BNM-SYRTE. Systèmes de Référence Temps-Espace. Me Félicitas Arias Pierre Uhrich Franck Pereira Do Santos. Gérard Petit David Valat Harold Marion

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1 BNMSYRTE Systèmes de Référence TempsEspace Contributions of BNMSYRTE : Team implied in Frequency measurements Contributions of BIPM : André Clairon Team implied in Time measurements Emeric De Clercq Joseph Achkar Sébastien Bize Me Félicitas Arias Pierre Uhrich Franck Pereira Do Santos Gérard Petit David Valat Harold Marion Peter Wolf François Taris Philippe Laurent Wlodzimierz Lewandowski Monique Prodhomme Michel Abgrall Zhiheng Jiang Ishan Ibntaieb Ivan Maksimovic Philippe Merck Jan Grünert Pascal Blondé Peter Rosenbusch JeanYves Richard Céline Vian CCTF Working Group ontai 31 mars 004 JeanYves Richard 1

2 Presentation of the Primary Standards at BNMSYRTE 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 FO FOM Uncertainty due to the dead times Frequency Comparison F_EAL F_PFS Conclusion BNMSYRTE CCTF WG TAI 004

3 Optical pumped caesium beam clock 3

4 Normalized Frequency difference y(hfo)(t) 6,9E013 6,90E013 6,88E013 y(maser805 FO) Duration of integration Uncertainties type A & type B of y(hfo)(t) y(maser805 FO) 6,86E013 6,84E013 6,8E013 6,80E013 y ( H FO) MJDstop MJDstart 9 January until 9 February 004 6,78E013 6,76E MJD Systematic Uncertainty Mean value of y on the entire period of integration Period MJD (30 days) Y(Maser FO) +68,57 u B 0,8 u Results of calibration. (scale is in 1 x ). A 0, u link / 0,5 maser Date of measurements In MJD UTC unit Statistical uncertainty Uncertainty on the Link between Maser & atomic Clock + Uncertainty due to the dead time 4

5 Physical origin nd order Zeeman Blackbody Radiation Cold Collisions + cavity pulling Others Total ( 1 σ ) uncertainty Correction 1773,0 307,0 173,0 17,0 95,0 0,0 0,0 0,0 Correction [ 10 ] Uncertainty +/ 5, +/ 4,7 +/,3 +/,1 +/ 3,0 +/ 1,0 +/ 3,0 +/ 3,0 ub 7,1 6,0 Uncertainty [ 10 ] Table I : Accuracy budget of the FOCS & Rb fountain involved in the 003 measurements. Physical origin Total ( 1 σ ) uncertainty nd order Zeeman Blackbody Radiation Cold Collisions + cavity pulling others 351,9 191,0 34,0 0,0 [ 10 ] +/,4 +/,5 +/ 5,8 +/ 3,7 ub 7,7 Table II : Accuracy budget of the FOM fountain involved in the 003 measurements. [ 10 ] u B systematic uncertainty u B Physical origin Correction [ 10 ] Uncertainty [ 10 ] nd order Zeeman Quadratic Doppler Cavity phase difference Light shift Blackbody Radiation Gravitational effect Asymmetry of microwave others / 14 +/ 6 +/ 40 +/ 4 +/ 5 +/ 3 +/ 10 +/ 8 Total ( 1 σ ) uncertainty Table III : Accuracy budget of the JPO. u 63.3 B u B 5

6 Atom number N Frequency shift due to collisions between cold Caesium atoms Frequency shift due to Cavity Pulling f(cavity pulling) + f(collision) y(effect_collision) 0,00E+000 1,00E014,00E014 3,00E014 4,00E014 5,00E014 6,00E014 Processing of FO fountain clock Relativ Shift Frequency Measurements due to Collisions and Cavity Puling effects Statistic uncertainty σ Collisioni y Collisioni 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 σ Collisioni other aspect is systematic 1 σ Collision = Syst 100 y Collision moy The displacement of frequency average due to the collisions is estimated : y Collisionmoy = ,00E MJD Duration of integration σ CollisionSyst = 5,5 x 10 Contribution to the type B uncertain 6

7 Measurements of FO relative frequency fluctuations from 9 January until 9 February 004 Date of beginning measurement in MJD UTC 53013, , , , , , , , , , , , , , , , , , , , , , ,69653 Date of end of Measurement in MJD UTC 53014, , , , , , , , , , , , , , , , , , , , , ,43333 Duration H:mn 1:16 49: 0:14 4:04 07: 15:01 46:43 3:06 1:15 06:7 03:58 14:48 46:0 14:37 1:06 4:3 5:54 58:57 15:08 05:8 38:10 07:17 65:41 Mean of normalized frequencies ymaser FO 6,9171E13 6,87847E13 6,8419E13 6,854E13 6,84188E13 6,87101E13 6,84649E13 6,880E13 6,781E13 6,81809E13 6,7974E13 6,8951E13 6,80663E13 6,8691E13 6,83644E13 6,873E13 6,81145E13 6,80636E13 6,77957E13 6,84675E13 6,7869E13 6,8871E13 6,79155E13 σ Stat A type uncertainty 1,55E16 7,44E17 1,19E16 1,15E16 1,86E16 1,34E16 7,99E17,16E16 3,17E16,4E15,03E15 9,48E16 5,44E16 1,41E16 8,03E16 1,05307E15 7,53015E16 5,18165E16 1,0095E15 1,75E15 6,0341E16 1,35E15 4,48E16 σ A σ Collision 3E16 3E16 3E16 5E16 3E16 3,16E16 8E16 1E15 4,36E16 3,65E15,75E15 E15 7,59E16 3E16 1,1E15 9,17675E16 1,08394E15 7,18863E16 1,6596E15,5E15 8,5754E16 1,88E15 6,4E16 σ A i 3,37676E16 3,09088E16 3,74E16 5,13055E16 3,598E16 3,4338E16 8,0398E16 1,0306E15 5,39059E16 4,853E15 3,4181E15,133E15 9,33819E16 3,31483E16 1,3781E15 1,39681E15 1,31983E15 8,86148E16 1,91041E15 3,05164E15 1,04855E15,3145E15 7,8859E16 Statistical uncertainties of y(hfo)(t) without Collisional effects Uncertainties on the Collisiona Cavity pulling s y_mean Maser_FO = 685, by Weighted least squares with σ Ai = σ Stati + σcollisi 7

8 Weighted least squares linear regression gives : y fit = a 1 + a x With weighted least square the frequency mean for FO is assorted by Statistic uncertainty computed by the propagation of uncertainty from the variance covariance matrix given by least square fit : u c ( y i ) = u( a 1 ) + x i u( a ) +. x i u( a 1 a ) Where x i is set to the middle date of the whole period : 1 x i = T 1 e T s u A = 1, For the period MJD to it gives Middle Date of end measurement Middle Date of start measurement 8

9 Allan deviation of the difference between synchronized FO & FOM Allan Deviation FO FOM Stability of FO or FOM 1E14,3E13 / sqrt(tau) Stability behavior : White Noise of Frequency up to 1 da sigma_y(tau) σ ( τ ) y,3 x 10 τ 13 1E15 at,37 days,718e16 For 10 days Time (second) statistical uncertainty FO alone : u σ y ( τ = 10d) A _ FO ( τ = 30d) = 1,6 x 10,5 x 10 9

10 Duration of Dead Times (day unit),0 1,5 1,0 0,5 0,0 ulink Distribution of Dead Times MJD / maser = σ link _ lab + σ dead _ time Dead times of measurements on y(maserh805 Fontaine FO) during the period MJD to End of each measurement Duration of dead Times H:m 53014,408 04: , : 53017, : , : , : , :1 5303, : , : ,604 11:3 5307, : ,6354 0: , : , : , : ,4479 0:7 5303, : , : , : ,375 00: ,615 00: 53034, : , : , : , : , : , : 53038, : : , : , : , : , : , : ,

11 (suite The instability of the maser during each dead times gives an estimate of the uncertainty related to each idle period in the measurement. 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 variations between masers. One uses the Time Allan Deviation TVAR to estimate the stability of x(h805 H816) 5 0 phase data x(maser805maser816) linear drift removed TVAR x k (Maser805Maser816) /ns MJD x(maser805 Maser 816) from 9 January MJD until 5 February 004 MJD slope removed Stability Temporal of the phase variations between Maser 805 and Maser 816 of January 9 MJD up to February MJD

12 End of date of measurements (MJD) Duration of each dead time (MJD) ( second) second σ x ,408 0, e10 (suite ) , , ,0158 0, , ,3658 0, e10 For dead times of duration more than 3600s we find the uncertainty σ from values of the TVAR x ( τ ) function. For dead time of duration less than 3600s and more than 1800 s, we set the uncertainty with value corresponding to 3600s : , , , , , ,0097 0,04167,0565 1,0431 0,3864 0, , , , , e e e e e e11 σ x ( tau3600s ) = second , , ,1158 0, , , e10 For dead times of duration less than 1800s, we consider that the uncertainty is negligible , , , , , , e e11 The uncertainty of frequency deviation is obtained by quadratic sum of each TVAR variation divided by the whole period of measurements of T = s (30,70416 days) , , , , ,375 0,1008 0, , , , , , e e e11 33 i = 1 ulink σ x ( τ m ( i )) T = σ deadtime = / maser = σ link _ lab + σ dead _ time , , , , , , , ,0158 0, ,05 0,0361 0,9861 0,0408 0, , , , , e e e10 σ link = _ Maser 4,4x 10 σ link_lab := , , ,0639 0, , , , , e e11 1

13 f(eal) f(hoorlogecs) 10^(15) 7,0 7,00 f(eal) f(pfs) 6,98 6,96 6,94 6,9 6,90 6,88 6,86 6,84 6,8 6,80 6,78 6,76 6,74 6,7 6,70 6,68 6,66 6, MJD SYRTEJPO SYRTEFOM SYRTEFO 1 x BNMSYRTE CCTF WG TAI

14 Statistical uncertainties have been better evaluated over 003 with three of our BNM SYRTE Primary Frequency Standards 004 will exploit FO1 fountain Further analysis of the data such as spectral density and confidence tests, will allow better evaluation of accuracy and uncertainty 14