1

BNM-SYRTESystèmes de Référence Temps-Espace

Team implied in Frequency measurementsAndré ClaironEmeric De ClercqSébastien BizeFranck Pereira Do SantosHarold MarionPhilippe LaurentMichel AbgrallIvan MaksimovicJan Grünert

Peter RosenbuschCéline Vian

Contributions of BNM-SYRTE : Contributions of BIPM :Team implied in Time measurementsJoseph AchkarPierre UhrichDavid ValatFrançois TarisMonique ProdhommeIshan IbntaiebPhilippe Merck

Pascal BlondéJean-Yves Richard

Me Félicitas AriasGérard PetitPeter WolfWlodzimierz LewandowskiZhiheng Jiang

CCTF Working Group onTAI 31 mars 2004 Jean-Yves Richard

BNM-SYRTE CCTF WG TAI 2004 2

• Presentation of the Primary Standards at BNM-SYRTE• Results• Uncertainty budget on systematic effects• Accuracy budget and uncertainties of PFS at BNM-

SYRTE• Evaluation of Collision effects • Mean frequency• Statistic uncertainty• Stability comparison FO2 - FOM• Uncertainty due to the dead times• Frequency Comparison F_EAL – F_PFS• Conclusion

3

Optical pumped caesiumbeam clock

4

53015 53020 53025 53030 53035 53040 53045

6,76E-013

6,78E-013

6,80E-013

6,82E-013

6,84E-013

6,86E-013

6,88E-013

6,90E-013

6,92E-013

y(M

aser

805

- FO

2)

MJD

y(Maser805 - FO2)

Date of measurementsIn MJD UTC unit

Uncertaintiestype A & type B of y(H-FO)(t)

NormalizedFrequencydifferencey(H-FO)(t)

Duration of integration

Bu Au maser/linku

0,50,20,8+682,5753014 – 53044

Y(Maser – FO2)Period MJD(30 days)

Results of calibration. (scale is in 1 x 10-15).

Systematic Uncertainty Statistical uncertainty

Uncertainty on theLink between

Maser & atomic Clock+ Uncertainty

due to the dead time

Mean value of y on the entire period of integration

9 Januaryuntil 9

February2004

MJDstop

MJDstartFOHy )( −

5

Correction

[ ]1610−

Uncertainty

[ ]1610−

Total (

σ1 ) uncertainty

Bu 7,1 6,0

+/- 5,2 +/- 4,7+/- 2,3 +/- 2,1+/- 3,0 +/- 1,0+/- 3,0 +/- 3,0

-1773,0 -3207,0173,0 127,095,0 0,00,0 0,0

2nd order ZeemanBlackbody RadiationCold Collisions + cavity pullingOthers

Physical origin

Table I : Accuracy budget of the FO2-CS & Rb fountain involved in the 2003 measurements.

Correction

[ ]1610−

Uncertainty

[ ]1610−

Total (

σ1 ) uncertainty

Bu 7,7

+/- 2,4+/- 2,5+/- 5,8+/- 3,7

-351,9191,034,00,0

2nd order ZeemanBlackbody RadiationCold Collisions + cavity pullingothers

Physical origin

Table II : Accuracy budget of the FOM fountain involved in the 2003 measurements.

Correction Uncertainty

σ1 ) uncertainty

[ ]1610−[ ]1610−

Total ( Bu 63.3

+/- 14+/- 26+/- 40+/- 24+/- 5+/- 3+/- 10+/- 28

-4 672 000+3 397-7 205

+87+192-61-13

0

2nd order ZeemanQuadratic DopplerCavity phase differenceLight shiftBlackbody RadiationGravitational effectAsymmetry of microwaveothers

Physical origin

Table III : Accuracy budget of the JPO.

Bu

Bu

Bu

systematicuncertainty

6

53010 53020 53030 53040-7,00E-014

-6,00E-014

-5,00E-014

-4,00E-014

-3,00E-014

-2,00E-014

-1,00E-014

0,00E+000

y(Ef

fect

_Col

lisio

n)

MJD

Relativ Shift Frequency Measurements due to Collisions and Cavity Puling effects

Frequency shift due to collisions between cold Caesium atomsAtom number N

Frequency shift due to Cavity Pulling

On each integration this effect=> depends on the duration of integration

and the stability of the clock⇒ two aspects on this frequency shift- one aspect is statistical- other aspect is systematic

f(Cavity pulling)+ f(Collision)

StatisticuncertaintyσCollisioni

yCollisioni

Duration of integration

σCollisioni

= σCollisionSyst

1100 yCollision moy

The displacement of frequency averagedue to the collisions is estimated :

Processing of FO2 fountain clock

= yCollisionmoy

-0.547155 10-13

Contribution to the type B uncertainty

1610 x 5,5 −=SystCollisionσ

7

Mean ofnormalized

frequencies

2FOMasery −

A typeuncertainty Aσ

Statσ Collisionσ iAσ

3,37676E-163,09088E-163,2274E-165,13055E-163,52982E-163,43238E-168,0398E-161,02306E-155,39059E-164,28253E-153,4181E-152,2133E-159,33819E-163,31483E-161,37812E-151,39681E-151,31983E-158,86148E-161,91041E-153,05164E-151,04855E-152,3145E-157,82859E-16

3E-163E-163E-165E-163E-163,16E-168E-161E-154,36E-163,65E-152,75E-152E-157,59E-163E-161,12E-159,17675E-161,08394E-157,18863E-161,62596E-152,5E-158,57524E-161,88E-156,42E-16

1,55E-167,44E-171,19E-161,15E-161,86E-161,34E-167,99E-172,16E-163,17E-162,24E-152,03E-159,48E-165,44E-161,41E-168,03E-161,05307E-157,53015E-165,18165E-161,00295E-151,75E-156,03412E-161,35E-154,48E-16

6,91712E-136,87847E-136,84129E-136,85422E-136,84188E-136,87101E-136,84649E-136,82802E-136,78122E-136,81809E-136,79724E-136,82951E-136,80663E-136,82691E-136,83644E-136,82723E-136,81145E-136,80636E-136,77957E-136,84675E-136,78692E-136,82871E-136,79155E-13

12:1649:2220:1424:0407:2215:0146:4323:0612:1506:2703:5814:4846:0214:3721:0624:2325:5458:5715:0805:2838:1007:1765:41

53014,2402853016,4923653017,3506953018,3652853018,7104253019,3777853023,3805653025,3673653026,2604253027,0097253027,6354253028,3673653030,3062553031,3791753032,4479253033,5659753034,8347253038,070835303953039,6083353041,3597253041,6805653044,43333

53013,7291753014,4354253016,5076453017,362553018,4034753018,7520853021,4340353024,4048653025,7553026,7409753027,4701453027,7506953028,3881953030,7701453031,5687553032,5553033,7555653035,6145853038,3694453039,3805653039,7694453041,3770853041,69653

DurationH : mn

Date of end ofMeasurement inMJD UTC

Date of beginning measurement in MJD UTC

Measurements of FO2 relative frequency fluctuations from 9 January until 9 February 2004

Statisticaluncertaintiesof y(H-FO)(t)

withoutCollisional

effects

Uncertaintieson the Collisional &Cavity pulling shift

= σAi

+ σStati

2σCollision

i

2= 6825,76 10-16y_meanMaser_FO2 by Weighted least squares with

8

With weighted least square the frequency mean for FO2 is assorted by Statistic uncertainty computed by the propagation of uncertainty from the variance covariance matrix given by least square fit :

= ( )uc yi2

+ + ( )u a12 xi

2 ( )u a22 2. xi ( )u a1 a2

Where xi is set to the middle date of the whole period :

= xi − 12Te

12Ts

= 1,63 10-16

For the period MJD53014 to 53044 it gives :

uA

Middle Date ofend measurement

Middle Date ofstart measurement

= yfit + a1 a2 xWeighted least squares linear regression gives :

9

1000 10000 100000

1E-15

1E-14

sigm

a_y(

tau)

Time (second)

Allan Deviation FO2 - FOM

2,3E-13 / sqrt(tau)

2,718E-16

Allan deviation of the difference between synchronized FO2 & FOM

ττσ

1310 x 322,2)(−

≈y

Stability of FO2 or FOM

at 2,37 days

1610 x 5,2)10( −≈= dy τσ

Stability behavior :White Noise of Frequency up to 1 day

For 10 days

162_ 10 x 6,1)30( −== du FOA τstatistical uncertainty FO2 alone :

10

Dead times of measurements on y(MaserH805 – Fontaine FO2)during the period MJD 53014 to 53044

End ofeach

measurement

Durationof dead

Times H:m

53010 53015 53020 53025 53030 53035 53040 53045

0,0

0,5

1,0

1,5

2,0

Dur

atio

n of

Dea

d Ti

mes

(da

y un

it)

MJD

Distribution of Dead Times53014,24028 04:4153016,49236 00:2253017,35069 00:1753018,36528 00:5553018,71042 01:0053019,37778 49:2153023,38056 24:3553025,36736 09:1153026,26042 11:3253027,00972 11:0353027,63542 02:4653028,36736 00:3053030,30625 11:0853031,37917 04:3353032,44792 02:2753032,73472 00:1153033,36389 01:1953033,56597 04:3353034,375 00:3253034,6125 00:2253034,83472 18:4353036,96667 00:3653037,37847 00:3453038,07083 07:1053038,41042 00:5853038,66597 00:2253038,73333 00:3853039 09:0853039,60833 03:5253040,37847 00:1053040,73819 00:1853041,35972 00:2553041,68056 00:2353044,43333 --

2_

2_/ timedeadlablinkmaserlinku σσ +=

11

TVAR

53015 53020 53025 53030 53035 53040 53045 53050 53055 53060

-20

-15

-10

-5

0

5

10

15

20

25

phase data x(Maser805-Maser816) linear drift removed

MJD

x k(Mas

er80

5-M

aser

816)

/ns

The instability of the maser during each dead times gives an estimate of the uncertainty related to each idle period in themeasurement.

The knowledge of the instability of the maser is carried out starting from measurements of phase variations every hour,compared to the second maser of the laboratory.

After having withdrawn the linear slope of regression obtained by least squares, one plots the curve of the phase variationsbetween masers. One uses the Time Allan Deviation TVAR to estimate the stability of x(H805 - H816)

(suite 1)

x(Maser805 - Maser 816) from 9 January MJD 53014 until 25 February 2004

MJD 53060 slope removedStability Temporal of the phase variations between Maser 805

and Maser 816 of January 9 MJD 53014 up to February 25 2004 MJD 53060

12

For dead times of duration more than 3600s we findthe uncertainty from values of the TVARfunction.For dead time of duration less than 3600s and morethan 1800 s, we set the uncertainty with valuecorresponding to 3600s :

( )σx τ

= ( )σx tau3600s 0.10552 10-9

The uncertainty of frequency deviation is obtainedby quadratic sum of each TVAR variation dividedby the whole period of measurements of

=

second

∑ = i 1

33

( )σx ( )τm i2

T

T = 2 652 839 s (30,70416 days)

= σdeadTime 0.43 10 -15

For dead times of duration less than 1800s,we consider that the uncertainty is negligible.

5.3042e-1113920,000020,1611153039,6083329

5.7034e-1132880,000010,380565303928

-2280,000030,0263953038,7333327

-13200,0152853038,6659726

1.0552e-103479,999990,0402853038,4104225

5.1233e-1125800,000030,2986153038,0708324

-20400,0236153037,3784723

-2159,999990,02553036,9666722

1.2834e-1067380,000010,7798653034,8347221

-13200,0152853034,612520

-1920,000010,0222253034,37519

4.8649e-1116379,999990,1895853033,5659718

1.0552e-1047400,0548653033,3638917

-6600,0076453032,7347216

6.3633e-1188200,1020853032,4479215

5.3042e-1116379,999990,1895853031,3791714

6.5637e-1140079,999980,4638953030,3062513

-1800,000010,0208353028,3673612

2.6019e-109959,999970,1152853027,6354211

6.5637e-11397800,4604253027,0097210

6.5637e-1141519,999980,4805653026,260429

5.7034e-11330600,3826453025,367368

2.0971e-10885001,0243153023,380567

7.7743e-10177659,999992,0562553019,377786

1.0552e-103600,000030,0416753018,710425

1.0552e-1033000,0381953018,365284

-1020,000020,0118153017,350693

-13200,0152853016,492362

7.1633e-10168600,1951453014,240281

secondDuration of each dead time(MJD) ( second)

End of date of measurements (MJD) σx

(suite 2)

:= σlink_lab 0.1 10-1516_ 10 x 4,4 −=Maserlinkσ

2_

2_/ timedeadlablinkmaserlinku σσ +=

BNM-SYRTE CCTF WG TAI 2004

13

52550 52600 52650 52700 52750 52800 52850 52900 52950 530006,646,666,686,706,726,746,766,786,806,826,846,866,886,906,926,946,966,987,007,02

f(EAL) - f(PFS)

f(EA

L) -

f(Hoo

rloge

Cs)

1

0^(-1

5)

MJD

SYRTE-JPO SYRTE-FOM SYRTE-FO2

1 x 10-14

14

• Statistical uncertainties have been better evaluated over 2003 with three of our BNM-SYRTE Primary Frequency Standards

• 2004 will exploit FO1 fountain• Further analysis of the data such as spectral

density and confidence tests, will allow better evaluation of accuracy and uncertainty