G.M. Tino, FPS-06, LNF, 22/3/2006

Atom Interferometers and Atomic Clocks:Atom Interferometers and Atomic Clocks:From Ground to SpaceFrom Ground to Space

Atom Interferometers and Atomic Clocks:Atom Interferometers and Atomic Clocks:From Ground to SpaceFrom Ground to Space

Università degli Studi di Firenze - Dipartimento di Fisica, LENS

Istituto Nazionale di Fisica Nucleare - Sezione di Firenze

Guglielmo M. TinoGuglielmo M. Tino

G.M. Tino, FPS-06, LNF, 22/3/2006

Laser cooling of atoms

vL L

Lab ref. frame

Atom ref. frame

L(1-v/c) L(1+v/c)

Idea: T.W. Hänsch, A. Schawlow, 1975Exp. demonstration: S. Chu et al., 1985

0

222

2

2 2/8(v) v = - v

[1 ]4 ( )L I IhF

c

Sr MOTLENS, Firenze

G.M. Tino, FPS-06, LNF, 22/3/2006

Laser cooling: temperatures

2

1rB

LM

hk T

c

2DB

hk T

Minimum temperature for Doppler cooling:

Examples: TD Tr

Na 240 K 2.4 KRb 120 K 360 nKCs 120 K 200 nK

Single photon recoil temperature:

Atomic Temperature : kBT = Mv2rms

G.M. Tino, FPS-06, LNF, 22/3/2006

The Nobel Prize in Physics 1997

G.M. Tino, FPS-06, LNF, 22/3/2006

The Nobel Prize in Physics 2001

G.M. Tino, FPS-06, LNF, 22/3/2006

Atom optics

lenses

mirrors

beam-splitters

atom

laser

interferometers

atom

laser

Oven

laser

Atomic beam

atom laser

G.M. Tino, FPS-06, LNF, 22/3/2006

Atom Michelson Interferometer on a Chip Using a Bose-Einstein Condensate

Ying-Ju Wang, Dana Z. Anderson, Victor M. Bright, Eric A. Cornell, Quentin Diot, Tetsuo Kishimoto, Mara Prentiss, R. A. Saravanan, Stephen R. Segal, Saijun Wu, Phys. Rev. Lett. 94, 090405 (2005)

G.M. Tino, FPS-06, LNF, 22/3/2006

Atomic clocksAtomic clocks

G.M. Tino, FPS-06, LNF, 22/3/2006

Accuracy realization of the standard Stability stability of the frequency: depends on of the oscillator

0

0

The measurement of time

OSCILLATOR COUNTER

G.M. Tino, FPS-06, LNF, 22/3/2006

Atomic clocks

.t = 1

The definition of the second

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the 133Cs atom

(13th CGPM, 1967)

The definition of the second

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the 133Cs atom

(13th CGPM, 1967)

G.M. Tino, FPS-06, LNF, 22/3/2006

Atomic fountain clock

NIST-F1

G.M. Tino, Firenze, 11/12/2003

G.M. Tino, FPS-06, LNF, 22/3/2006

Cold Atoms Clocks in SpaceCold Atoms Clocks in Space• Interrogate fast (hot) atoms over

long distances T = 10 ms

• Use laser cooled atoms, limitation due to the presence of gravity T = 1 s

• Use laser cooled atoms in microgravity T = 10 s

C. Salomon et al., C.R. Acad. Sci. 2, 1313 (2001)

PHARAO

G.M. Tino, FPS-06, LNF, 22/3/2006

Accuracy of the atomic timeAccuracy of the atomic timeAccuracy of the atomic timeAccuracy of the atomic time

1950 1960 1970 1980 1990 2000 201010-17

1x10-16

10-15

1x10-14

1x10-13

1x10-12

1x10-11

1x10-10

1x10-9

NPL

?

PTB

Optical clocks

NIST

Ca PTB

H MPQ

Cold atoms

Microwave clocksSlope: gain of 10 every 10 years

ACCURACY OF THE ATOMIC TIME

SYRTE

PTBNIST

PTBNRCNBSVNIIFTRI

NPLNBSLSRH

RE

LAT

IVE

AC

CU

RA

CY

YEAR

from C. Salomon

G.M. Tino, FPS-06, LNF, 22/3/2006

Optical clocks: Towards 10-18-10-19

• Direct optical-wave connection by optical frequency comb

• Narrow optical transitions o ~ 1 Hz, 0 ~ 1015 Hz

• Candidate atoms

Trapped ions: Hg+, In+, Sr+, Yb+,…

Cold neutral atoms: H, Ca, Sr, Yb,… (Fermions?)

cycle

0 average fringe

1 1

2y

atom

TNoise

Q Signal CN

Th. Udem et al., Nature 416 , 14 march 2002

G.M. Tino, FPS-06, LNF, 22/3/2006

G.M. Tino, FPS-06, LNF, 22/3/2006

Ca clock example

From L. Hollberg, Hyper symposium 2002

G.M. Tino, FPS-06, LNF, 22/3/2006

• Method: (H. Katori)

Interrogate atoms in optical lattice without frequency shift• Long interaction time• Large atom number (108)• Lamb-Dicke regime

Excellent frequency stability

• Small frequency shifts:• No collisions (fermion)• No recoil effect (confinement below optical wavelength)• Small Zeeman shifts (only nuclear magnetic moments)…

87Sr optical clock

G.M. Tino, FPS-06, LNF, 22/3/2006

Towards a Sr clock – The experiment in Firenze

-400 -200 0 200

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

87Sr

88Sr

84Sr

86Sr

Laser detuning (MHz)

Flu

ore

sce

nce

sig

na

l (V

)

1S0 - 3P1 (7.5 kHz) 1S0 - 3P0 (1 mHz, 87Sr) 1S0 - 3P2 (0.15 mHz)

Optical trapping in Lamb-Dicke regime with negligible change of clock frequency

• Optical clocks using visible intercombination lines

Firenze 2003, Magneto-optical trapping of all Sr isotopes

Comparison with different ultra-stable clocks(PHARAO/ACES)

PHARAO

G. Ferrari, P.Cancio, R. Drullinger, G. Giusfredi, N. Poli, M. Prevedelli, C. Toninelli and G.M. Tino, Phys. Rev. Lett. 91, 243002 (2003)

G.M. Tino, FPS-06, LNF, 22/3/2006

Atomic clocksAtomic clocks

• Location finding• Precision navigation and navigation in outer space• Variability of Earth’s rotation rate and other periodic

phenomena• Earth’s crustal dynamics• Secure telecommunications

• Very Long Baseline Interferometry (VLBI)• Spectroscopy• Expression of other physical quantities in terms of time• Tests of constancy of fundamental constants• Tests of the special and general theories of relativity

G.M. Tino, FPS-06, LNF, 22/3/2006

Atom InterferometersAtom Interferometers

G.M. Tino, FPS-06, LNF, 22/3/2006

Quantum interference

Initial state

|i

Final state

|f

Interference of transition amplitudesP(|i|f) = |AI + AII|2 = |AI|2 + |AII|2 + 2 Re(AI AII

*)

path II

amplitude AII

path I

amplitude AI

G.M. Tino, FPS-06, LNF, 22/3/2006

Atomic clocks: Interference fringes

G.M. Tino, FPS-06, LNF, 22/3/2006

Time-domain Ramsey-Bordé interferences with cold Ca atoms (PTB)

G.M. Tino, FPS-06, LNF, 22/3/2006

atomic flux at exit port 1 at exit port 2Phase difference

21

Flux

Atom InterferometryAtom Interferometry

Atom interferometer

G.M. Tino, FPS-06, LNF, 22/3/2006

2driftacc Tk

a

a

Ah

m22 at

rot

Matter wave sensors

rotations:

10at

ph

mat 105h

cm~

1711

2

atph

mat 1010v

c~

accelerations:

G.M. Tino, FPS-06, LNF, 22/3/2006

Maximum interaction time : 90 ms3 rotation axes2 acceleration axes

Cycling frequency 2Hz

Expected sensitivity (106 at):• gyroscope : 4 10-8 rad.s-1.Hz-1/2

• accelerometer : 3 10-8 m.s-2.Hz-1/2

50

cm

30 cm

One pair of Raman lasers switched on 3 times

Magneto-Optical Traps

DetectionsLaunching velocity: 2.4 m.s-1

SYRTE cold atom gyroscope

G.M. Tino, FPS-06, LNF, 22/3/2006

Interferometer

MOT 1

15 cm

3 mm

A

PreparationDetection

MOT 2

C. Jentsch, T. Müller, E. Rasel, and W. Ertmer, Gen. Rel. Grav, 36, 2197 (2004)& Adv. At. Mol. Physics

IQO Cold Atom Sagnac Interferometer

G.M. Tino, FPS-06, LNF, 22/3/2006

MAGIA

• Measure g using free falling atoms and atom interferometry

• Add known source masses

• Measure change of g Determine G

g

aM

Misura Accurata di G mediante Interferometria Atomica

G.M. Tino, in “2001: A Relativistic Spacetime Odyssey”, World Scientific (2003)

M. Fattori, G. Lamporesi, T. Petelski, J. Stuhler, G.M. Tino, Phys. Lett. A 318, 184 (2003)

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

G.M. Tino, FPS-06, LNF, 22/3/2006

I

1

2

II

1

2

z1

z2

In collaboration with LNF, Frascati

Misura Accurata di G mediante Interferometria Atomica

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

MAGIA

G.M. Tino, FPS-06, LNF, 22/3/2006

Laser and optical system

Phase locked lasers for Raman transitionsL. Cacciapuoti et al., Rev. Scient. Instr. 76, 053111 (2005)

MAGIA: Firenze atom gravity gradiometer apparatus

Source masses and support

G.M. Tino, FPS-06, LNF, 22/3/2006

MAGIA: first results

G.M. Tino, FPS-06, LNF, 22/3/2006

Precision Measurement of Gravity at Micrometer Scale using Ultracold Sr Atoms

= m g /2 h

optical latticebeam

mirror

probebeam

trappedatoms

CCDcamera

red MOTbeams

g

• G. Ferrari et al., 2006, to be published

G.M. Tino, FPS-06, LNF, 22/3/2006

Test of the gravitational 1/r2 law in the sub-mm range with atom interferometry sensors (Casimir?)

a = 2Gd

Example:

Au 19 g/cm3

d 200 m a 2 x 10-9 ms-2

-d-

95% confidence level constraints on a Yukawa violation of the gravitational inverse-square law. The vertical axis represents the strength of a deviation relative to that of Newtonian gravity while the horizontal axis designates its characteristic range. The yellow region has been excluded (From S. J. Smullin et al., 2005)

• G.M. Tino, in “2001: A Relativistic Spacetime Odyssey”, Firenze, 2001, World Scientific (2003)• G.M. Tino, Nucl. Phys. B 113, 289 (2002)• G. Ferrari et al., 2006, to be published

optical latticebeam

mirror

probebeam

trappedatoms

CCDcamera

red MOTbeams

g

= m g /2 h

G.M. Tino, FPS-06, LNF, 22/3/2006

From Earth Laboratories to SpaceFrom Earth Laboratories to Space

G.M. Tino, FPS-06, LNF, 22/3/2006

Atomic Clock Ensemble in SpaceAtomic Clock Ensemble in Space

PHARAO : Cold Atom Clock in Space. CNES (France)

A. Clairon, P. Laurent, P. Lemonde, M. Abgrall, S. Zhang, C. Mandache, F. Allard, M. Maximovic, F. Pereira, G. Santarelli, Y. Sortais, S. Bize, H. Marion, D. Calonico, (BNM-LPTF), N. Dimarcq (LHA), C. Salomon (ENS)

SHM : Space Hydrogen Maser. ON (Switzerland)

L. Jornod, D. Goujon, L.G. Bernier, P. Thomann, G. Busca

MWL : Microwave link. Kayser-Threde-Timetech (Germany)

W. Schaefer, S. Bedrich

ACES is open to any interested scientific userW. Knabe, P. Wolf, L. Blanchet, P. Teyssandier, P. Uhrich, A. SpalliciNew members :2001: UWA (Australia), A. Luiten, M. Tobar, J. Hartnett, R. Kovacich2002: LENS (Italy), G.M. Tino, G. Ferrari, L. Cacciapuoti

ESA: MSMStephen Feltham CNES:C. Sirmain + team of 20 engineers at CST, Toulouse

Support: ESA, CNES, BNM, CNRS

• A cold atom clock in space• Worldwide access• Fundamental physics tests

H= 400 kmV=7 km/sT= 5400 s

G.M. Tino, FPS-06, LNF, 22/3/2006

ACES ON COLUMBUS EXTERNAL ACES ON COLUMBUS EXTERNAL PLATFORMPLATFORM

ACES ON COLUMBUS EXTERNAL ACES ON COLUMBUS EXTERNAL PLATFORMPLATFORM

M = 227 kg P = 450 W

Launch date : 2009Mission duration : 18 months

ACES

G.M. Tino, FPS-06, LNF, 22/3/2006

ACES objectives

L. Blanchet, C. Salomon, P. Teyssandier, and P. Wolf, A&A 370, 320 (2001)

G.M. Tino, FPS-06, LNF, 22/3/2006

ESA-AO-2004Life and Physical Sciences and Applied Research Projects

G.M. Tino, FPS-06, LNF, 22/3/2006

PARCSPrimary Atomic Reference Clock in Space

G.M. Tino, FPS-06, LNF, 22/3/2006

HYPER

Differential measurement between two atom gyroscopes and a star tracker orbiting around the Earth

~h/mImproving knowledge offine-structure constant

Mapping Lense-Thirring effect close to the Earth

Atomic gyroscope control of a satellite

Testing EP with microscopic bodies

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

G.M. Tino, FPS-06, LNF, 22/3/2006

ESA-AO-2004 AI

G.M. Tino, FPS-06, LNF, 22/3/2006

Laser Cooled Atom (LCA) Sensor

for Ultra-High-Accuracy Gravitational Acceleration

and Rotation Measurements

in response to ESA ITT No. AO-1-4477/03/NL/CH

G.M. Tino, FPS-06, LNF, 22/3/2006

Prototype field ready sensor

Laser system

Sensor optomechanicsSensor head

From M. Kasevich talk atSpacePart '03 Conference Washington D.C., December 10th - 12th, 2003.

W.W. Hansen Experimental Physics Laboratory, Stanford, CA 94305

SpacePart ‘03

G.M. Tino, FPS-06, LNF, 22/3/2006

JPL

http://horology.jpl.nasa.gov/quantum/atominterferometry.html

G.M. Tino, FPS-06, LNF, 22/3/2006

BEC in space

G.M. Tino, FPS-06, LNF, 22/3/2006

pumps

µ-metal shielding

Battery pack

Laser

DC-DC transformer

Computer control

From E. Rasel, 2005

G.M. Tino, FPS-06, LNF, 22/3/2006

G.M. Tino, FPS-06, LNF, 22/3/2006

Applications of new quantum sensors based on atom interferometry

• Development of transportable atom interferometers

• Short-distances forces measurement

• Test of equivalence principle

space

• New detectors for gravitational waves ? geophysics

• Search for electron-proton charge inequality

• New definition of kg

• Measurement of fundamental constants G

G.M. Tino, FPS-06, LNF, 22/3/2006

Future prospects:Atomic clocks

• New optical clocks with fractional stability ~ 10-17-10-19

• mm-scale positioning and long-distance clock syncronization

• Very large baseline interferometry (VLBI) and geodesy

• Search for variation of fundamental constants

• Tests of SR and GR in Earth orbit (ACES, OPTIS)

• Improved tests of GR in solar orbit: Shapiro delay, red shift, …

G.M. Tino, FPS-06, LNF, 22/3/2006

Conclusions

• New atomic quantum devices can be developped with unprecedented sensitivity New atomic quantum devices can be developped with unprecedented sensitivity using ultracold atoms and atom opticsusing ultracold atoms and atom optics

• Applications: Fundamental physics, Earth science, Space research, CommercialApplications: Fundamental physics, Earth science, Space research, Commercial

• Well developped laboratory prototypesWell developped laboratory prototypes

• Work in progress for transportable/space-compatible systemsWork in progress for transportable/space-compatible systems

G.M. Tino, FPS-06, LNF, 22/3/2006

Fine

G.M. Tino, FPS-06, LNF, 22/3/2006

LINKS

G.M. Tino, FPS-06, LNF, 22/3/2006

h/m and fine structure constant

S. Chu et al., 2002

G.M. Tino, FPS-06, LNF, 22/3/2006

vgmUI

Goal: Redefinition of kg on microscopic quantities with accuracy better than 10-8

Idea: Watt-balance compares electrical and mechanical realization of Watt

ztU

vmgz

I

Watt balance groups working at NPL (UK), NIST (USA), METAS (Switzerland), BNM (France)

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram (1st CGPM, 1889)

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram (1st CGPM, 1889)

Unit of mass

G.M. Tino, FPS-06, LNF, 22/3/2006

Tests of weak equivalence principle

Best tests so far: EOT-Wash group (Adelberger, Gundlach), See “http://www.npl.washington.edu/eotwash/”Long range EP tested at the level of 10-13

Atoms:

Prospects

• different isotopes, e.g. 85Rb vs 87Rb • different atoms, e.g. Rb vs Cs • bosons vs fermions, e.g. Rb vs 40K • different spins • anti-matter (?)

Space: MICROSCOPE 10-15

STEP 10-18

Fray S, et al. PRL. 93, 240404 (2004)g/g=(0.4+/-1.2)x10-7( )

10-12 - 10-13

G.M. Tino, FPS-06, LNF, 22/3/2006

Test of equivalence principle for anti-matter

H• Compare g

g/g 10-9 ?

- Time of flight

- Atom interferometry • Raman transitions between 2S HFS sublevels

• 2Shigh-P levels transitions (T. Heupel et al., Europhys. Lett. 57, 158 (2002))

H

anti-H production (ATHENA, ATRAP)

anti-H selective state population

anti-H cooling

anti-H trapping

g measurement:

• Steps:

1s1/2

2s1/2 2p

243 nm

121.6 nm

243 nm

1/2

3/2

1420 MHz

0

1

0

1

177 MHz

3s1/2 3p

4 45 5

H levelspartial scheme(not to scale)

1/23/2

10968 MHz

59 MHz

24 MHz

g/g 10-3 ?

G.M. Tino, FPS-06, LNF, 22/3/2006

Search for electron-proton charge inequality

• Electrostatic, ferromagnetic, diamagnetic levitation Millikan (1935), Morpurgo (1966-1984), Braginsky (1970), Stover (1967), Rank (1968), LaRue (1979)

• Gas flow Piccard and Kessler (1925), Hillas & Cranshaw (1960), King (1960)

• Acoustic cavity Dylla and King (1973)

• Atomic and molecolar beams Hughes (1957), Chamberlain & Hughes (1963), Fraser (1965), Shapiro (1957), Shull (1967)

Present limit ep< 1x10-21 e

(From G. Carugno and G. Ruoso)

G.M. Tino, FPS-06, LNF, 22/3/2006

Chiu - Hoffmann (1964)Indipendenza della carica dell’elettrone dalla velocità e trasformazioni di Lorentz

Con atomi di vario Z miglioro limite

Neutralità materia

Einstein (1929)Spiegare campi magnetici terra e sole ep+ rotazione -> i -> B si aspettava ep= 3x10-19 e

ep= qe+ qp; qn ; q

Bondi - Lyttleton (1959); Hoyle (1960)se ep~ 2x10-18 e => espansione universo

Feinberg - Goldhaber (1959); Gell-Mann - Nambu (1960)

ep ≠ 0 per spiegare leggi di conservazione (es. numero barionico)

Motivazioni: digressione storica

Limiti su qn e q

Se C e CPT conservati da qn = qe + qp + qricavo limiti

Attualmenteqn < 10-21 e Esp. con fasci di neutroni termici (1988)

q < 10-15 e Da astrofisica, Barbiellini - Cocconi (1987)

qe (v) qe (0)[1 a(v /c)2]

(Da G. Carugno and G. Ruoso)

G.M. Tino, FPS-06, LNF, 22/3/2006

Search for electron-proton charge inequality

ep< 1x10-25 e ?

G.M. Tino, FPS-06, LNF, 22/3/2006

Gravitational wave detection by atom interferometry

Presentation at 2004 Aspen Winter College on Gravitational Waves:See http://www.ligo.caltech.edu/LIGO_web/Aspen2004/pdf/vetrano.pdf

See also: Chiao RY, Speliotopoulos AD, J. Mod. Opt. 51, 861 (2004)A. Roura, D.R. Brill, B.L. Hu, C.W. Misner, gr-qc/0409002

1E-3 0,01 0,1 1 10 100 1000 100001E-24

1E-23

1E-22

1E-21

1E-20

1E-19

1E-18

1E-17

1E-16

h (1

/Sqr

t(Hz)

)

/2 (Hz)

Virgo

G.M. Tino, FPS-06, LNF, 22/3/2006

LMXRBs&

Perturbed“newborn”NS

SlowPulsars

(1 y)

Sources - Detectors

-24

-22

-20

-18

h [1/sqrt Hz]

f [Hz] - 4 - 2 0 2 4

10 10 10 10 10

Galactic binaries

Coalescence ofmassive BH

NS-NS andBH-BH Coalescence

SN corecollapse

msPulsars

(1 y)

12

3

1 LISA2 LIGO – Virgo3 A.I.

G.M. Tino, FPS-06, LNF, 22/3/2006

Gravimeters

Comparison between instruments Spring gravimeter(1) Optical interferometry

dropping gravimeter(2,3) Superconducting

gravimeter(3,4) Atom interferometry

gravimeter(5)

Resolution g/g

5 x 10-9

only for short periods and distances

1 x 10-8/Hz

1 x 10-8/Hz

2 x 10-8 in 1.3 s

Accuracy g/g Or Repeatibility

0.5 x 10-6

only for short periods and distances

4 x 10-9

1 x 10-9

1 x 10-9

Measurement

Relative

Absolute

Relative

Absolute

Size and Weight

21.5 x 22 x 31 cm 9 kg

1.5 m3 320 kg

No field operation estimated 1 m3

250 kg

Error sources

temperature and random drift

Clibration varies in time and with position

magnetic and

electrostatic effects

thermal drift magnetic and

electrostatic effects

?

(1) www.LaCosteRomberg.com (2) www.microgsolutions.com (3)O. Francis, T.M. Niebauer, G. Sasagawa, F. Klopping, and G. Gschwind, “Calibration of a superconducting gravimeter by comparison with an absolute gravimeter FG5 in Boulder”, Geoph. Res. Lett.25 (1998) 1075-1078. (4) J.M. Goodkind “The superconducting gravimeter”, Rev. Scient. Instr., 70 (1999) 4131-4152. (5) A. Peters, K.Y. Chung, and S. Chu “Measurement of gravitational acceleration by dropping atoms”, 400 (1999) 849-852.

Resolution: 3x10-9 g after 1 minute

Absolute accuracy: g/g<3x10-9

A. Peters, K.Y. Chung and S. Chu, Nature 400, 849 (1999)

G.M. Tino, FPS-06, LNF, 22/3/2006

Gravimeter application in geophysics

Gravimetric measurements at Etna Pizzi DeNeri site during a 48-h-long period encompassing the beginning of the 2002-2003 eruption (Branca et al. Geoph. Res. Lett. 30 2077 (2003))

G.M. Tino, FPS-06, LNF, 22/3/2006

Gravimeter Application

Geophysical researchMonitoring of magma migration in active volcanic areasDetection of vertical crustal motion in seismogenic areasPost glacial rebound studiesMeasuring uplift in subduction areasEarthquake (strain accumulation in tectonic areas during interseismic phase)Calibrating measurement made by other techniques: height measurements, relative gravimeter

Environmental monitoringWater table monitoring in deep and/or multiple acquifersMonitoring of mining effectSlope and earth fill dam stabilityGlobal sea level studies for earth warming assessmentOn site inspection of sites for nuclear test or else.

Mineral exploration

G.M. Tino, FPS-06, LNF, 22/3/2006

Gradiometer applications

Airborne gravity measurement for oil and mineral exploration hazard investigation

Satellite gravity meausrement : GOCE projectGRACE Project

Gravity gradiometry gives higher resolution inMonitoring of anomaliesData processingJoint gravimetric-seismological data inversion

Gradiometer based on absolute Gravimeter combines complementary range of sensitivity for different mass/distance source

Tensorometer

G.M. Tino, FPS-06, LNF, 22/3/2006

ACES: Relativity tests

G.M. Tino, FPS-06, LNF, 22/3/2006

Search for variation of

G.M. Tino, FPS-06, LNF, 22/3/2006

Search for variation of