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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

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

outline
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

continuous fountain focs 1

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

signal to noise ratio

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

continuous ramsey interrogation

/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

instability measurements

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

present clock stability

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

theoretical description of intermodulation effects

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

slide9

---- 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

slide10

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

prediction for white phase noise

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

degradation of local oscillator

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

experimental allan dev with white phase noise injected square wave phase modulation
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

experimental allan dev with white phase noise injected square wave phase modulation1
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

experimental allan dev with white phase noise injected square wave phase modulation2
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

experimental allan dev with white phase noise injected square wave phase modulation3
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

experimental allan dev with white phase noise injected square wave frequency modulation
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

experimental allan dev with white phase noise injected square wave frequency modulation1
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

observed vs predicted intermodulation effect

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

conclusion and outlook
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

characteristics of our free local oscillator
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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