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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
Stimulated Raman Transitions
keff = k1-k2
|F=2 = |b
k2, 2k1, 1
87Rb |5P3/2
780 nm
|i >
ωatome
|F=1 = |a|5S1/2
Laser 2 → emission k2, 2
Laser 1 → absorption k1 ,1|a, p
ħkeff
|a,p+|b,p+ħkeff
Laser 2 → emission k2, 2
Laser 1 → absorption k1 ,1|a, p
ħkeff
|a,p+|b,p+ħkeff
Two photon transition couple |a and |b
3 level atoms Coherent beam splitter
Key advantage of Raman transitions- State labelling- Detection of the internal states
Mirror
( pulse)
Beam splitter
(/2 pulse)
,e + h effp k,f p
( ),12
, ef + + h effp kp
,f p
0 20 40 60 80 100 120
0.0
0.2
0.4
0.6
0.8
Tra
nsit
ion
Pro
babi
lity
Pulse duration (µs)
Analogy : Optical/Atomic Interferometry
)cos1(2
1
C
NN
NP
eff
eff
eff
kpp
kp
kpp
tz
|p+ ħ keff
|p
π/2
|p
|p+ ħ keff A
BC
D
0 T 2T
|p
π π/2
I
II
tz
|p+ ħ keff
|p
π/2
|p
|p+ ħ keff A
BC
D
0 T 2T
|p
π π/2
I
II
Optical Atomic
Atomic Interferometer analogous to Mach-Zehnder Interferometer
Coherent splitting and recombination
Two complementary output ports
Intensity modulation
)cos1(0 II
Two momentum states
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
Principle of Measurements
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)
• 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
Principle of Measurements
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)
• 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
Principle of Measurements
• 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
• 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 …)