Atomic gyroscope: present status and prospective
Transcript of Atomic gyroscope: present status and prospective
Atomic gyroscope: present status and prospective
Arnaud Landragin Walid Chaibi Alexandre Gauguet Thomas Lévêque Franck Michaud
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Introduction
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Optical gyroscope
Two waves formula
Mach-Zehnder interferometer
SYRTE-Observatoire de Paris
Optical gyroscope
Two waves formula
Mach-Zehnder interferometer
SYRTE-Observatoire de Paris
Optical gyroscope
Two waves formula
Mach-Zehnder interferometer
Rotating the interferometer : Sagnac effect
€
ΔΦSAGNAC =4πλc
r Ω .
r A
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Optical gyroscope
Ring laser gyro used in aircraft
Increase the area !...?
« Giant » laser gyro
Optical fibre gyro : FOG
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Optical gyroscope
Ring laser gyro used in aircraft
Increase the area !...?
« Giant » laser gyro
orThe energy E
Optical fibre gyro : FOG
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Atomic gyroscope
Matter waves : E ≈ mc2
Feasibility to realised high sensitive gyroscope !
€
ECs
Evisible
=mc 2
hω≈1011
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Atomic gyroscope
Matter waves : E ≈ mc2
Feasibility to realised high sensitive gyroscope !
€
ECs
Evisible
=mc 2
hω≈1011
Interferometer with atomic wave packets
Atomic waves manipulating with lasers
€
ΔΦSAGNAC =2E
r A ⋅
r Ω
hc 2
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Atomic gyroscope
Matter waves : E ≈ mc2
Feasibility to realised high sensitive gyroscope !
€
ECs
Evisible
=mc 2
hω≈1011
Interferometer with atomic wave packets
Atomic waves manipulating with lasers
€
ΔΦSAGNAC =2E
r A ⋅
r Ω
hc 2
Three parameters: AreaEnergy of the particleFlux (signal to noise)
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Stimulated Raman transitions
6S1/2 9,2 GHz
6P3/2
852 nm
Raman transitions
D2 line for Cs
Transition between 2 momentum states
Coherent superimposition of the two momentum states
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Wave packet manipulation
Rabi oscillations between
Tran
sitio
n pr
obab
ility
ΩRabiτ
π/2 π
and
π pulseAtomic mirror
π/2 pulseAtomic beam splitter
€
12
f , p + e, p + hkeff eiφ( )
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Double interferometer
(Sagnac effect)
π/2 π/2π
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Double interferometer
Rotation phase shift:Direction of atoms
π/2 π/2π
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Double interferometer
Rotation phase shift:Direction of atoms
Source B Source A
Two atomic sources of opposite directions
∆ΦA ∆ΦB
Sum: acceleration
Difference: rotation
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Out-line
Atomic beam gyroscope
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Sensitivity
6.10-10 rad.s-1 in 1 seconde
( ~ 8.10-6 ΩΩE)
Atomic beam gyroscope (laboratoire Stanford/Yale)
Magnetic shield
Oven of Cs
Manipulationof the atomic wavepackets
Atomic beams
Statepréparation
LaserCooling
Detection
Rotation rate (x10-5) rad/s-10 -5 0 5 10 15 20
Nor
mal
ized
sign
al
-1
0
1
Interference pattern
2 m
high velocity: 300 m.s-1
high flux ~ 1011 at.s-1
Area: 20 mm2
T L Gustavson, A. Landagin and M. Kasevich, Class. Quantum Grav. 17 (2000) 1–14.
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Stanford/Yale laboratory gyroscopeRotation signal
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Stanford/Yale laboratory gyroscopeRotation signal
Impoved long term stabilitybut compromise with short term:
6.10-8 rad.s-1.Hz-1/2
at 1000s: 2.5 10-9 rad.s-1 (not compensated)
at 10 000s: 6 10-10 rad.s-1 (temperature-compensated by optimal Kalman filter)
D.S. Durfee, Y.K. Shaham, M. Kasevich 2006
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Out-line
Cold Atom experiment
MOT A MOT B
Z
X
Y
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PARAMETERS
2 MOT of Cs Tatoms~1 µK
Launch velocity 2,4 m/sAngle 8° Vl=0,33 m.s-1
Tc = 0,58 sFlux ~ 106 at.s-1
Cold atoms gyroscope
MOT A MOT B
Z
X
Y
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Cold atoms gyroscope
3 cm
Area: 4 mm2
MOT A MOT B
Z
X
Y
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Cold atoms gyroscope
probe 3 cm
Area: 4 mm2
MOT A MOT B
Z
X
Y
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Cold atoms gyroscope
probe 3 cm
Area: 4 mm2
Unique laser beam modulated on timeLong term stability and knowledge of the scaling factor
Cold atomsGood control of the mean velocitySmall velocity dispersion
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6 axes of inertia
B. Canuel et al., PRL 97, 010402 (2006)
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6 axes of inertia
B. Canuel et al., PRL 97, 010402 (2006)
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Interference fringes2T = 80 ms and Contrast 30 %
€
P = O + Ccosr k eff ⋅
r g T 2 ±
r k eff
r V ΩT 2 + ΔΦlaser( )
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Continuous measurements
36 hours
5.10-8 g
Time (s) Time (s)
Rotation Acceleration
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Rotation & acceleration stability
Rotation limited by Quantum Projection Noisedue to reduced atomic flux
Acceleration limited by vibrations
5,5 10-7 m.s-2 at 1 second
≈ 10-8 m.s-2
2,4 10-7 rad.s-1 at 1 second
≈ 10-8 rad.s-1
Time (s)
Alla
n va
rianc
e de
viat
ion
of ro
tatio
n (r
ad.s
-1)
Time (s)A
llan
varia
nce
devi
atio
nof
acc
eler
atio
n (m
.s-2
) 2.4 10-7 rad.s-1/√τ
5.5 10-7 m.s-2/√τ
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Rotation & acceleration stability
Rotation limited by Quantum Projection Noisedue to reduced atomic flux
Acceleration limited by vibrations
5,5 10-7 m.s-2 at 1 second
≈ 10-8 m.s-2
2,4 10-7 rad.s-1 at 1 second
≈ 10-8 rad.s-1
Time (s)
Alla
n va
rianc
e de
viat
ion
of ro
tatio
n (r
ad.s
-1)
Time (s)A
llan
varia
nce
devi
atio
nof
acc
eler
atio
n (m
.s-2
)
room temperature fluctuationsImperfection in Raman laser wavefront and control of the trajectories of the atoms
2.4 10-7 rad.s-1/√τ
5.5 10-7 m.s-2/√τ
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Test the linearity
NS
O
Changing the orientation of the experiment - modulate the projection of the Earth rotation- changes the rotation rate in controlled way
a Z
XY
π/π/
Ω
π
bias : 28.3 mrad ± 0.7 mrad
€
ΔΦ = ΔΦBias +K sin θ −θ0( )Fit by the equation :
Gyroscope linearity : quadratic term <10-5
The scale factor: 15124 ± 12 rad /(rad.s-1)
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Cold atom gyroscope summery
Access to the six components of inertia (may be interesting for earthquake-induced rotational ground motions)
Sensitivity to rotation: short term: quantum projection noise (limited flux) long term: wave front imperfections and fluctuations of the sources
gyroscope accuracy: bias : => wave front errors scaling factor (quadratic term < 10-5 study limited by long term stability)
Performances similar to best commercial optical gyroscope and closed to beam gyroscope (factor 4) (D. Durfee et al. PRL 97, 240801 (2006))
SYRTE-Observatoire de Paris
Cold atom gyroscope summery
Access to the six components of inertia (may be interesting for earthquake-induced rotational ground motions)
Sensitivity to rotation: short term: quantum projection noise (limited flux) long term: wave front imperfections and fluctuations of the sources
gyroscope accuracy: bias : => wave front errors scaling factor (quadratic term < 10-5 study limited by long term stability)
No fundamental limits
Performances similar to best commercial optical gyroscope and closed to beam gyroscope (factor 4) (D. Durfee et al. PRL 97, 240801 (2006))
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ProspectsHigher flux (2D MOT) x 100Change of geometry with cold atoms => increase of the area
Atomic beam experiment: 20 mm2
This first cold atom experiment: 4 mm2
SYRTE-Observatoire de Paris
ProspectsHigher flux (2D MOT) x 100Change of geometry with cold atoms => increase of the area
Atomic beam experiment: 20 mm2
This first cold atom experiment: 4 mm2
interferometer
cold atom source 1
preparationdetection
15 3
π/2
ππ/2
cold atom source 2
A
Split the Raman laser 3 pulses straight trajectories (E. Rasel University of Hannover) (34 mm2)
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ProspectsHigher flux (2D MOT) x 100Change of geometry with cold atoms => increase of the area
Atomic beam experiment: 20 mm2
This first cold atom experiment: 4 mm2
4 pulses sequences (under development) (up to 11 cm2)expect 10-9 rad.s-1 in 1 s
in the range of 10-10-10-11 rad.s-1 in 1 less than 1h
interferometer
cold atom source 1
preparationdetection
15 3
π/2
ππ/2
cold atom source 2
A
Split the Raman laser 3 pulses straight trajectories (E. Rasel University of Hannover) (34 mm2)
S. Merlet, et al., Metrologia 46, 87–94, (2009) arXiv:0806.0164
Acquisition without isolation
Earthquake in China 2 Mars 20th 2008 (magnitude 7,7)
Wave front distortions
Flat wave front: φ1 = φ2 = φ3
€
φ1 − 2φ2 + φ3 = 0
Wave front distortions
Flat wave front: φ1 = φ2 = φ3
€
φ1 − 2φ2 + φ3 = 0
Distortions of wave front : φ1 ≠ φ2 ≠ φ302 321 ≠+− φφφ
Wave front distortions
Flat wave front: φ1 = φ2 = φ3
Double interferometer :superposition : δφ1-2δφ2+δφ3=0 Bias cancel on the rotation signal
€
φ1 − 2φ2 + φ3 = 0
Distortions of wave front : φ1 ≠ φ2 ≠ φ302 321 ≠+− φφφ
Wave front distortions
Flat wave front: φ1 = φ2 = φ3
Double interferometer :superposition : δφ1-2δφ2+δφ3=0
non superposition : δφ1-2δφ2+δφ3≠0
Bias cancel on the rotation signal
€
φ1 − 2φ2 + φ3 = 0
Distortions of wave front : φ1 ≠ φ2 ≠ φ302 321 ≠+− φφφ