Experimental study of intermodulation effects in a continuous fountain

EFTF 2007, Geneva I Guéna et al. I 1

Federal Office of Metrology METAS

Experimental study of intermodulation effects in a continuous fountain

J. Guéna3, G. Dudle1, P. Thomann2

1 Federal Office of Metrology METAS, Bern-Wabern, Switzerland2 LTF-IMT, University of Neuchâtel, Switzerland3 Present address: LNE-SYRTE, Paris, France

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

EFTF 2007, Geneva I Guéna et al. I 3

Continuous fountainFOCS-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

Ttrans=0.49 s

Δ0 1 Hz

3F=4

6S

EFTF 2007, Geneva I Guéna et al. I 4

Signal-to-noise ratio4

3

2

1

0

noi

se (

10-2

pA.H

z-1/2

)

12108642

Fourier frequency (Hz)

nearly white noise

without atomic flux

with atomic flux

Rms noise of fluo PD signal

fitted power law N = Sk, k=0.56 ± 0.02 ~ atomic shot noise

Noise vs signal

1

2

nois

e N

(10

-2pA

.Hz-1

/2)

0.1 1signal S (10 pA)

Useful atomic flux

= 2 ×(S/N)² 2×105 at/s

EFTF 2007, Geneva I Guéna et al. I 5

Continuous Ramsey interrogation

DLA

/2 phase

modulated at fmodfmod

reference waveform

PM

RF synthesizer

f x 9 f x102

Ramsey resonator

Correction signal

PD signal

9.192…GHz

Locking loop

10 MHzVCXO

Local osc. (LO)

FOCS-1

Sig Gen

PM

12.631...MHz

9.180 GHz

/2 phase step of -wave at fmod= Δ0 =1 Hz

Tmod= 2T = 1s

+/4

-/4

EFTF 2007, Geneva I Guéna et al. I 6

Instability measurements

DLA

/2 phase

modulated at fmod fmod

reference waveform

PM

f x 9 f x102

Correction signal

PD signal

9.192…GHz

Locking loop

10 MHzVCXO FOCS-1

Sig Gen

PM

12.631...MHz

Freq compMaser

EFTF 2007, Geneva I Guéna et al. I 7

10-15

10-14

10-13

y(

100

101

102

103

104

Averaging time (s)

2.0 x 10-13

x -½

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

2/113

2/1

108.1

.

11)(

NS

Qy

EFTF 2007, Geneva I Guéna et al. I 8

Theoretical description of intermodulation effects

SyLLO( f ) = G( Sy

LO(f), Ttrans , fmod , Cmod-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 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 9

SyLLO(f) 2 k c2k

2 sinc2 (2kfmodTtrans) SyLO(2kfmod)

Cavity filtering LO noise at even-harmonics of fmod

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 Ttrans

1.0

0.8

0.6

0.4

0.2

0.076543210

Fourier frequency f / Ramsey width (FWHM)

|H(f

)/H

(0)|

Tmodmod/2 = TtransTmodmod/2 > Ttrans

---- location of down-converted harmonics

Ttrans=0.5 s choose fmod=1Hz to cancel intermod effect

Theoretical description of intermodulation effects

EFTF 2007, Geneva I Guéna et al. I 10

From PSD to Allan variance

SyLLO(f) = constant in the bandwidth of locking loop

white frequency noise

computation of Allan variance

2

)0()(

LLO2

inter,

fS yy for 10 s

SyLLO(f) 2 k c2k

2 sinc2 (2kfmodTtrans) SyLO(2kfmod)

valid at Fourier frequencies 0 < f < floop (<< fmod = 1 Hz)

For definite prediction, parametrize free l.o. noise

SyLO(f) = h2 f2 + h1 f1 + h0

+ …

EFTF 2007, Geneva I Guéna et al. I 11

Prediction for white phase noise

Contribution to Allan Deviation due to the intermodulation effectas a function of the modulation frequency

10-14

10-13

10-12

10-11

y,in

ter(

= 1

s)

1.81.61.41.21.00.80.60.40.2

fmod (Hz)

white phase noise

h2=1.0 x 10-23

Hz-3

SyLO(f) = h2 f 2

Present short term instability of FOCS-1

10mrad Hz-1/2

EFTF 2007, Geneva I Guéna et al. I 12

Degradation of local oscillator

Noise gen

DLA

Phase or Freq.

modulated at fmodfmod

reference waveform

PM

f x 9 f x102

Correction signal

PD signal

9.192…GHz

Locking loop

10 MHzVCXO FOCS-1

Sig Gen

PM

12.631...MHz

Freq compMaser

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)

10-14

10-13

y (

1 10 100 1000

averaging time(s)

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

10-14

10-13

y (

1 10 100 1000

averaging time(s)

1.0 Hz 1.3 Hz 0.85 Hz 0.6 Hz

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)

10-14

10-13

y(

1 10 100 1000

averaging time(s)

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

10-14

10-13

y(

1 10 100 1000

averaging time(s)

3 Hz 3.15 Hz 3.25 Hz 2.55 Hz

EFTF 2007, Geneva I Guéna et al. I 17

Experimental Allan Dev with white phase noise injected Square-wave frequency modulation

10-14

10-13

y(

1 10 100 1000

averaging time(s)

Modulation frequency = 1 Hz

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

10-14

10-13

y(

1 10 100 1000

averaging time(s)

1.0 Hz 1.25 Hz 0.85 Hz

EFTF 2007, Geneva I Guéna et al. I 19

9

8

7

6

5

4

3

2

1

0

y,in

ter(

s

) (

x10-1

3 )

3.22.82.42.01.61.20.8

fmod (Hz)

Observed vs predicted intermodulation effect

y,inter from quadratic subtraction

y2 = y,inter

2 + y,ref2

observed without injected noise

observed with injected noise

Allan deviations vs frequency modulation

● SQ-PM ▲ SQ-FM

♦ ref

9

8

7

6

5

4

3

2

1

0

y,in

ter(

s

) (

x10-1

3 )

3.22.82.42.01.61.20.8

fmod (Hz)

● SQ-PM ▲

SQ-FM ● Predicted

9

8

7

6

5

4

3

2

1

0

y(

s)

(x1

0-13 )

3.22.82.42.01.61.20.8

fmod (Hz)

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.

EFTF 2007, Geneva I Guéna et al. I 21

EFTF 2007, Geneva I Guéna et al. I 22

Characteristics of our free local oscillator

7

8

9

10-13

2

3

y(

0.12 3 4 5 6

12 3 4 5 6

102 3 4 5 6

100 (s)-152

-148

-144

-140

-136

-132

-128

-124

Scr

ipt

L (d

B)

1 10 100 1000

fourier frequency (Hz)

10-27

10-26

10-25

10-24

Sy(

f)

(Hz-1

)

2 3 4 5 61

2 3 4 5 610

2 3 4 5 6100

fourier frequency (Hz)

BVA 860711 #349 from oscilloquartz

spectral purity

PSD Sy(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