Precision measurement of the

Gravitational Constant by

matter-wave interferometry

The MAGIA experiment

Gabriele Rosi

Physics Department of Florence

INFN

LENS

100° Congresso SIF

Outline

The Gravitational constant problem

MAGIA experiment and “big G”

measurement

Results

G. Rosi 100° Congresso SIF – PISA

A very hard measurement

Cavendish

1798

Quinn

2001

G. Rosi 100° Congresso SIF – PISA

Why G is difficult to Measure

1. WEAKNESS

2. NON-SCREENABILITY

3. SYSTEMATICS EFFECT

4. ISOLATED

Competing effects of other forces

Perturbation of surrounding masses

- Source mass density homogeneity

- Mass geometry

- Source-probe distance

- Not easy to generate accurately known

gravitational fields

No connection with other fundamental

constants

“Big G is the Mt. Everest of precision measurement science,

and it should be climbed.”

James Faller

University of Colorado, Boulder

G. Rosi 100° Congresso SIF – PISA

Atom Interferometry for gravity measurement

Ingredients:

A source of Cold Atoms (~ μ K or less)

(the sample must be slowly expanding and weakly interacting )

A laser system to cool the sample and to manipulate

the wavepacket

Atom Interferometry can measure accelerations

We use Cold Atoms as free falling microscopic masses

Quantum features of matter allow to improve the sensitivity

(not just a time-of-flight measurement in the “classical way”)

G. Rosi 100° Congresso SIF – PISA

Atom / light Interferometry: the analogy

Once you have an atomic two level system

you can make the analogy with light looking

at the Rabi’s population oscillations scheme 2

Interaction time τ [1/Ω]

P1-

2

ππ/2

|1 ›

|2 ›

•π /2 pulse works like a beamsplitter

momentum transfer

•π pulse works like mirror;

momentum transfer

2

state |2>

state |1>beamsplitter

interference

fringe

Optical interferometer

Atom interferometer

SPLIT RECOMBINEREFLECT

G. Rosi 100° Congresso SIF – PISA

Atom Interferometry: theory

0g

)cos1(2

12 totP )cos1(

2

11 totP

0 tot

Wave function PHASE evolution

2

2

|1>

|2>

T T20

II

IA

C

If

0g

BC

D

B

D

2gTkefftot

Population on final State depends

On the interferometer phase

2

2

1gTDDCC

22gTBB

GRAVITY BREAKSTHE SIMMETRY

fringes

varying RAMAN laser’s phase

z

t

totally symmetric

evolution

G. Rosi 100° Congresso SIF – PISA

MAGIAMisura Accurata di G mediante Interferometria Atomica

http://www.fi.infn.it/sezione/esperimenti/MAGIA/home.html

G

SOURCE MASSESWell-characterized tungsten cylinders

PROBE MASSESCold, freely falling 87Rb atoms

MEASUREMENT METHODRaman atom interferometry (local acc.)Spatial & temporal differential scheme

CALCULATION of gravitational attraction

MAGIA - the procedure

G. Rosi 100° Congresso SIF – PISA

MAGIA - the experimental sequence

G. Rosi 100° Congresso SIF – PISA

The G measurement (1)

1 G. Rosi et al., “Precision measurement of the Newtonian gravitational constant using cold atoms”, Nature 510, 518-521

Features:

Source masses modulation

time: 30 mins

Integration time:

more than 100 hours over 2

weeks (July 2013)

Sensitivity: 3x10-9 g/Hz1/2

Final sensitivity: ~ 10-11 g

ΔΦ = 0.547870(63) rad

(116 ppm stat.)

Systematic (2)

Error budget:

Most of the entries are evaluated through MonteCarlo simulation of the experiment, evaluating

the derivative of Φ with respect to each parameters

Final inaccuracy: 92 ppm

Limiting parameters: atomic samples dimensions, source masses position (Radial), Coriolis

Effect

2 M. Prevedelli et al., “Measuring the Newtonian constant of gravitation G with an atomic interferometer”, Phil. Trans. R. Soc. A 372 no. 2026

Current status

6.67191(77)stat

(62)sys

× 10-11 m3 Kg-1 s-2

G. Rosi 100° Congresso SIF – PISA

People

People on G measurement

Gabriele Rosi (Florence University, INFN)

Fiodor Sorrentino (INFN)

L. Cacciapuoti (ESA - Noordwijk)

M. Prevedelli (Associate Professor, Bologna University)

G. M. Tino (Group Leader)

Thanks for your attention

G. Rosi 100° Congresso SIF – PISA