1. EFTF 2007, Geneva I Guéna et al. I 1 Experimental study of intermodulation effects in a continuous fountain J. Guéna 3, G. Dudle 1, P. Thomann 2 1 Federal Office of Metrology METAS, Bern-Wabern, Switzerland 2 LTF-IMT, University of Neuchâtel, Switzerland 3 Present address: LNE-SYRTE, Paris, France

2. EFTF 2007, Geneva I Guéna et al. I 2 Outline  Continuous fountain and Signal-to-noise ratio  Continuous Ramsey interrogation and present clock stability  Predicted intermodulation effect  Experimental demonstration

3. EFTF 2007, Geneva I Guéna et al. I 3 Continuous fountain FOCS-1 3D-optical molasses Transverse cooling Micro-wave cavity Parabolic flight Probe detection beam of F = 4 Optical pumping to F=3 0.7 m T trans =0.49 s Δ 0  1 Hz 3 F=4 6S

4. EFTF 2007, Geneva I Guéna et al. I 4 Signal-to-noise ratio  nearly white noise without atomic flux with atomic flux Rms noise of fluo PD signal fitted power law N = S k, k=0.56 ± 0.02 ~ atomic shot noise Noise vs signal Useful atomic flux  = 2 ×(S/N)²  2×10 5 at/s 

5. EFTF 2007, Geneva I Guéna et al. I 5 Continuous Ramsey interrogation DLA  /2 phase modulated at f mod f mod reference waveform PM RF synthesizer f x 9 f x102 Ramsey resonator Correction signal  PD signal 9.192…GHz Locking loop 10 MHz VCXO Local osc. (LO) FOCS-1 Sig Gen PM 12.631...MHz 9.180 GHz  /2 phase step of  -wave at f mod = Δ 0 =1 Hz T mod = 2T = 1s +/4+/4 -/4-/4

6. EFTF 2007, Geneva I Guéna et al. I 6 Instability measurements DLA  /2 phase modulated at f mod f mod reference waveform PM f x 9 f x102 Correction signal  PD signal 9.192…GHz Locking loop 10 MHz VCXO FOCS-1 Sig Gen PM 12.631...MHz Freq compMaser

7. EFTF 2007, Geneva I Guéna et al. I 7 Present clock stability Allan deviation of the frequency difference FOCS-1 – MASER H-Maser: EFOS (Neuchâtel) BIPM ID 140-57-01 2.0 x 10 -13 x  -½ atomic shot noise

8. EFTF 2007, Geneva I Guéna et al. I 8 Theoretical description of intermodulation effects S y LLO ( f ) = G( S y LO (f), T trans, f mod, C mod-demod ) PSD of free-running LO transit time mod-demod scheme 0.5 s A. Joyet, G. Mileti, G. Dudle, P. Thomann, IEEE Trans.Instr.Meas., 50, 150 (2001) A non-linear effect in the mod-demod-process in the locking loop: Down conversion of the l.o. noise at high harmonics of f mod into the low frequency band of the loop (“Dick effect”) Aim of the model: Find expression of the PSD of the locked local oscillator for any type of interrogation Ingredients

9. EFTF 2007, Geneva I Guéna et al. I 9 S y LLO (f)  2  k c 2k 2 sinc 2 (2k  f mod T trans ) S y LO (2kf mod ) Cavity filtering LO noise at even- harmonics of f mod Mod-demod A. Joyet, G. Mileti, G. Dudle, P. Thomann, IEEE TIM, 50, 150 (2001) Interpretation: Continuous interrogation: no dead time  averaging of frequency fluctuations over the transit time T trans |H(f)/H(0)| mod T mod /2 = T trans mod T mod /2 > T trans ---- location of down- converted harmonics T trans =0.5 s  choose f mod =1Hz to cancel intermod effect Theoretical description of intermodulation effects

10. EFTF 2007, Geneva I Guéna et al. I 10 From PSD to Allan variance S y LLO (f) = constant in the bandwidth of locking loop  white frequency noise  computation of Allan variance for   10 s S y LLO (f)  2  k c 2k 2 sinc 2 (2k  f mod T trans ) S y LO (2kf mod ) valid at Fourier frequencies 0 < f < f loop (<< f mod = 1 Hz) For definite prediction, parametrize free l.o. noise S y LO (f) = h 2 f 2 + h 1 f 1 + h 0 + …

11. EFTF 2007, Geneva I Guéna et al. I 11 Prediction for white phase noise Contribution to Allan Deviation due to the intermodulation effect as a function of the modulation frequency S y LO (f) = h 2 f 2 Present short term instability of FOCS-1 10mrad Hz -1/2

12. EFTF 2007, Geneva I Guéna et al. I 12 Degradation of local oscillator Noise gen DLA Phase or Freq. modulated at f mod f mod reference waveform PM f x 9 f x102 Correction signal  PD signal 9.192… GHz Locking loop 10 MHz VCXO FOCS-1 Sig Gen PM 12.631...MHz  Freq compMaser

13. EFTF 2007, Geneva I Guéna et al. I 13 Experimental Allan Dev with white phase noise injected Square-wave phase modulation Modulation frequency = 1 Hz (= Ramsey linewidth)

14. EFTF 2007, Geneva I Guéna et al. I 14 Experimental Allan Dev with white phase noise injected Square-wave phase modulation Modulation frequency varied around 1 Hz

15. EFTF 2007, Geneva I Guéna et al. I 15 Experimental Allan Dev with white phase noise injected Square-wave phase modulation Modulation frequency = 3 Hz (3rd harmonics of Ramsey linewidth)

16. EFTF 2007, Geneva I Guéna et al. I 16 Experimental Allan Dev with white phase noise injected Square-wave phase modulation Modulation frequency varied around 3 Hz

17. EFTF 2007, Geneva I Guéna et al. I 17 Experimental Allan Dev with white phase noise injected Square-wave frequency modulation Modulation frequency = 1 Hz

18. EFTF 2007, Geneva I Guéna et al. I 18 Experimental Allan Dev with white phase noise injected Square-wave frequency modulation Modulation frequency varied around 1 Hz

19. EFTF 2007, Geneva I Guéna et al. I 19 Observed vs predicted intermodulation effect   y,inter from quadratic subtraction  y 2 =  y,inter 2 +  y,ref 2 observed without injected noise observed with injected noise Allan deviations vs frequency modulation ● SQ-PM ▲ SQ-FM ♦ ref ● SQ-PM ▲ SQ-FM ● Predicted

20. EFTF 2007, Geneva I Guéna et al. I 20 Conclusion and outlook Successfully validated theoretical model of intermodulation effect for continuous interrogation Commercial BVA exhibits too small a phase noise to be measurable with a continuous fountain FOCS-1 is mainly atomic shot-noise limited and S/N increases with atomic flux  the short term instability can thus be decreased if the flux is increased The assembly of a second fountain with a higher flux (FOCS-2) has been completed at METAS : see Poster by F.Füzesi et al.

21. EFTF 2007, Geneva I Guéna et al. I 21

22. EFTF 2007, Geneva I Guéna et al. I 22 Characteristics of our free local oscillator BVA 860711 #349 from oscilloquartz spectral purity PSD S y (f) Flicker floor of free l.o. is well below present Allan deviation ( 2 x10 -13, nearly atomic shot noise limited)  Expected intermodulation effect unobservable…  Need to increase l.o.noise… Allan deviation