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Experimental study of intermodulation effects in a continuous fountain

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. Outline.

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Experimental study of intermodulation effects in a continuous fountain

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  1. Experimental study of intermodulation effects in a continuous fountain J. Guéna3, G. Dudle1, P. Thomann2 1 Federal Office of Metrology METAS, Bern-Wabern, Switzerland 2 LTF-IMT, University of Neuchâtel, Switzerland 3 Present address: LNE-SYRTE, Paris, France EFTF 2007, Geneva I Guéna et al. I 1

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

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

  4. Useful atomic flux • = 2 ×(S/N)²  2×105 at/s Rms noise of fluo PD signal Signal-to-noise ratio with atomic flux  nearly white noise without atomic flux Noise vs signal fitted power law N = Sk, k=0.56 ± 0.02 ~ atomic shot noise EFTF 2007, Geneva I Guéna et al. I 4

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

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

  7. atomic shot noise 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 EFTF 2007, Geneva I Guéna et al. I 7

  8. SyLLO( f ) = G( SyLO(f),Ttrans ,fmod ,Cmod-demod) PSD of free-running LO transit time mod-demod scheme 0.5 s Theoretical description of intermodulation effects 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 fmod 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 EFTF 2007, Geneva I Guéna et al. I 8

  9. ---- location of down-converted harmonics Tmod/2 > Ttrans |H(f)/H(0)| Theoretical description of intermodulation effects A. Joyet, G. Mileti, G. Dudle, P. Thomann, IEEE TIM, 50, 150 (2001) SyLLO(f)  2 kc2k2sinc2 (2kfmodTtrans)SyLO(2kfmod) Mod-demod Cavity filtering LO noise at even-harmonics of fmod Tmod/2 = Ttrans Interpretation: Continuous interrogation: no dead time  averaging of frequency fluctuations over the transit time Ttrans Ttrans=0.5 s  choose fmod=1Hz to cancel intermod effect EFTF 2007, Geneva I Guéna et al. I 9

  10. From PSD to Allan variance SyLLO(f)  2 kc2k2sinc2 (2kfmodTtrans)SyLO(2kfmod) valid at Fourier frequencies 0 < f < floop (<< fmod = 1 Hz) • SyLLO(f) = constant in the bandwidth of locking loop • white frequency noise • computation of Allan variance for t  10 s For definite prediction, parametrize free l.o. noise SyLO(f) = h2 f2 +h1 f1 +h0 + … EFTF 2007, Geneva I Guéna et al. I 10

  11. SyLO(f) =h2 f 2 Prediction for white phase noise Contribution to Allan Deviation due to the intermodulation effectas a function of themodulation frequency 10mrad Hz-1/2 Present short term instability of FOCS-1 EFTF 2007, Geneva I Guéna et al. I 11

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

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

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

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

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

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

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

  19. y2= y,inter2+ y,ref2 observed with injected noise observed without injected noise Allan deviations vs frequency modulation Observed vs predicted intermodulation effect  y,inter from quadratic subtraction ● SQ-PM ▲ SQ-FM♦ ref ● SQ-PM▲ SQ-FM● Predicted EFTF 2007, Geneva I Guéna et al. I 19

  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. EFTF 2007, Geneva I Guéna et al. I 20

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

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

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