value of 1.5 × 10−7 T,this results in an uncertainty on the clock transition frequencyof 0.7 × 10−16.

1000 10000 100000 10000001E-11

1E-10

Relative signal

Ove

rlapp

ing

Alla

n D

evia

tion

/ T

Time /s

Figure 11. Long-term stability of the time-averaged magnetic field.

Combining all the contributions, the total uncertainty forthe magnetic field correction is 0.8 × 10−16.

Therefore, the second-order Zeeman bias δνZ relative tothe caesium clock frequency νCs is

δνZ

νCs= (1075.0 ± 0.8) × 10−16.

3.3. Blackbody radiation

The blackbody radiation shift is strongly reduced inITCsF2 compared with other PFS, because of the cryogenictemperature of the interaction region. As discussed in thephysical package description, the temperature is measured withthree Pt-100 sensors, one placed between the state selectionand the Ramsey cavities, a second 50 cm above, near the atomapogee, and a third at the top of the drift tube.

The interaction region of ITCsF2 is, to a goodapproximation, a blackbody radiator. In fact, there isonly a single aperture to the external environment at roomtemperature, that is the lower hole of the state selectioncavity, 10 mm in diameter. Moreover, the structure designis conceived to strongly reduce the radiation propagation at

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Metrologia 51 (2014) 270 F Levi et al

Analog

Loop

Maser

Analog

Loop

BVA

X4 X5 DRO

SSB20MHz 100MHz

5MHz

9.2GHz

9.1926…GHz

DDS

7.369…MHz

Digital control/FSK

X4 X5 DRO

DDS

Figure 12. Scheme of the synthesis chain used in ITCsF2.

low reflection angles within the drift tube. This implies thatcaesium atoms interact with the room temperature radiation ata very small solid angle. For an atom in the Ramsey cavity, thebottom aperture to the external environment is a diaphragm of1 cm diameter at a distance of 10 cm, corresponding to a solidangle of 6 × 10−4 sr. Rising along the drift tube, this solidangle further decreases to 4 × 10−5 sr at the apogee [26].

The average temperature in the drift tube is 89.4 K, stablewithin 100 mK. The thermal gradient along the tube is <2 K,which is also considered as the temperature uncertainty.

The blackbody radiation shift δνBBR relative to the clocktransition frequency νCs is evaluated using the well-knownrelation

δνBBR

νCs= β

(�

300

)4[

1 + ε

(�

300

)2]

(2)

where� is the blackbody temperature, β = −1.718(3)×10−14

[27] and ε = 1.3(1) × 10−2 [28]. As the thermodynamictemperature of the ITCsF2 drift region is � = (89.4±2) K, theblackbody radiation shift is (−1.36 ± 0.09) × 10−16. Takinginto account the small solid angle aperture to the externalenvironment at room temperature (296 K), the final bias is

δνBBR

νCs= (−1.45 ± 0.12) × 10−16.

3.4. Gravity

The elevation of INRIM’s laboratory was accurately measuredin 2007 during a levelling campaign reported in [29].

The atom apogee in ITCsF2 has an orthometric elevationh = (238.71 ± 0.10) m on the Geoid. As the INRIM siteis located at 45◦00′54.467′′ N latitude and 7◦38′21.842′′ Elongitude, the relative frequency sensitivity to the orthometricheight is 1.0911×10−16 m−1, evaluated from the local absolutegravity acceleration on the Geoid, g = 9.806 32(1) m s−2. Thefrequency shift δνG relative to the caesium clock frequency νCs

for ITCsF2 integrated along the free flight trajectory is

δνG

νCs= (260.4 ± 0.1) × 10−16.

3.5. Microwave generation and related shifts

The design of the microwave synthesis and the distribution andthe assessment of its spectral performances are a relevant issuefor a microwave PFS. In fact, the microwave related shifts arethe main contribution to ITCsF2 uncertainty.

In a proper design, spurious components of the microwavespectrum must be negligible; also microwave leakage fromthe synthesizer during the atom free flight must be avoided;any modulation of the microwave frequency must not produceany thermal transient resulting in a microwave phase variationbetween the first and the second Ramsey pulses; the Dick effectmust be minimized.

The microwave synthesis chain was designed taking intoaccount the previous requirements [30]. Its scheme is shownin figure 12. Starting from the 5 MHz generated by a BVAquartz phase locked to a HM, a direct synthesis scheme,which uses two multiplication modules (×4 and ×5), producesthe intermediate 100 MHz frequency. A dielectric resonantoscillator (DRO) provides the 9.2 GHz carrier, phase lockedto the 100 MHz signal. Thereafter, to obtain the 9.192 Csfrequency, a single sideband mixer (SSB) subtracts from thecarrier the 7.4 MHz signal generated by a DDS. Two identicalsynthesizers were developed, one for the Ramsey excitationand one to feed the state selection cavity.

The measured spectrum is shown in figure 13. Undesiredshifts from spurious components are excluded, since the onlydetected components are at 50 Hz and its harmonics, whosepower is highly symmetric with respect to the carrier. Thepresence of spurs very close to the carrier, possibly comingalso from the fountain cycle, can be observed by detectingthe spectrum of the beat note between the two independentsynthesis chains. No spurious lines were detected except the50 Hz harmonics.

Figure 14 shows the stability of the synthesis chain interms of the overlapping Allan deviation. In the medium term,the stability is limited by the temperature phase sensitivity ofthe first multiplication stage.

Microwave leakage is always present to a certain levelin fountain clocks. To reduce it as much as possible and toensure that the resonant microwave radiation interacts with

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Metrologia 51 (2014) 270 F Levi et al

-200 -100 0 100 200

-100

-80

-60

-40

-20

Pow

er /d

Bm

Frequency - 9192631770 / Hz

Figure 13. RF spectrum of the synthesized microwave.

0,1 1 10 100 1000 100001E-17

1E-16

1E-15

1E-14

1E-13

Ove

rlapp

ing

Alla

n de

viat

ion

Time /s

Figure 14. Frequency stability of the synthesizer, measured bybeating two identical systems (two chains are used, one for Ramseyspectroscopy and the other for the state selection).

the atoms only during the Ramsey interaction, once the atomsexit the cavity after the downward passage, the microwave isdetuned using FSK modulation. FSK modulation is applied tothe DDS; thus, no power change is induced in the SSB-mixer,avoiding the phase rotation due to temperature transients. FSKmodulation is also applied to the state selection synthesizerimmediately after the state selection Rabi pulse.

Following the work reported in [18], ITCsF2 has beentested at varying microwave power and under differentexperimental conditions.

Depending on the shape of the atomic cloud and on itsconvolution with the microwave field inside the Ramsey cavity,identical fields can produce different transition probabilities.Since several bias analyses on microwave sensitivity areperformed at precise pulse amplitudes (π /2, 3π /2, 5π /2, etc),it is necessary to calibrate the pulse amplitudes. However,since the spatial expansion of the atomic cloud between thefirst passage and the second is significant, the same pulse cancause different transition probabilities on the two passages.

To calibrate precisely the pulse amplitude seen by theatoms during the Ramsey spectroscopy, a single microwave

0,00 0,15 0,30 0,45 0,600,0

0,2

0,4

0,6

0,8

1,0

Rabi pulse way upRabi pulse way down Probability difference

Excitation amplitude / a.u.

Tra

nsi

tion

pro

ba

bili

ty

-0,4

-0,2

0,0

0,2

0,4

Pro

ba

bili

ty d

iffe

ren

ce

Figure 15. Transition probability with an exciting pulse of variableamplitude applied either on the way up or down (left vertical scale).The blue line (right vertical scale) represents the excitationprobability difference.

pulse (instead of the two pulses used during the standardinterrogation) was applied to the atoms only when they wererising or when they were descending inside the cavity. Adifference in the transition probability was observed and itis shown in figure 15 for different values of the microwavepulse amplitude. Whereas Rabi oscillations are evident, aslight difference in the transition probability is observed at anygiven excitation amplitude between the upward and downwardcavity passage. The higher the microwave power, the largerthe difference. Therefore, to avoid any ambiguity in settingthe given pulse amplitude we decided to scale it proportionallyto π /2 pulse amplitude and not to measure the transitionprobability.

3.6. Microwave leakage

Two different kinds of microwave leakages may be present ina fountain frequency standard.

The first kind is typically created by a leakage fieldpresent in the drift tube and then occurs between the twoRamsey interactions; this leakage is almost symmetric becauseof the trajectory path reversal and generally causes a smallfrequency shift. The second one happens when a microwavefield is present before or after the Ramsey interaction, and it ishence intrinsically asymmetric, causing a larger shift. ITCsF2implements several design solutions to reduce the overallleakage present inside the drift tube and thus experienced bythe atoms during their free flight time. The Ramsey cavitybody is joined to the drift tube by a cylindrical below cut-offwaveguide, 5 cm long and 1 cm in diameter, that provides anominal attenuation of 150 dB [15]. On the top of the drifttube a second below cut-off waveguide is present, with anattenuation of ≈30 dB. The low attenuation of the latter isprobably a limitation and a replacement is planned to get ahigher attenuation.

The presence of leakage can be observed by measuring thefrequency shift of the clock transition at pulses �= (2n + 1)π/2.As described in [15], this type of leakage has a linear frequencysensitivity around the optimal excitation amplitude, shown in

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Metrologia 51 (2014) 270 F Levi et al

0 1 2 3 4 5 6260

280

300

320

340IT

CsF

2 -H

M3

/10-1

5

Ramsey Pulse Amplitude /π/20 1 2 3 4 5

159

160

161

162

163

164

ITC

sF2-

HM

3 /1

0-15

Ramsey Pulse Amplitude / π/2

(a) (b)

Figure 16. Relative frequency sensitivity to the excitation field. (a) Pulse amplitude varied around the nominal value, (b) pulse amplitudeset to maximize the transition probability.

Table 1. Power sensitivity around optimal excitation pulses.

Pulse amplitude DDS amplitude/mV Slope/(10−15 mV−1)

π /2 39.9 0.085 ± 0.0813π /2 119.7 0.37 ± 0.075π /2 199.5 0.55 ± 0.06

figure 16(a). Table 1 reports the measured slope at variousexcitation pulses, which are found to be proportional to thepulse amplitude within the stated uncertainty.

Note that it is incorrect to compare the data at variouspulses amplitudes of figure 16(a). In fact, differentialmeasurements were separately performed around π /2, 3π /2and 5π /2. Between different datasets there is a temporalseparation ranging from several days to a few weeks. Inthese periods, the maser drift is accumulated and only roughlycorrected. For this reason, a separate differential measurementwas made at nominal pulse amplitudes (2n − 1)π/2, asreported in figure 16(b).

To confirm that the shift measured is consistent with thepresence of leakage during the Ramsey time, the measurementof figure 16(a) was repeated by inserting in the microwavefeeding line an interferometric switch [16], which can attenuatethe microwave output between the two Ramsey interactions by50 dB, without significant effects on the microwave phase atthe 10−15 level. As expected, the shift amplitude was reducedby one order of magnitude. Nevertheless, the switch is notused during normal fountain operation because it is not yetfully characterized at the microradian level.

The measurements of figure 16(b) were interpolated withthe function δν/ν ∝ nsin(nπ/2). The behaviour describedby the previous function is valid not only for the microwaveleakage, but also for other effects like the lensing effect[17] and, partially, the distributed cavity phase (DCP) shift.According to the experimental data reported in figure 16(b), thefrequency shift δνleak relative to the caesium clock frequencyνCs for ITCsF2 is

δνleak

νCs= (−2.0 ± 1.5) × 10−16.

3.7. DCP shift

Another effect that may limit the accuracy of fountain PFS isthe DCP shift.

The DCP shift is caused by the microwave power flowingin the cavity. Specifically, due to losses in the cavityconducting walls, a small travelling wave is superimposedon the standing wave defining the electromagnetic mode.This travelling wave is responsible for a spatially varyingphase shift, so that different atomic trajectories interact witha different phase, resulting in a shift that affects the clockfrequency.

From a mathematical point of view, the magneticcomponent H(r) of the electromagnetic mode can be writtenas

H(r) = H0(r) + (�ωC/ + i)g(r)/(1 + �ω2C/2) (3)

where H0(r) represents the standing wave satisfying theboundary conditions of a perfect conductor for a well specifiedmode (TE011 in ITCsF2), g(r) is a small dissipative field, isthe half-width of the cavity profile at half-maximum and �ωC

is the cavity detuning from the clock frequency. A similarexpression holds for the electric field component.

The source of the DCP shift is g(r) that is weightedby the cavity profile, as shown in equation (3). As alreadymentioned in the physical package description �ωC is ≈4

for ITCsF2. Consequently, the imaginary component of thefield responsible for the DCP shift is reduced compared withthe situation of the on-resonance cavity (see equation (3)).However, we notice that in the off-resonance case more poweris required to flow into the cavity to excite the mode of interestto a given level (namely to produce π /2 pulses). Also, thedegenerate mode TM111 may play a significant role in theevaluation of the DCP shift in the off-resonance cavity, evendespite the presence of mode chokes.

However, we can state that, in general, the high qualityfactor (45 000 for ITCsF2) compensates to a good extent thedrawbacks of the higher driving power compared with what isreported in other Cs fountains [4, 7, 8, 18].

To gain physical insight into the evaluation of the DCPshift, we consider the approach reported in [18, 19] in which

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Metrologia 51 (2014) 270 F Levi et al

-2,50 -1,25 0,00 1,25 2,50

-12

-8

-4

0

4

8

12 π/23π/2 5π/2

left-

right

rel

ativ

e fr

eque

ncy

shift

(10

-15 )

North-South tilt / mrad

-2 -1 0 1 2

-15

-10

-5

0

5

10

15 π/23π/25π/2

left-

right

rel

ativ

e fr

eque

ncy

shift

(10

-15 )

East-West tilt angle (mrad)

(a) (b)

Figure 17. Frequency sensitivity to vertical tilting of the fountain: (a) tilt orthogonal to the feedings, (b) parallel to the feedings. The linesrepresent a weighted linear fit of the data.

g(r) is expressed in terms of an azimuthal Fourier modalexpansion:

g (r) =∑m

gm(ρ, z) cos(mφ). (4)

The modal expansion (4) converges rapidly and it is sufficientto analyse the first three terms m = 0, 1, 2.

The m = 0 mode is not generally expected to give asignificant DCP shift when the cavity is fed symmetricallyand the symmetry breaking between the two passages is keptlow; the ITCsF2 cavity has four feeds evenly spaced on theequatorial plane and, moreover, the high quality factor reducesthe power flow to the walls. Another element that helps inreducing the m = 0 magnitude is the size of the loadedmolasses (φ = 13 mm at 1/e). The launched molasses cloudis cut by the cavity holes already on the way up, so thatquite similar cavity volume is sampled on both Ramsey cavitypassages.

The effect of the m = 1 mode produces a DCP shift sincethe average trajectories of the atoms and the phases of the fieldon the two passages are different. According to the analysisreported in [31, 32], the effect of this modal component hasbeen tested by enhancing the asymmetry of the feeding systemand by measuring its effect on the clock transition for differentvertical tilting of the fountain with respect to the perpendicular.

The ITCsF2 cavity is fed by four irises placed at 90◦ onthe equatorial plane; the irises are fed two by two by meansof an external waveguide cavity lying on the external wall ofthe Ramsey cavity [22]; two irises on the north side of thefountain are fed by the same waveguide cavity, and similarly,the other two irises on the south side by a second waveguide.This feeding method guarantees ‘by construction’ a quite goodphase and amplitude balance on each pair of irises fed by thesame waveguide and allows one to balance the two pairs usingan external attenuator and a phase shifter.

The overall phase and amplitude balance is set at 1 mradin phase and at 0.01 dB in amplitude. Both settings are doneby minimizing the difference of the atomic response to a fullyasymmetric feeding.

As reported in [31], a high sensitivity measurementconsists in the analysis of the difference between ‘North’ and‘South’ feeding at increasing power and different tilting, wherethe ‘North’ direction is identified by one pair of feeds andthe ‘South’ direction by the other pair. We performed thismeasurement by tilting the fountain on the North–South axisand on the East–West axis. Figure 17 shows that the tiltingsensitivity at the optimum power (π /2) on North–South axis is(0.2 ± 0.2) × 10−15 mrad−1, whilst on the East–West axis thesensitivity measures (1.2 ± 0.5) × 10−15 mrad−1.

The fountain is perpendicular to both axes within0.125 mrad by construction, but the measured tilt sensitivityallows one to state that the system is vertically aligned at thelevel of 50 µrad. The power balance between left and rightfeedings is better than 1% and the maximum shift due to thecombined effect of vertical misalignment and the m = 1 modeof the DCP field expansion is <1 × 10−17.

Another test was done at 3π /2 with symmetric feeding,and fountain tilting on the North–South axes. It did not producea measurable shift at the level of δνDCP/νCs = (0.03 ± 1.2) ×10−15 mrad−1. Also this value confirms that the maximumexpected shift coming from the m = 1 term of the modeexpansion is <1 × 10−17 when the fountain is operated at π /2.

According to the theory developed in [31], thesemeasurements also provide an independent evaluation of therelative phase difference ϕ between left and right feeding lines:

�νC

tan(ϕ) = Sym(2ϕ) − 1

2 (Asym1 + Asym2)

Asym1 − Asym2(5)

where Asym1 (Asym2) is the frequency shift when feedingonly from one side (from the other side) and Symrepresents the clock frequency measurement when feedingwith the two lines together (Sym = (Asym1 + Asym2)/2).The measurements from the DCP shift characterizationgive ϕ = (0.026 ± 0.023) rad. This result agrees with anindependent measurement of ϕ, obtained by observing thefrequency of the Ramsey central fringe when an asymmetricpulse is applied on the North feeding on the way up and on theSouth feeding on the way down (and vice versa).

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Metrologia 51 (2014) 270 F Levi et al

The contribution to DCP of the m = 2 mode is expectedto be highly suppressed by the ITCsF2 feeding geometry (fourfeeds). This is probably the larger difference between a cavitywith two and four feedings with respect to DCP shift.

In conclusion, the total shift δνµW/νCs associated withmicrowave imperfections, leakages and DCP is

δνµW

νCs= (−2.0 ± 1.5) × 10−16.

3.8. Cavity pulling

Since the ITCsF2 Ramsey cavity is operated off-resonance, thecavity pulling effect is reduced.

Considering the second-order cavity pulling, the biasδνCP2 relative to the caesium frequency νCs is described bythe formula [33]

δνCP2

νCs= f (�νC)

1

νCs

8

π2

(QL

QA

)2

bτ cot (bτ) (6)

where �νC is the cavity detuning, QL the cavity loadedquality factor, QA the atomic transition quality factor, b theRabi frequency, τ the Rabi time, and f (�νC) is a functiondescribing the dependence of the shift on the cavity detuning.Even not considering the analytical expression of f (�νC), itis well known [33] that f (�νC) has a dispersive shape andexhibits extreme values for �νC = ±, being the half-width of the cavity. Thus, a conservative evaluation of thecavity pulling is obtained using the linearization of f (�νC) atthe maximum value for �νC = ±, that is |f (�νC)| = .

In ITCsF2, the optimal excitation power is set within1% uncertainty, therefore using equation (6) the second-ordercavity pulling is <3 × 10−17.

On the other hand, the first-order pulling effect, due to thestimulated emission of the atoms inside the cavity, is linearwith the atom density. Hence, it is evaluated together with theatomic density shift. An estimate of its magnitude, however,gives a quite low absolute value. According to the calculationsmade in [34], the first-order cavity pulling δνCP1 can be writtenas

δνCP1

νCs≈ − 2

hµ0µ

2Bη′nτ

QL

QAcos(bτ)

�

1 + �2(7)

where h is the Planck constant, µ0 is the vacuum permeability,µB is the Bohr magneton, η′ is the cavity filling factor, n isthe atomic density, τ is the Rabi time and � is the normalizedcavity detuning � = 2QL�νC/νCs.

In ITCsF2, the filling factor, deduced from [35], is ∼0.1,the density is of the order of 105 atoms cm−3, and � is 8; thus,δνCP1/νCs < 2 × 10−17.

3.9. Other shifts

The background gas pressure in the fountain UHV regionis below 1 × 10−7 Pa. In the Ramsey interaction region,as a result of the cryo-pumping process, the pressure isexpected to be even lower. According to the pressure shiftcoefficients reported in the literature [36, 37] for the most

Table 2. Accuracy budget of ITCsF2.

Physical effect Bias/10−16 Uncert./10−16

Zeeman effect 1075.0 0.8Blackbody radiation −1.45 0.12Gravitational redshift 260.4 0.1Microwave leakage −2.0 1.5DCP — 0.2Second-order cavity pulling — 0.3Background gas 0.5Total type Ba 1.9Atomic density (typical LD)b −3.2 1.3Total 1328.75 2.3

a All other effects not reported here are estimated to have amagnitude <10−17.b The density bias changes from run to run depending on thetype of differential measurement performed and on the lengthof the measurement.

common background gas the frequency bias is expected to be<5×10−17.

Spectroscopy of the |F = 4, mF = 0〉 → |F = 3, mF =±1〉 and |F = 4, mF = ±1〉 → |F = 3, mF = ±1〉transitions shows a highly symmetric pattern (asymmetry iswithin the measurement uncertainty), indicating that Rabi andRamsey pulling are not a significant bias in ITCsF2.

3.10. Total accuracy budget of ITCsF2

Table 2 summarizes the biases and the uncertaintycontributions of ITCsF2. The total type B uncertainty is1.8 × 10−16 and the type A uncertainty associated with thebias evaluation is 1.3 × 10−16. The combined uncertainty, i.e.the ITCsF2 accuracy, is 2.2 × 10−16.

4. Comparison with TAI

Along with its accuracy evaluation, several frequencycomparisons of ITCsF2 to TAI have been performed. Thecomparison technique is the standard two-way satellite link[38] where a local HM participating in the realization ofUTC(IT) is measured by ITCsF2. These frequency data arecommunicated to the BIPM and used to estimate the frequencyvalue of TAI measured by our fountain.

Figure 18 shows the daily data relative to two successivemeasurements. The PFS is alternatively operated at high andlow atomic densities on a fixed schedule basis, and then thefrequency is extrapolated to zero density. It can be observedthat the drift of the maser is quite stable for extended periodsof time; its value is 6 × 10−16/day.

Figure 19 reports the statistical instability of themeasurement. The typical Allan deviation is σy(τ ) = 2.5 ×10−13τ−1/2.

During the reported evaluation period, the HM (BIPMcode 1401103) was used as the local oscillator. Aftercorrecting the raw data for the biases reported in table 2, theaverage frequency 〈y(ITCsF2-HM3)〉 over the measurementperiod was calculated with a weighted linear fit, with the epochcoordinate origin on the centre of the evaluation interval.

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Metrologia 51 (2014) 270 F Levi et al

56190 56200 56210 56220 56230 56240 562500,00E+000

1,00E-014

2,00E-014

3,00E-014

4,00E-014

5,00E-014

6,00E-014

Fra

ctio

nal F

requency

, IT

CsF

2-H

M1

MJD

Low densityHigh density

Figure 18. Frequency measurement of ITCsF2 fountain versus HM.

1 10 100 1000 10000 1000001E-16

1E-15

1E-14

1E-13

Tota

l Devi

atio

n σ

y(τ)

Averaging time τ /s

Figure 19. Stability of the fountain when operated in thehigh-density regime.

Unavoidable fountain dead (lost) time is present duringthe evaluation and, in principle, the dead time may be neitherevenly spaced nor symmetric with respect to the centre of theevaluation period. Under these conditions, simply averagingthe data would produce a bias of the frequency estimation, thusthe fitting is needed.

A certain amount of dead time is scheduled to monitor theC-field or to implement additional characterizations during themeasurement. The scheduled dead time amounts to 1.5% andit is almost homogeneously distributed.

The choice of a linear model for the maser driftis supported by the experimental observation of itsstability for extended periods of time (typically severalmonths). The uncertainty associated to the average frequency〈y(ITCsF2-HMn)〉 is estimated by the least-squares algorithm.

The dead time in fountain operation (figure 20) introducesa further uncertainty to the frequency comparison. Theestimation of this uncertainty contribution requires theknowledge of the HM noise properties. The stability of the HMcould be modelled in terms of Allan variance as

σ 2y (τ ) = σ 2

yWF (τ ) + σ 2yFF (τ ) + σ 2

yRW (τ )

where σ 2yWF(τ ), σ 2

yFF(τ ) and σ 2yRW(τ ) are, respectively, the

contribution due to the white, the flicker and the random

walk frequency noise. A conservative estimation of thesecontributions is

σyWF (τ ) < 2 × 10−13τ−1/2

σyFF (τ ) < 3 × 10−16

σyRW (τ ) < 2 × 10−19τ 1/2.

The dead time uncertainty is evaluated by implementing thealgorithm reported in [39–41].

TAI is a convenient means to compare ITCsF2 with otherPFS worldwide. Therefore, ITCsF2 data were reported to theBIPM to evaluate the frequency difference between the TAIinterval unit and ITCsF2. At the same time, BIPM used allthe available data provided by PFS to estimate the value ofTAI. Since ITCsF2 is not yet contributing to TAI, this processevaluates the difference between ITCsF2 and the other PFSwithout correlations.

The best estimate of the TAI value is reported monthly inthe Circular T [42]. The results of the comparisons are reportedin table 3, where uA, uB and ulab are the type A, the type B andthe dead time uncertainties respectively; utot is the combineduncertainty, d(ITCsF2-TAI) and d(circT) are, respectively, thefrequency difference evaluated by BIPM and deduced fromCircular T; �d is the difference between the two methods.The values are expressed in fractional 10−15 units.

The four measurements reported in table 3 show goodagreement between ITCsF2 and all the other fountainsparticipating in TAI used to steer its frequency. Withoutknowing the exact weight of the various standards in each TAIcomputation, it is not possible to discriminate between type Aand type B uncertainty and perform an exact statistical analysison �d . Nonetheless, the biases of the fountains’ contributionsto TAI are highly uncorrelated, thus d(circT) has a purestatistical meaning and could be combined with the statisticalcomponent of the fountain, considering fully correlated onlythe type B uncertainty of ITCsF2. The weighted average�d = (−0.17 ± 0.32) × 10−15 is obtained, showing goodagreement between ITCsF2 and the other PFS. During themeasurement periods reported above, BIPM used data comingfrom the PFS NPL-CSF2, SYRTE-FO1, SYRTE-FO2, PTB-CSF1, PTB-CSF2 and NIST-F1.

5. Conclusions

We have reported the accuracy analysis of ITCsF2, the newItalian PFS developed at INRIM. ITCsF2 and its twin NIST-F2 are the first Cs primary frequency standards operating atcryogenic temperature to reduce the magnitude and uncertaintyof the blackbody radiation shift. The overall type B totaluncertainty is 1.9 × 10−16, and the major contribution comesfrom imperfections in the microwave excitation scheme. TypeA uncertainty is related to the density shift evaluation and to themethod used to estimate the average frequency of the flywheelmaser. Its magnitude can change from one measurement toanother and is typically 3 × 10−16. The calibrations of TAIperformed with our fountain compared with those obtained by

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Metrologia 51 (2014) 270 F Levi et al

56232 56234 56236 56238 56240 56242 56244 56246 56248 56250 562520,000

0,025

0,050

0,075

0,100

Dai

ly fr

actio

n of

dea

d tim

e

MJD56392 56396 56400 56404 56408 56412 56416 56420 56424 56428

0,00

0,25

0,50

0,75

1,00

MJD

Dai

ly fr

actio

n of

dea

d tim

e

Figure 20. Epoch distribution of unscheduled dead time during two distinct evaluations (note the different vertical scale).

Table 3. Measurements of TAI performed with ITCsF2; the values are expressed in fractional 10−15 units.

Measurement period uA uB ulab utot d (ITCsF2-TAI) d (circT) �d

56079–56099 0.32 0.32 0.2 0.53 2.38 2.5 ± 0.2 −0.12 ± 0.5756194–56214 0.42 0.21 0.2 0.58 −0.11 −0.2 ± 0.3 0.09 ± 0.6556234–56249 0.31 0.19 0.1 0.52 −0.93 −0.3 ± 0.3 −0.63 ± 0.6056394–56424 0.34 0.19 0.2 0.48 −0.2 −0.3 ± 0.2 0.10 ± 0.52

the fountains of other national metrological institutes are inagreement at the level of 3 × 10−16.

The primary frequency standard described here is amongthe more accurate Cs primary frequency standards developedworldwide.

Acknowledgments

The authors wish to thank S R Jefferts, T P Heavner and E ADonley for their invaluable contribution to the realization ofITCsF2; T E Parker for providing comparison data betweenITCsF2 and NIST standards; E K Bertacco and L Lorinifor their help at different stages of the project; V Pettitifor providing the Maser data and G Petit for providing thecomparison data against TAI.

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