MisuraAccurata diG medianteInterferometria Atomica

…towards a high precision measurement of the gravitational constant

using atom interferometry

M. Fattori G. Lamporesi T. Petelski M. Prevedelli G. M. Tino

in collaboration with

J. Stuhler (university of Stuttgart)A. Peters (University of Berlin)

The goal of MAGIA experiment is the high precision measurement of the Newtonian gravitational constant G using atom interferometry.

Despite some 300 measurements, G remains the least accurately known fundamental constant: the 1998 CODATA recommended value of G has an uncertainty of 1500 parts per million.

PAST MEASUREMENTS

Up to now only few conceptually different methods have been used: -the torsion balance-the torsion pendulum -the beam balance -the pendulum cavity.

All this methods have in common that masses, which probe the acceleration caused by well known source masses, are suspended, eg. with fibers.

MAGIA – THE IDEA

This possible source of systematic effects can be eliminated if one performs a free-falling experiment.

Free falling 87Rb atoms will be used as probe masses to test the gravitational acceleration of nearby source masses.

The combination of Raman atom interferometry and laser cooling will allow us to achive high sensitivity.

Using atoms with well known properties, instead of macroscopic probe masses, will help to reduce systematic errors and permit an accuracy at the level of 10-4.

g g

aM

Advantages:

- no suspension

- small probe masses with well-known properties

- well-controlled external degrees of freedom with laser cooling

- internal degrees of freedom offer new measurement possibilities

- less (or at least different) systematic effects

- the atoms position with respect to the wavefronts of a phase stabilized laser is encoded in the atomic wavefunction

How to obtain a cold cloud of free falling atoms? ATOMIC FOUNTAIN

1. Trapping Magneto-Optical Trap (MOT)

3. Launching upwards Atomic Fountain

2. Cooling Optical Molasses

launch velocity

proportional to

laser detuning δ

When the cold atom cloud pass through a horizontal sheet of light a fluorescence signal is emitted

0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45

0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

0,18

Segn

ale

di fl

uore

scen

za (V

)

tempo (s)

(V)

Time (s)

1st pass: UPWARDS

2nd pass: DOWNWARDS

How to make a precision measurement of g? RAMAN ATOM INTERFEROMETER

9 10 atomsN

T 5 K

maxh 1 m

Optical Raman transitions- momentum transfer to the atoms- velocity selectivity

1

2

R1ω R2ω

i

87Rb ground state hyperfine splitting

87Rb D2 line

TRANSVERSAL PULSES-the interferometer encloses an area-used to measure rotations (GYROSCOPES)

LONGITUDINAL PULSES-no area enclosed-used to measure accelerations (GRAVIMETERS)

3 pulse sequence-1st pulse (/2 pulse) …………splitting-2nd pulse ( pulse) ……………..inversion-3rd pulse (/2 pulse) ………...recombination

Each Raman pulse induces:• a change of the internal state• a momentum transfer• an additional phase term

2e e g eΔΦ = k gT + Φ = Δφ + Φ

Final population: |1

NN = (1+cosΔΦ)

2 |1N

N1

0eΦ0

2

2

For T=150 ms a phase term of 2 corresponds to an acceleration of 10-6 g

For S/N=1000 the sensitivity is 10-9 g per shot

How to measure the Newtonian Gravitational Constant with a high accuracy? DOUBLE-DIFFERENTIAL MEASUREMENT

With a single atom interferometer

one can measure local accelerations GRAVIMETER(gravity)

Using two simultaneous but vertically

displaced atom interferometers it is GRADIOMETERpossible to measure local gradients of accelerations (gravity gradient)

g

2e

Δφg=

k T

All the effects that induce the same acceleration all over the experimental region are rejected by a differential measurement :

- constant gravity - accelerations seen because of optics vibrations- uniform e.m. fields

Trapping, cooling and launching cell

Interferometer 1

Interferometer 2

Detection region

Adding well-known source masses around the interferometric tube the atoms trajectory is perturbed in a known way

So, using a further differential method, it is possible to deduce the value of the Gravitational Coupling Constant

TOTΔΦ G

Appropriate trajectories

Performing the measurement around the maximum of the total gravitational field we get less stringent requirements to initial atomic position and velocity to reach an accuracy of 10-4

Acceleration induced by source masses along the central vertical axes of the tube

Acceleration induced by source masses + the effect of gravity gradient along the central vertical axes of the tube

Configuration C1 Configuration C2

cloud 1

cloud 2

PUBLICATIONS

G.M. Tino, “High Precision Gravity Measurements by Atom Interferometry” in 2001: A Relativistic Spacetime Odyssey, I. Ciufolini, D. Dominici, L. Lusanna eds., p. 147, World Scientific (2003).

T. Petelski, M. Fattori, G. Lamporesi, J. Stuhler e G.M. Tino, “Doppler-free Specroscopy Using Magnetically Induced Dichroism of Atomic Vapour: a New Scheme for Laser Frequency Locking”, Eur. Phys. J. D 22, 279 (2003).

M. Fattori, G. Lamporesi, T. Petelski, J. Stuhler e G.M. Tino, “Towards an Atom Interferometric Determination of the Newtonian Gravitational Constant”, Phys. Lett. A 318, 184 (2003).

J. Stuhler, M. Fattori, T. Petelski, G.M. Tino, “MAGIA : Using atom interferometry to determine the Newtonian gravitational constant”, J. Opt. B: Quantum Semiclass. Opt. 5, S75 (2003).

• Portable gravimeters/gradiometers

• Test of 1/r2 gravity dependence at small distances

• Detection of gravitational waves ?

Geophysical applications

Experiments in spaceFUTURE PROSPECTS

EXPERIMENTAL APPARATUS

VACUUM SYSTEM

Non-magneticHigh resistivityLow thermal expansionLight but hard

Glue (AREMCO 631)orLead o-rings

leadcrossedo-rings

20 Aluminium

foils

FIBER SYSTEM

• Lasers delivered with polarization preserving fiber system including power stabilization

• 1 to 3 fiber splitters for MOT with combination of cooling and repumping lasers.The splitters are optimized for high stability and minimum power loss

• MOT laser beams expansion possible up to 37 mm diameter

In collaboration with Scheafter&Kirchhoff GmbH

MOT cell in 1-1-1 configuration

Fiber splitter

Fiber mount directly fixed on the MOT cell

PHASE LOCK FOR RAMAN BEAMS

•Diode laser phase lock laser system•combined analog-digital lock for high stability and large bandwidth•max. bandwidth ~ 10 MHz•phase noise less than 0.07 rad (integrated between 300 Hz and 10 MHz)•laser power amplification with MOPA•lower phase noise expected for longer laser cavities ( at the moment only 1 cm long )

SOURCE MASSES

•Two cylinders of 470 kg each

•sintered material (95% W, 3,5% Ni, 1,5% Cu)•produced by PLANSEE and called Densimet 180K

•Density = 18 g cm-3

•resistivity = 12x10-8 Wm•thermal expansion = 5x10-6 K-1

•surface roughness = 3 mmDensimet sinterized at 1500 oC and 1 atm presents holes (f»150 mm) in the center region of big blocks.These holes cause a change of the average density of ~3x10-4

Simulations on random distribution of these holes in different regions of the cylinder show a maximum shift in the value of G of 1x10-4

Additional treatment and characterization

•HIP (Hot Isostatic Pressing) of the cylinders at 1200 oC and 1500 atm to reduce holes

•Destructive test with density comparison at different points of the cyliders (relative measurements will reveal differences smaller than 0.002 g cm-3)

Systematic effects due to the mass distribution can be controlled at the 10-4 level

Induced acceleration g 10-7g

Sensitivity 10-9g

Relative error 10-9 10-2

Eart

h

Sour

ce

Mas

ses

Integration over 10000 measurements

4ΔG10

G

In collaboration with LNF (Laboratori Nazionali di Frascati)

Any other effect that induces different accelerations in different places is in fact cancelled out repeating the double launch just moving the masses from configuration C1 to configuration C2

REQUIREMENTS

•Number of atoms: 106

• v < vrec (vrec~ 6 mm/s )•detection: SNR = 1000

Istituto Nazionale di Fisica Nucleare Sezione di Firenze

Università degli Studi di FirenzeDipartimento di Fisica/LENS

3-11

2

mG = (6.673 0.010) x 10

kg s

•launch accuracy: 1 mm•knowledge of gravity gradient: 1%•knowledge of th distance between masses: 0.01 mm•movement accuracy of source masses: 0.1 mm

The critical parts of the vacuum system are made of a Titanium alloy

• Optical windows are connected to Titanium alloy with new sealing techniques

Mass holder and elevator

R2ω

R1ω

| 2

| 2

| 1

| 1

| 1

| 1A

BC

D

| 2

R1ω R2ω

| 1

| 1

| 1

| 1

| 2

| 2

| 2

A

B C

D

t

R1k

R1k

R2k

R2k

R2k

T T

ππ2

π2

z(t)

| 2

| 2

| 2

| 1

| 1

| 1

| 1