Observatoire de Paris BNM-SYRTE

Franck Pereira Dos SantosArnaud LandraginDavid HollevilleAndré Clairon

Patrick Cheinet Julien Le GouëtKasper Therkildsen

Construction of an absolute gravimeter using atom interferometry with cold

87Rb atoms

Observatoire de Paris BNM-SYRTE

Summary

Use of the gravimeter: The Watt Balance

Principle of our gravimeter, atom interferometry

Lasers frequency locks…

Sensitivity to phase noise

Sensitivity to vibrations and rejection method

Advancement : the traps

Conclusion

Observatoire de Paris BNM-SYRTE

The Watt Balance project

BIPM standard Kg

Objective :

Why :

Mass metrology:

Principle :

replace the standard Kg with a definition linked to

the Planck’s constant h

the standard Kg is the last artifact of the international

system, observed drift on the primary and secondary

standards of 5.10-8 Kg over 30 years

goal of 10-8 of relative precision

Balance a mechanical power

with an electrical power

Observatoire de Paris BNM-SYRTE

The Watt Balance projectstatical Phase Dynamical Phase

constant speed motion

B

i

Fg = m × g

L

B × i × L = m gB × i × L = m g

L

v

E = B × L × vE = B × L × v

m g v = E im g v = E i

hvg

fkm J

×=

2

FLaplace = i L × B

Planck’sConstant

JosephsonFrequency

B

Necessity of a precise g mesurement

Observatoire de Paris BNM-SYRTE

Push beam

π/2

π/2

π

Raman laser Beams

Detection

Raman pulses2T=100 ms

Total interaction time=

interferometer

87Rb atoms cooledIn a 2D-MOT

108 atoms trapped in 100 msCooled to a few µK

In a 3D-MOT

109 to 1010

atoms.s-1

State selection|5S1/2, F=1, m F=0 >

∆Φ= keff .g.T 2

Raman laser Beams

General Principle

Observatoire de Paris BNM-SYRTE

Trappingsame lasers for trapping and Raman

π/2 pulse : Atomic beam Splitter

π pulse : Atomic mirror

Tran

sitio

n P

roba

bilit

y

ΩRabiτπ/2 π

The lasers couple the |f1> and |f2> states in a quantum superposition

=> Rabi oscillations

- k2

k1

k2

k1

optkkkp 221 ≈−=

During the transition, the atom takes two photon recoils and

change its trajectory

|5S1/2 >

|5P3/2 >

|f1 >

|f2 >

|e0 >

|e1 >|e2 >

|e3 >

virtual state |i >

≤2 GHz

6.8 GHz

δ => Doppler cooling

87Rb780 nm

Stimulated Raman Transitions

Raman

Detection

Observatoire de Paris BNM-SYRTE

Optical Bench1 single bench for cooling and Raman pulses

ECL1Réf HYPER

ECL2 MOPA 2

ECL3 MOPA 1

F-LOCK

AOM

F or φ-LOCK

RAMANSTRAPS

DETECTION

4.8 à 6.8 GHz (YIG)

6.8 GHz

Locked onspectroscopy line

Observatoire de Paris BNM-SYRTE

Transition to φ-lock

0 5 10 15 20 25 30 35 40 45 5050

100

150

200

250

300

-1500

-1000

-500

0

500

1000

1500

Err

or S

igna

l (M

Hz)

Time (ms) F

requ

ency

cha

nge

(MH

z)

2 GHz Sweep in 800µs, lasers unlocked

MasterRepumperYIG

0 1 2 3 4 5 6 7 8 9 10-2,5

-2,0

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

2,0

2,5

-1500

-1000

-500

0

500

1000

1500

Err

or S

igna

l (M

Hz)

Time (ms)

2 GHz Sweep in 800µs, lasers locked

Fre

quen

cy c

hang

e (M

Hz)

MasterRepumperYIG

Fixed rampsapplied on lasers

controls

-2 0 2 4 6 8-4

-2

0

2

4

6

8

Pha

se e

rror

(mra

d)

Time (ms)

0.8 ms to sweep by 2 GHz

3 ms to reach the 1 mrad level

Observatoire de Paris BNM-SYRTE

|5S1/2 >

|5P3/2 >

|f1 >

|f2 >

|i >2 GHz

6.8 GHz

87Rb

780 nm

π/2

π

π/2

0)0( =φ

2

21)( gTkT eff=φ

22)2( gTkT eff=φ

)2()(2)0( TT φφφ +−=Φ

ϕ1(t) = k1z(t) +ϕ10(t)

Interferometer’s phase shift

ϕ2(t) = −k2z(t) +ϕ20(t)

φ(t) =ϕ2(t) −ϕ1(t)is printed on the

atomic phase

Atomic interferometer

2)cos(1 Φ+

=•P)2()(2)0(.. 0002 TTTgkeff φφφ +−+=Φ

T=50ms => ~106 rad

Observatoire de Paris BNM-SYRTE

Transfer function H(ω) for laser phase noise

101 102 103 104 105 1061E-3

0,01

0,1

1

10

<H(f

)2 >

Frequency (Hz)

2/(2πf/Ω) 2

σΦ2 = H(ω)∫ 2

Sϕ(ω)dω

Theory (T=5ms):

Experiment (gyroscope)

0 100 200 300 400 500 6001E-4

1E-3

0,01

0,1

1

10

H(f)

²

Frequency (Hz)

)(ωϕS Phase power spectral density

TheoryExperiment

13100 13150 13200 13250 133001E-4

1E-3

0,01

0,1

1

10

H(f)

2

Frequency (Hz)))

2sin()

2)2()(cos(

2)2(sin(4)( 22

TTTiH RR ωω

τωτωω

ωω Ω+

++Ω−Ω

−=

Observatoire de Paris BNM-SYRTE

Raman laser phase noiseTwo possible sources:

Total contribution: = 1.75 mrad => 9 ng/shot

Experimental result

Weighted with H(ω): 2T=100ms and τ=10 µs

σΦ =1.3 mrad

Reference frequency phase stability: 1.2 mradσΦ =

Residual noise of the Phaselock loop:Estimated for state of the art quartz oscillator

σΦ

1 10 100 1000 10000 100000 1000000 1E71E-12

1E-11

1E-10

1E-9

1E-8

Sφ(

f) (r

ad2 .H

z-1)

Frequency (Hz)

Observatoire de Paris BNM-SYRTE

Sensitivity to vibrations

∫=Φ ωωωωσ dSHk aeff )()(

4

222phase/position

δφ <=> keffδz

Required vibration noise level (>0.3 Hz) :1 ng/Hz1/2

Noise level in the labWeighted noise

Up to 80 Hz :

Need for vibration isolationand compensation

0,1 1 10 1001E-16

1E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1E-9

acce

lera

tion

nois

e (m

2 s-4/H

z)

Frequency (Hz)

Observatoire de Paris BNM-SYRTE

Vibration rejection

Act on the Raman phase difference to compensatefor vibrations

Method tested on auxiliary experiment

With a seismometer

ECL

PLL

Seismometer

Interferometer

Raman laser

Observatoire de Paris BNM-SYRTE

Progress report

0,0 0,5 1,00,0

5,0x108

1,0x109

1,5x109

2,0x109

Atom

s lo

aded

Time (s)0 20 40 60 80

0

1x108

2x108

3x108

4x108

5x108

flux

dens

ity (a

t.m-1)

speed (m.s-1)

Detection Photodiode

2D-MOT 3D-MOT

2D-MOT total flux =1010 atoms.s-1

Cold atomstrapping lasers

3D-MOT loading rate = 3.109 atoms.s-1

3D-MOT 2D-MOT

Observatoire de Paris BNM-SYRTE

Conclusion

- Cold atom sources obtained- Raman lasers phase-locked

-First atom interferometry signals: early 2005Limited by vibrationsPreliminary vacuum chamber => test the system

-Implement the vibration isolation platform and the vibration rejection

Expected sensitivity : 10-9 g after a few secondsExpected accuracy : 10-9 g