Post on 17-Mar-2020
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
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
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