Transcript Presentazione di PowerPoint - Istituto Nazionale di Fisica

Misura
Accurata di
G mediante
Interferometria
Atomica
Istituto Nazionale di Fisica Nucleare
Sezione di Firenze
Università degli Studi di Firenze
Dipartimento di Fisica/LENS
G = (6.673  0.010) x 10
2. Cooling
1. Trapping
Magneto-Optical Trap (MOT)
T
Optical Molasses
3. Launching upwards
Atomic Fountain
i
Segnale di fluorescenza (V)
launch velocity
0,14
proportional to
0,12
laser detuning δ
|2
Time (s)
C
B
ΔΦ = kegT2 + Φe = Δφg + Φe
Final population:
|1
|2
T
|1
kR1
N |1
1
N
(1+cosΔΦ)
2
N
|1
T
kR1
0

t
p
2
0
g=
|1
p
2
p
Φe
Δφg
keT 2
For T=150 ms a phase term of 2p corresponds to an acceleration of 10-6 g
For S/N=1000 the sensitivity is 10-9 g per shot
Appropriate trajectories
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
Configuration C1
REQUIREMENTS
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
So, using a further differential method, it is possible to deduce the value
of the Gravitational Coupling Constant
106
•Number of atoms:
• Dv < vrec (vrec~ 6 mm/s )
•detection: SNR = 1000
•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
ΔΦTOT  G
Acceleration
by source
along
the
vertical axes
tube
Configuration C2
induced
masses
central
of the
Induced
acceleration
g
Sensitivity
Interferometer 2
Trapping, cooling and
launching cell
10-9
10-2
Integration over 10000
measurements
Acceleration induced
by source masses +
the effect of gravity
gradient along the
central vertical axes
of the tube
cloud 2
10-7g
10-9g
Relative error
cloud 1
Detection region
N |1 =
DOUBLE-DIFFERENTIAL MEASUREMENT
Adding well-known source masses around the interferometric tube the
atoms trajectory is perturbed in a known way
GRADIOMETER
kR2
|2
|1
A
kR2
|2
C
ωR2
GRAVIMETER
kR2
|2
|1
|2
π
2
π
|1
D
tempo (s)
Interferometer 1
- constant gravity
- accelerations seen because
of optics vibrations
- uniform e.m. fields
ωR2
|1
|1
0,45
How to measure the Newtonian Gravitational Constant with a high accuracy?
All the effects that induce the
same acceleration all over the
experimental region are rejected
by a differential measurement :
|2
A
0,40
π
2
LONGITUDINAL PULSES
-no area enclosed
-used to measure accelerations (GRAVIMETERS)
|2
0,35
z(t)
|2
|1
B
0,04
0,30
Each Raman pulse induces:
•
a change of the internal state
•
a momentum transfer
•
an additional phase term
-1st pulse (p/2 pulse) …………splitting
-2nd pulse (p pulse) ……………..inversion
-3rd pulse (p/2 pulse) ………...recombination
|1
109 atoms
Using two simultaneous but vertically
displaced atom interferometers it is
possible to measure local gradients of
accelerations (gravity gradient)
ground state hyperfine
splitting
D
0,00
With a single atom interferometer
one can measure local accelerations
(gravity)
D2 line
87Rb
|1
2nd pass: DOWNWARDS
0,25
RAMAN ATOM INTERFEROMETER
ωR1
0,08
0,20
- the atoms position with respect to the
wavefronts of a phase stabilized laser is
encoded in the atomic wavefunction
- momentum transfer to the atoms
- velocity selectivity
TRANSVERSAL PULSES
-the interferometer encloses an area
-used to measure rotations (GYROSCOPES)
ωR1
0,15
- internal degrees of freedom offer new
measurement possibilities
g
- less (or at least different) systematic
effects
3 pulse sequence
1
0,02
N
87Rb
2
0,10
0,10
g
Optical Raman transitions
ωR2
ωR1
1m
0,16
0,05
- well-controlled external degrees of
freedom with laser cooling
aM
How to make a precision measurement of g?
1st pass: UPWARDS
0,06
- small probe masses with well-known
properties
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.
When the cold atom cloud pass through a horizontal sheet
of light a fluorescence signal is emitted
0,18
- no suspension
The combination of Raman atom interferometry and
laser cooling will allow us to achive high sensitivity.
5 K
hmax
Advantages:
Free falling 87Rb atoms will be used as probe masses
to test the gravitational acceleration of nearby
source masses.
ATOMIC FOUNTAIN
How to obtain a cold cloud of free falling atoms?
J. Stuhler (university of Stuttgart)
A. Peters (University of Berlin)
This possible source of systematic effects can be
eliminated if one
performs a free-falling
experiment.
All this methods have in
common that masses, which
probe
the
acceleration
caused by well known source
masses, are suspended, eg.
with fibers.
m3
kg s2
in collaboration with
MAGIA – THE IDEA
Up to now only few
conceptually
different
methods have been used:
-the torsion balance
-the torsion pendulum
-the beam balance
-the pendulum cavity.
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.
-11
…towards
a high precision measurement
of the gravitational constant
using atom interferometry
PAST
MEASUREMENTS
The goal of MAGIA experiment is the high
precision measurement of the Newtonian
gravitational
constant
G
using
atom
interferometry.
M. Fattori
G. Lamporesi
T. Petelski
M. Prevedelli
G. M. Tino
ΔG
G
10 4
EXPERIMENTAL APPARATUS
VACUUM SYSTEM
FIBER SYSTEM
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 )
• Lasers delivered with
polarization
preserving
fiber system including
power stabilization
MOT cell in 1-1-1 configuration
The critical parts of the
vacuum system are made of a
Titanium alloy
Non-magnetic
High resistivity
Low thermal expansion
Light but hard
• Optical
windows
are
connected to Titanium alloy
with new sealing techniques
Glue (AREMCO 631)
or
Lead o-rings
20 Aluminium
foils
lead
crossed
o-rings
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 mm
Densimet 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
• 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
Fiber splitter
Mass holder and elevator
Additional treatment and characterization
In collaboration with
Scheafter&Kirchhoff
GmbH
•HIP (Hot Isostatic Pressing) of the
cylinders at 1200 oC and 1500 atm to reduce
holes
• MOT
laser
beams
expansion possible up to
37 mm diameter
•Destructive test with density comparison
at different points of the cyliders (relative
measurements will reveal differences
smaller than 0.002 g cm-3)
Fiber mount
directly fixed on
the MOT cell
Systematic effects due to the mass
distribution can be controlled at the 10-4
level
In collaboration with LNF
(Laboratori Nazionali di Frascati)
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).
FUTURE
PROSPECTS
• Portable gravimeters/gradiometers
• Test of
1/r2
gravity dependence at small distances
• Detection of gravitational waves ?
Geophysical applications
Experiments in space