Transcript Atom interferometry and its applications

Light Pulse Atom Interferometry for
Precision Measurement
Jaewan Kim
Myongji 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 …)
Navigation (submarine…)
Tests of
fundamental physics
(equivalence principle,
tests of gravitation …)
g
Metrology:
Watt Balance
(new definition of the kg)
Absolute Gravimeters
Commercial Gravimeter : FG5
Principle : Michelson
interferometer with falling corner
cube
Accuracy : 2 µGal
1 µGal = 10-8 m/s2 ~ 10-9g
Atomic gravimeter
Stanford experiment in 2001 :
– Resolution: 3 µGal after 1 minute
– Accuracy: <3 µGal
From A. Peters, K.Y. Chung and S. Chu
Principle of Atom Interferometry
Stimulated Raman Transitions
3 level atoms
87Rb
|5P3/2
|i >
780 nm
Coherent beam splitter
k1, 1
|a,p
+
|b,p+ħkeff
k2, 2
ħkeff
|F=2 = |b
Laser 2 → emission k2, 2
ωatome
keff = k1-k2
|F=1 = |a
Two photon transition couple |a and
|b
Key advantage of Raman
transitions
- State labelling
- Detection of the internal states
Transition Probability
|5S1/2
Laser 1 → absorption k1 ,1
|a, p
0.8
Mirror
0.6
f,p
e, p + hkeff
(p pulse)
0.4
f,p
0.2
Beam splitter
1
( f , p + e, p + h keff )
2
(p/2 pulse)
0.0
0
20
40
60
80
100
Pulse duration (µs)
120
Analogy : Optical/Atomic Interferometry
Atomic
Optical
z 0
T
|p
|p
2T
D
t
I
A
|p+ ħ keff 
B
II
C
π/2
Coherent splitting and recombination
π
Intensity modulation
I  I 0 (1  cos)
 |p+ ħ keff 
π/2
Two momentum states
Two complementary output ports
P p  p  k

eff
N p k
eff
N p  N p k
 |p
eff
1
 (1  C cos)
2
Atomic Interferometer analogous to Mach-Zehnder Interferometer
Interferometer Phase Shift
Laser phase gets
imprinted
p
2
b
b
+
a
a
p

2
A
2
p
2
1
3
-
 A  1   2A
 B  2B  3
 2B
   A   B
 1  22  3
 2A   2B
2 
2
Case of an Acceleration
 
(t )  keff .r (t )
1 2
at
2
T
T
2
3

a
1
1  2
 2 (t 2 )  keff .aT
2
  2
  1(t1) – 22 (t2) + 3 (t3) =
keff .aT
1 (t1 )  0
1 
 3 (t3 )  keff .a (2T ) 2
2
Implementation of Raman Laser
• Vertical Raman lasers
Laser 1
• Retroreflect two (copropagating) Raman lasers
Pulse 1
z0
Pulse 2
z (T ) 
1
gT 2
2
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
Pulse 3
z (2T )  2 gT 2 attached to position of retroreflecting mirror
Laser 2
Miroir
Interferometer measurement
= relative displacement atoms/mirror
Principle of Measurements
• Free fall → Doppler shift of the resonance condition of the Raman transition
1  2  e   f  k eff v(t ) 
hkeff2
2m
• Ramping of the frequency difference to stay on resonance :
DDS1 (Hz)
π
π /2
  keff g T   T
2
-125.718
2
Probabilité de transition
π/2
  0   t
-125.716
-125.714
0.7
0.6
0.5
C~45%
0.4
0.3
0.2
-25.1435
-25.1430
 (MHz.s-1)
Principle of Measurements
• Free fall → Doppler shift of the resonance condition of the Raman transition
1  2  e   f  k eff v(t ) 
hkeff2
2m
• Ramping of the frequency difference to stay on resonance :
DDS1 (Hz)
π
π /2
  keff g T   T
2
-125.718
2
Probabilité de transition
π/2
  0   t
-125.716
-125.714
0.7
0.6
0.5
C~45%
0.4
0.3
0.2
-25.1435
-25.1430
 (MHz.s-1)
Principle of Measurements
• Free fall → Doppler shift of the resonance condition of the Raman transition
1  2  e   f  k eff v(t ) 
hkeff2
2m
• Ramping of the frequency difference to stay on resonance :
DDS1 (Hz)
π
π /2
  keff g T   T
2
-125.718
2
Probabilité de transition
π/2
  0   t
-125.716
-125.714
0.7
0.6
0.5
C~45%
0.4
0.3
0.2
-25.1435
-25.1430
 (MHz.s-1)
Principle of Measurements
• Free fall → Doppler shift of the resonance condition of the Raman transition
1  2  e   f  k eff v(t ) 
hkeff2
2m
• Ramping of the frequency difference to stay on resonance :
DDS1 (Hz)
π
π /2
-125.718
  keff g T   T
2
• Dark fringe :
independent of T
g
2
0
k eff
Probabilité de transition
π/2
  0   t
-125.716
-125.714
0.7
0.6
0.5
C~45%
0.4
0.3
0.2
-25.1435
-25.1430
 (MHz.s-1)
Experiments
Experimental Setup
2nd generation vacuum chamber
• 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
Experimental Setup
seismometer
double
magnetic
shields
2D-MOT
87Rb
L2 : repumper / Raman 1
L3 : cooling / Raman 2
σ+
σ-
Raman collimator
with adjustable /4
West 3D-MOT beam
East 3DMOT
beam
3D-MOT
detection
detection
σ-
σ+
λ/4
retro-reflection
mirror
isolation
platform
Experimental Setup
Commercial fiber splitters
Fibered angled MOT collimators
Symmetric detection
Passive isolation platform
Baking 2~3 months at 120 °C
MOT fluorescence (a.u.)

 atoms in 1s
0.2
 = 60s
0.1
0.0
-200
-100
0
Time (s)
100
200
Optical Bench
Compact : 60 by 90 cm
3 ECDL, 2 TA
Key feature : Use the same lasers for Cooling and Raman beams
Noise
Transition probability
0.8
Parameters
0.7
0.6
2T=100 ms
 = 6 µs
sv ~ v r
Ndet = 106
Tc = 250 ms
Contrast ~ 45 %
0.5
0.4
0.3
0.2
-180 0
180 360 540 720 900 1080 1260 1440 1620 1800 1980
Phase (degrees)
SNR = 25
σΦ = 1/SNR = 40 mrad/shot
sg/g = 10-7 /shot
Sources of noise
- laser phase noise
- mirror vibrations
- detection noise
Influence of Laser Phase Noise
ECL1
2T=100 ms
ECL2
Source
PLL
DDS
190 MHz
PhC
6,834 GHz
7,024 GHz
HF synthesis
2L ~ 1 m
L
a
s
e
r
s
σΦ
σg
(mrad/shot)
(g/Hz1/2)
100 MHz reference
1,0
1,3·10-9
Synthesis HF
0,7
0,9·10-9
PLL
1,6
2,0·10-9
Optical fiber
1,0
1,3·10-9
Retroreflection
2,0
2,6·10-9
Total
3,1
3,9·10-9
100 MHz
Negligible with respect to observed interferometer noise
1/2
Vibration noise (g/Hz )
Vibration Noise
Measurement of the
vibration noise
with a very low noise
seismometer
(Guralp T40)
-5
10
ON (day)
OFF (day)
OFF (night)
-6
10
-7
10
-8
10
0.1

100
4
 sin(pkfcT ) 
 S a (2pkfc )
s g2 ( )   
 k 1  pkfcT 
1
1
10
Frequency (Hz)
@ 1s : 2,9 · 10-6 g ; 1,4 · 10-6 g ; 7,6 · 10-8 g
OFF (day) OFF (night) ON (day)
Correlation : Gravimeter - Seismometer
  k eff K s
Us(t) velocity signal => Expected phase shift
s
vib
s
T
s
Without filter
With filter
Transition probability
0.8
Transition probability
 g (t ) U (t ) dt
Platform Off
Platform on
0.5
0.4
-0.5
T
0.0
0.5
S
Calculated phase shift 
vib
(rad)
0.7
0.6
0.5
0.4
0.3
-8
-6
-4
-2
0
2
4
6
S
Calculated phase shift 
vib
8
(rad)
 Use the seismometer to correct the interferometer phase
Vibration Correction
Seismometer
PC
keffgT²
Post correction
v(t) → vibS
Interferometer
Probabilité de transition
0.52
Sans correction
Avec correction
keffgT² + vibS
Typical sensitivity
Without correction (day) : 8 10-8g @ 1 s
With correction (night) : 5 10-8g @ 1 s
0.48
With correction : 2-3 10-8g @ 1 s
→ Gain ~ 3
0.44
Best result
Night – Air conditioning OFF
With correction : 1.4 10-8g @ 1 s
0.40
0.36
Nombre de coups
Long Term Measurements
4 continuous days in April 2010 reveal earth tides
Long-Term Stability
Allan standard deviation of tide-corrected gravity data
Allan standard deviation
of g fluctuations(µGal)
10
1
4 10-10g
0.1
100
1000
10000
100000
Time (s)
Long term stability comparable to the accuracy of the tide model
Wavefront Aberrations
Wavefronts are not flat : gaussian beams, flatness of the optics …
Case of a curvature
→ δφ = K.r2 (with K = k1/2R)
1 =(vr = 0)
t=0
t=T
R
vr≠0
 R > 10 km !
2> 1
 (v = 0)
3 > 
t = 2T
 (v = 0)
 ≠ 0
Δg < 10-9 g with T = 2 µK
 = 0
→ flatness better than
λ/300 !!!
Measure aberrations
with wavefront sensor
+ excellent optics
+ colder atoms
Characterization of Optics
Mirror
• 40mm diameter
• PV= /10
• RMS =/100
Simulation :
• T = 2.5mK
• s = 1.5mm
g/g = 1.4 10-9
PV
/4
g/g = 8 10-9
Compact Atomic Gravimeter
➡
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
sensor head:
-Few dm3
-no mechanical moving part
-Magnetic shield
Pyramidal reflector
(2X2 cm2)
30 cm
Laser and electronic ensemble:
19 inches/12 U
Conclusion
 CAG
Laboratory experiment – (for Watt Balance project)
Aimed at ultimate accuracy <10-9g
Need for ultra cold atoms
 Towards on-field sensors
Technology is now mature
 Transfer to industry
First step : Miniatom
Soon on the market?
 New schemes
Trapped geometries : optical lattices, atom chips ?
Further reduction in the size
 New applications
Geophysics, fundamental physics (tests of EP, space missions …)