light pulse atom interferometry for precision measurement jaewan kim myongji university

Light Pulse Atom Interferometry for Precision Measurement

Jaewan KimMyongji University

AI for Precision Measurements

• Inertial Sensing – Gravimeters, Gyroscopes, Gradiometers

• Newton’s constant G• Fine-structure constant and h/M• Test of Relativity• Interferometers in space• …

Gravity Measurements

Geophysics Gravity field mapping (crustal deformations, mass changes, definition of the geoid …)

Tests offundamental physics (equivalence principle, tests of gravitation …)

Metrology: Watt Balance (new definition of the kg)

g

Navigation (submarine…)

Absolute Gravimeters

Commercial Gravimeter : FG5

Principle : Michelson interferometer with falling corner cube

Accuracy : 2 µGal

Atomic gravimeter

Stanford experiment in 2001 :

– Resolution: 3 µGal after 1 minute

– Accuracy: <3 µGal

From A. Peters, K.Y. Chung and S. Chu 1 µGal = 10-8 m/s2 ~ 10-9g

Principle of Atom Interferometry

Interferometer Phase Shift

1

23

B2

AA21

32 BB

BA 222

2

BA 321 2

A22

2

+ + a

b- -

a

bLaser phase gets imprinted

Case of an Acceleration

2. Takeff

1(t1) – 22 (t2) + 3 (t3) =

233 )2(.

2

1)( Takt eff

0)( 11 t 222 .

2

1)( Takt eff

a

1

23

T T)(.)( trkt eff

2

2

1ta

Implementation of Raman Laser

Miroir

0z

2

2

1)( gTTz

22)2( gTTz

Laser 2

Laser 1

Pulse 1

Pulse 2

Pulse 3

Interferometer measurement = relative displacement atoms/mirror

• Vertical Raman lasers

• Retroreflect two (copropagating) Raman lasers

Reduces influence of path fluctuations (common mode) 4 laser beams 2 pairs of counterpropragating Raman lasers

with opposite keff wavevectors

• Position of planes of equal phase difference attached to position of retroreflecting mirror

Principle of Measurements

-25.1435 -25.14300.2

0.3

0.4

0.5

0.6

0.7

-125.718 -125.716 -125.714

Pro

bab

ilit

é d

e tr

ansi

tion

(MHz.s-1)

DDS1

(Hz)

C~45%

• Free fall → Doppler shift of the resonance condition of the Raman transition

• Ramping of the frequency difference to stay on resonance :

π/2 π π /2

22 TTgkeff

t 0

m

hktvk eff

efffe 2)(

2

21


C~45%C~45%

-25.1435 -25.14300.2

0.3

0.4

0.5

0.6

0.7

-125.718 -125.716 -125.714

Pro

bab

ilit

é d

e tr

ansi

tion

(MHz.s-1)

DDS1

(Hz)



π/2 π π /2

22 TTgkeff

t 0

m

hktvk eff

efffe 2)(

2

21


C~45%

-25.1435 -25.14300.2

0.3

0.4

0.5

0.6

0.7

-125.718 -125.716 -125.714

Pro

bab

ilit

é d

e tr

ansi

tion

(MHz.s-1)

DDS1

(Hz)



π/2 π π /2

22 TTgkeff

t 0

m

hktvk eff

efffe 2)(

2

21




π/2 π π /2

22 TTgkeff

t 0

• Dark fringe :independent of T

C~45%

effk0

g

-25.1435 -25.14300.2

0.3

0.4

0.5

0.6

0.7

-125.718 -125.716 -125.714

Pro

bab

ilit

é d

e tr

ansi

tion

(MHz.s-1)

DDS1

(Hz)

m

hktvk eff

efffe 2)(

2

21

Experiments

Experimental Setup

• Titanium vacuum chamber(non magnetic)

• 14 + 2 + 4 viewports

• Indium seals

• Pumps : 2 × getter pumps 50 l/s 1 × ion pump 2 l/s 4 × getter pills

• Two layers magnetic shield

• Retroreflecting mirror under vacuum

2nd generation vacuum chamber

Experimental Setup

2D-MOT

3D-MOT

L2 : repumper / Raman 1L3 : cooling / Raman 2

retro-reflectionmirror

87Rb

λ/4

σ+

σ-

σ-

σ+

isolationplatform

seismometer

detection

Raman collimatorwith adjustable /4

detection

double magneticshields

West 3D-MOT beamEast 3D-MOT beam

2D-MOT

3D-MOT

L2 : repumper / Raman 1L3 : cooling / Raman 2

retro-reflectionmirror

87Rb

λ/4

σ+

σ-

σ-

σ+

isolationplatform

seismometer

detection

Raman collimatorwith adjustable /4

detection

double magneticshields

West 3D-MOT beamEast 3D-MOT beam

Experimental Setup

Commercial fiber splitters

Fibered angled MOT collimators

Symmetric detection

Passive isolation platform

Baking 2~3 months at 120 °C

-200 -100 0 100 2000.0

0.1

0.2

atoms in 1s

MO

T f

luor

esce

nce

(a.u

.)

Time (s)

= 60s

Optical Bench

Compact : 60 by 90 cm

3 ECDL, 2 TAKey feature : Use the same lasers for Cooling and Raman beams

Noise

Parameters

2T=100 ms = 6 µsv ~ vr

Ndet = 106 Tc = 250 msContrast ~ 45 %

-180 0 180 360 540 720 900 1080 1260 1440 1620 1800 19800.2

0.3

0.4

0.5

0.6

0.7

0.8

Phase (degrees)

Tra

nsit

ion

prob

abil

ity

Sources of noise- laser phase noise - mirror vibrations- detection noise

SNR = 25σΦ = 1/SNR = 40 mrad/shotg/g = 10-7 /shot

Influence of Laser Phase Noise

DDS190 MHz

PLL

6,834 GHz

2L ~ 1 m

ECL1

ECL2

PhC

100 MHz

HF synthesis

7,024 GHz

DDS190 MHz

PLL

DDS190 MHz

PLL

DDS190 MHz

PLL

6,834 GHz

2L ~ 1 m

ECL1

ECL2

PhC

100 MHz

HF synthesis

7,024 GHz

SourceσΦ

(mrad/shot)

Lasers

100 MHz reference 1,0

Synthesis HF 0,7

PLL 1,6

Optical fiber 1,0

Retroreflection 2,0

Total 3,1

σg (g/Hz1/2)

1,3·10-9

0,9·10-9

2,0·10-9

1,3·10-9

2,6·10-9

3,9·10-9

2T=100 ms

Negligible with respect to observed interferometer noise

Vibration Noise

0.1 1 10 100

10-8

10-7

10-6

10-5 ON (day) OFF (day) OFF (night)

Vib

rati

on n

oise

(g/

Hz1/

2 )

Frequency (Hz)

)2()sin(1

)(1

4

2ca

k c

cg kfS

Tkf

Tkf

@ 1s : 2,9 · 10-6 g ; 1,4 · 10-6 g ; 7,6 · 10-8 g

OFF (day) OFF (night) ON (day)

Measurement of the vibration noise with a very low noise seismometer(Guralp T40)

Correlation : Gravimeter - Seismometer

T

Tssseff

s

vib dttUtgKk )()(Us(t) velocity signal => Expected phase shift

-8 -6 -4 -2 0 2 4 6 8

0.3

0.4

0.5

0.6

0.7

0.8 Without filter With filter

Tra

nsi

tion

pro

ba

bili

ty

Calculated phase shiftS

vib (rad)

Use the seismometer to correct the interferometer phase

-0.5 0.0 0.5

0.4

0.5

Tran

sitio

n pr

obab

ility

Calculated phase shift S

vib (rad)

Platform OffPlatform on

Vibration Correction

Post correction

Typical sensitivityWithout correction (day) : 8 10-8g @ 1 sWith correction (night) : 5 10-8g @ 1 s

With correction : 2-3 10-8g @ 1 s→ Gain ~ 3

0.36

0.40

0.44

0.48

0.52

Prob

abil

ité

de tr

ansi

tion

Nombre de coups

Sans correction Avec correction

Best resultNight – Air conditioning OFFWith correction : 1.4 10-8g @ 1 s

Seismometer PC

v(t) → vibS

keffgT² + vibSInterferometer

keffgT²

Long Term Measurements4 continuous days in April 2010 reveal earth tides

Long-Term Stability

100 1000 10000 1000000.1

1

10

All

an s

tand

ard

devi

atio

n of

g f

luct

uati

ons(

µG

al)

Time (s)

4 10-10g

Long term stability comparable to the accuracy of the tide model

Allan standard deviation of tide-corrected gravity data

Wavefront Aberrations

Δg < 10-9 g with T = 2 µK

R > 10 km !

→ flatness better than λ/300 !!!

Case of a curvature → δφ = K.r2 (with K = k1/2R)

Measure aberrations with wavefront sensor+ excellent optics+ colder atoms

t = 0

t = T

t = 2T

(v = 0)

(v = 0)

= 0 ≠ 0

vr≠0

1 =(vr = 0)

2> 1

3 >

Rt = 0

t = T

t = 2T

(v = 0)

(v = 0)

= 0 ≠ 0

vr≠0

1 =(vr = 0)

2> 1

3 >

R

Wavefronts are not flat : gaussian beams, flatness of the optics …

Characterization of Optics

• 40mm diameter• PV= /10• RMS =/100

Mirror

Simulation :• T = 2.5K• = 1.5mm

g/g = 1.4 10-9

g/g = 8 10-9

/4PV

Compact Atomic Gravimeter

Pyramidal reflector (2X2 cm2)

sensor head:-Few dm3

-no mechanical moving part-Magnetic shield 30 cm

Laser and electronic ensemble: 19 inches/12 U

➡ Principal demonstrations of key elements done➡ New prototype under realization (automne 2010)➡ High repetition rate (4 Hz)➡ Expected performances: 50 µGal/√Hz

Transportable device: field applications

Conclusion CAGLaboratory experiment – (for Watt Balance project)Aimed at ultimate accuracy <10-9gNeed for ultra cold atoms

Towards on-field sensorsTechnology is now mature Transfer to industryFirst step : MiniatomSoon on the market?

New schemesTrapped geometries : optical lattices, atom chips ?Further reduction in the size

New applicationsGeophysics, fundamental physics (tests of EP, space missions …)

light pulse atom interferometry for precision measurement jaewan kim myongji university

Documents

pulse slide

c slide

space slide

imprinted slide

experimental setup slide

raman transition ramping

resonance condition

principle of measurements