1

Inertial Sensors

Based on Cold AtomsErnst Rasel and Wolfgang Ertmer

2 Many disadvantages of

INERTIA

how to benefit from the inertia of atoms

A T

utor

ial…

3

Atomic Sensors

-an alternative technique

4O

utlin

e

Principle of Atom Interferometry

Accelerometers and Gyroscopes

Applications & Alternative Techniques

Outlook

5

Principle of

Atom Interferometry

6Th

e at

omic

rule

r

Louis Victor de Broglie Nobel prize 1929

dBatat

atatatat

hvm

kpvm

λ=

⋅==⋅

dBat

2kλπ

=

Atomic momentum

De-Broglie wavelength

Planck‘s constant

Classical World Quantum World

λdB Units in de Broglie wavelength

7A

tom

ic S

enso

rs…

for the local measurement of tiny accelerations/forces and rotations with high resolution:

Measuring displacements with cold atoms

Markers

Scale

8C

ompa

ring

2 ru

lers

..

Generating spatial modes of matter waves

…with Atom Interferometers

using Light as coherent Beam Splitter:

9 …based on

the mechanical effect of light

Laser|g, pat⟩

|e, pat+ k⟩

|g, pat⟩

Lk

Ato

mic

Bea

m S

plitt

er

10

Laser 1

Laser 2

Laser 1 Laser 2

Ig1, 0 k>Ig2, +2 k>

Ie, +1 k>

2-P

hoto

n Tr

ansi

tion

…transfer of two recoils by absorption & stimulated emission:

Bragg or Raman type beam splitter

11 … made out of Light

Opt

ics

Com

pone

ts

MIXER

pulse2/ −π

pulse2/ −π

pulse−π

[ ]k2p,gek0p,g

k0p,g

2i

121

1

+++

→+Φ

k2p,gek0p,g 2i

1 +→+ Φ

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

++++

+++

→+++

Φ−

Φ

Φ

k2p,gek2p,g

k0p,gek0p,g

k2p,gek0p,g

2i

2

1i

1

21

2i

1

12 Atomic Mach-Zehnder Interferometer

|e⟩

|g⟩

13

Accelerometers & Gyroscopes

14

constant accelerations:

⋅=∆ kTacc2ϕ a

Acc

eler

omet

er

to be used as…

15 Accuracy of ∆ g resp. g:

1part in 109

1 Gal=10-2 m/s2G

ravi

met

er

A. Peters et al., Metrologia 38, 25 (2001)

16

constant rotations:

Gyr

osco

pe

17 Sagnac-Effect

Rotational induced Phase shift:

Gain by de Broglie-Waves : ∼ 1011

for Light :

for Atoms :

18 Definition of the Area

constant rotations:

LAtom

rück km

1v =

Lk

TTrec 1vvA ×=

Differential Interferometry

19

Sensitivity:

close to shot noise

5*10-10 rad/s

4.8 µrad = 1 arcsec

Earth‘s rotation: 72 µrad/s

2 atom sources

thermal Cs-beams

transverse laser coolingG

yros

cope

T. L. Gustavson, et al., Classical and Quantum Gravity, 17, 2385 (2000)

20 Definition of the Area

constant rotations:

Cold atoms

)cos(v

v)cos(

1

2 ϑ

ϑ

Ω=

Ω

recL

A

LAtom

rück km

1v =

Lk

TTrec 1vvA ×=

Definition of the Area

21 Noise Sources

( ) …++++=∆ γσϕ δ2

22 211

J

N

PhJJges NnNN

Atomic projections noise

Shot noise of photon detection

Noise of electronics for detection

Raman-Laser

„quantum limit “, all contributions negligible compared to 1/NJ

1

2

3

J

D

22

for (ultra-)cold atomic inertial sensors

Con

cept

s…

23C

old

Ato

m G

yros

Pics by courtesy of A. Landragin

Gyromètre d‘ ondes matières(A. Landragin, SYRTE Paris)

Cold Atom Sagnac Interferometer (W.E., IQ Hanover)

24A

dvan

ced

Gra

vim

eter

MAGGIA(G. Tino, Univ. Florence)

Paris Gravimeter(F.Pereira d. Santos,

SYRTE, Paris)

25A

dvan

ced

Gra

vim

eter

Mobile Atomic Gravity Gradiometer Prototype Instrument (MAGGPI)Accelerometer Arrays(M. Kasevich, Stanford Univ., US)Airborne System, 140 dB common mode suppression

Space Gravigradiometer

(L. Maleki, JPL, US)

26 Applications of inertial sensors based on cold atoms

Atomic Sensor

27

• Fundamental Physics

• Applied Physics and connected fields

28 Watt Balance:Replacement of the kg artifact

AQ

S &

Sta

ndar

ds

AQS serves for measuring local gravity with a relative accuracy of 1 part in 109

2 Steps:

1) Weighing by balancingwith the magnetic force

Fg=m g = I∇Φ

2) Measuring the flux gradient

29A

QS

for …

… the determination of the Gravitational constant „G“

G- the worst known constantcomplementary methodExp. Accuracy: 1 part in 104

General Problem: The perfect Test mass Pendulum of the

„EotWash“ group

30

Earth Observation: The Geoid

31global and high-resolution models of the static and the time variable components of the Earth's gravity :

•global mass distribution •ocean heat flux, •long term sea level change, •upper oceanic heat content•large scale evapo-transpiration and soil moisture changes, •glaciology (Greenland ice sheet changes)•Space Exploration (Mars!)

Ear

th O

bser

vatio

n…

32 Earth and Planetary Observation The Geoid

AQ

S &

App

lied

Sci

ence

33 Correction of the non-gravitational accelerations

AQ

S &

App

lied

Sci

ence

STAR & SUPERSTAR Sensors

P.Touboul, ONERA Paris

Hz1010@Hzg103

Hz10/10@Hzg103

1411

1210

−−−

−−−

−⋅

⋅

34

Earth Observation: The Spin

35 High resolution rotation sensors

Applications:

- Investigation of the Earth‘s rotation

- Geology

- Star motion

- Satellite navigation

- Relativistic effects

- …

Gravity Probe B

VLBI

Effects:

- seismology

- Tidal forces- Variation of the

Earth‘s rotation

- Relativistic Effects

Resolution:

10-8 – 10-9 rad in 24 h

Resolution:

10-9 rad in 1 year

ΩE

10-4

10-5

10-6

10-7

10-8

10-9

10-10

Resolution:

10-10 – 10-11

rad/s √Hz-1

The Earth‘s rotation:ΩE ≈ 7,2·10-5 rad/s

Ring laserRot

atio

n se

nsin

g

36

Outlook

37

• Absolute inertial references

• The measurement of relativistic effects

• Testing the Equivalence Principle

• Drag-free sensors perhaps in gravitational wave detectors ?

are a promising alternative and complimentarytechnique for experiments in fundamental physics, like

Ato

mic

Qua

ntum

Sen

sors

38

LISA

µCOPE

AQ

S &

Fun

dam

enta

l Phy

sics

Observing the Lense-Thirring effect <1%

(Results end of the year!)

Testing the Equivalence Principle

1 part in 1015/1018

Detecting Gravitational Waves

39

HYPER:

http://sci.esa.int/home/hyper/index.cfm

Precision Atom Interferometryin Space

Aim:spatial resolution of the Lense-Thirring-Effect:Schiff effect

40 Lense-Thirring-effect measured by HYPER

θ

y

x

Ω

Signature for HYPER

0.5 1 1.5 2

3

2

1

1

2

310-14 rad/s

t/TOrbit

y

x

Lense-Thirring-Rotation:

θ

y

x

Ω

41 …performance

HY

PE

Rs2 atomic MOTsLaunch of 108 at @ 1µK with 20 cm/s, 2TDrift = 3 s Length: 60 cm

ΩSNL=2·10-12 rad/s/√HzASNL

=4·10-14 g/√Hz per shot, 0.3 Hz

42N

eed

for F

emto

-g

With cold atoms ?

43N

eed

for F

emto

-gTime: 3s → ? + Resolution: ~TDrift

2

- Tat < 1µK

- Dynamic Range

Atoms: 108→ ? + Resolution: ~√N- Tat ?- USO-Phase noise ?

Beam splitter: Multiphoton?- New Beam splitters?

„All-atomic“ Gravitational Wave detector? Thermal Atoms: + High Flux

small de Broglie wavelength Large Distances in short timeBeam splitter ?

44Cold Atom Sagnac Interferometer

Michael Gilovski

Thijs Wendrich Christian JentschTobias Müller (now at SYRTE)

Ernst M. RaselW.E.

CA

SI-T

eam

45

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46