atomic gyroscope: present status and prospective

Atomic gyroscope: present status and prospective

Arnaud Landragin Walid Chaibi Alexandre Gauguet Thomas Lévêque Franck Michaud

SYRTE-Observatoire de Paris

Introduction


Optical gyroscope

Two waves formula

Mach-Zehnder interferometer


Optical gyroscope

Two waves formula

Mach-Zehnder interferometer

Rotating the interferometer : Sagnac effect

€

ΔΦSAGNAC =4πλc

r Ω .

r A


Optical gyroscope

Ring laser gyro used in aircraft

Increase the area !...?

« Giant » laser gyro

Optical fibre gyro : FOG


Optical gyroscope

Ring laser gyro used in aircraft

Increase the area !...?

« Giant » laser gyro

orThe energy E

Optical fibre gyro : FOG


Atomic gyroscope

Matter waves : E ≈ mc2

Feasibility to realised high sensitive gyroscope !

€

ECs

Evisible

=mc 2

hω≈1011


Atomic 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


Atomic 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)


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


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( )


Double interferometer

(Sagnac effect)

π/2 π/2π



Rotation phase shift:Direction of atoms

π/2 π/2π



Rotation phase shift:Direction of atoms

Source B Source A

Two atomic sources of opposite directions

∆ΦA ∆ΦB

Sum: acceleration

Difference: rotation


Out-line

Atomic beam gyroscope


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.


Stanford/Yale laboratory gyroscopeRotation signal


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


Out-line

Cold Atom experiment

MOT A MOT B

Z

X

Y


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



3 cm

Area: 4 mm2

MOT A MOT B

Z

X

Y



probe 3 cm

Area: 4 mm2

MOT A MOT B

Z

X

Y



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


6 axes of inertia

B. Canuel et al., PRL 97, 010402 (2006)


Interference fringes2T = 80 ms and Contrast 30 %

€

P = O + Ccosr k eff ⋅

r g T 2 ±

r k eff

r V ΩT 2 + ΔΦlaser( )


Continuous measurements

36 hours

5.10-8 g

Time (s) Time (s)

Rotation Acceleration


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


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


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)


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))


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))


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)





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



€

φ1 − 2φ2 + φ3 = 0

Distortions of wave front : φ1 ≠ φ2 ≠ φ302 321 ≠+− φφφ



Double interferometer :superposition : δφ1-2δφ2+δφ3=0 Bias cancel on the rotation signal

€

φ1 − 2φ2 + φ3 = 0




Double interferometer :superposition : δφ1-2δφ2+δφ3=0

non superposition : δφ1-2δφ2+δφ3≠0

Bias cancel on the rotation signal

€

φ1 − 2φ2 + φ3 = 0


atomic gyroscope: present status and prospective

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