Gravity measurements with atom interferometry

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Gravity measurements with atom interferometry

Fiodor Sorrentino, 28/10/2010

Dipartimento di Fisica e Astronomia, Università di Firenze & INFN,

Polo Scientifico di Sesto Fiorentino,via Sansone 1 -50019 Sesto Fiorentino (FI)

Istituto di Cibernetica CNR, via Campi Flegrei 34, 80078 Pozzuoli (NA), Italy.

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F. Sorrentino, 28/10/10 Gravity measurements...

Matter-wave interferometry

Interference of transition amplitudes

P ( |ψ

ⁱ

! → |ψ

^f

!) = |A

^I

+ A

_II

|

²

= |A

^I

|

²

+ |A

^II

|

²

+ 2Re(A

_I

A

^∗_II

)

de Broglie wave λ _dB = h/mv

with electrons since 1953

with neutrons since 1974

with atoms since 1991

Initial state

|ψ

_i

〉

Final state

|ψ

_f

〉

path II

amplitude A

_II

path I

amplitude A

_I

Quantum interf erence

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Atom interferometry

atom optics

different internal states/isotopes

phase difference may depend on:

accelerations

rotations

photon recoil

laser phase

laser frequency detuning

electric/magnetic fields

interactions with atoms/molecules

Flux

atomic flux at exit port 1 Δϕ

at exit port 2

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Matter-wave vs optical inertial sensors

a

Ω

∆Φ _rot = 2π ^2m _h

^at

A · Ω

∆φ

_mat

∆φ

_ph

∼ ^m

^at

_h ^λc ≈ 5 · 10 ¹¹

Accelerations

Rotations

∆Φ _acc = kT _{drif t} ² · a

∆φ

_mat

∆φ

_ph

∼ !

c

v

_at

" 2

≈ 10 ¹¹ ÷ 10 ¹⁷

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Raman interferometry

Final population:

N

_a

= N/2(1 + cos [∆Φ])

with ∆Φ = k

_e

gT

²

T = 150 ms → 2π = 10

⁻⁶

g

S/N=1000 → Sensitivity 10

⁻⁹

g/launch

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Raman interferometry

Final population:

N

_a

= N/2(1 + cos [∆Φ])

with ∆Φ = k

_e

gT

²

T = 150 ms → 2π = 10

⁻⁶

g

S/N=1000 → Sensitivity 10

⁻⁹

g/launch

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AI Gradiometer

G. T. Foster et al., Opt. Lett 27, 951 (2002)

∆Φ = k _e gT ²

T=5 ms

resol. = 2.3 × 10

⁻⁵

g/shot

T=50 ms

resol. = 1.0 × 10

⁻⁶

g/shot

T=150 ms

resol. = 3.2 × 10

⁻⁸

g/shot

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AI gravimeters

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Comparison with other techniques

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Comparison with other techniques

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Comparison with other techniques

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Comparison with other techniques

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Applications of absolute gravimeters

Mineral exploration

Environmental monitoring

Water table monitoring in deep and/or multiple acquifers

Monitoring of mining effect

Slope and earth fill dam stability

Global sea level studies for earth warming assessment

On site inspection of sites for nuclear test or else

Geophysical research

Detection of vertical crustal motion in seismogenic areas

Post glacial rebound studies

Monitoring of magma migration in active volcanic areas

Calibrating measurement needed by other techniques (height measurements,

relative gravimeter)

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Applications of accurate gradiometers

• Airborne gravity measurement for

oil and mineral exploration

hazard investigation

• Satellite gravity measurement

GOCE Project

GRACE Project

MICROSCOPE Project

• Gravity gradiometry gives higher resolution in

Monitoring of anomalies (A.J. Romaides JPD, R. Bell Sci. Am).

Data processing (M. Fedi...)

Joint gravimetric-seismological data inversion (...)

• Gradiometer based on absolute Gravimeter combines complementary range of

sensitivity for different mass/distance source

• Tensorometer

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Stanford atom gravimeter

A. Peters, K.Y. Chung and S. Chu, Nature 400, 849 (1999) H. Müller et al., Phys. Rev. Lett 100, 031101 (2008)

resolution: 8 × 10

⁻⁹

g in 1 second

accuracy: ∆g/g ≤ 3 × 10

⁻⁹

limited by tidal models

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Sanford/Yale gravity gradiometer

J. M. McGuirk et al., Phys. Rev. A 65, 033608 (2002)

limited by QPN

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Stanford/Yale gyroscope

T.L. Gustavson, A. Landragin and M.A. Kasevich, Class. Quantum Grav. 17, 2385 (2000) D. S. Durfee, Y. K. Shaham, M.A. Kasevich, Phys. Rev. Lett. 97, 240801 (2006)

sensitivity: 6 × 10

⁻¹⁰

rad· s

⁻¹

√

Hz

scale factor stability < 5 ppm

bias stability < 70 µdeg/h

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Other AI sensors

SYRTE

absolute gravimeter

gyroscope

six-axis inertial sensor

IQO

gyroscope

JPL

gradiometer

MAGIA

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MAGIA

Measure g by atom interferometry

Add source masses

Measure change of g

Misura Accurata di G mediante Interferometria Atomica

a

_M

g

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

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Atom gradiometer + source masses

Sensitivity 10

⁻⁹

g/shot

one shot → ∆G/G ∼ 10

⁻²

500 Kg tungsten mass

Peak mass acceleration a

_g

∼ 10

⁻⁷

g

10000 shots → ∆G/G ∼ 10

⁻⁴

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MAGIA sensitivity

**Present sensitivity to differential acceleration: 1.4*10**

^-8

g @ 1 s

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MAGIA results

F. Sorrentino, Y.H. Lien, G. Rosi, L. Cacciapuoti, M. Prevedelli, G.M. Tino, arXiv:1002.3549 corresponding to a statistical

uncertainty

of 400 ppm on G

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Future of AI inertial sensors

Compact and transportable system without performance

degradation

ground applications (geophysic)

space applications (satellite geodesy, inertial navigation,

tests of fundamental physics):

Novel schemes to improve sensitivity/accuracy

high-momentum beam spitters

coherent/squeezed atomic states to surpass QPN detection

large size AI and ultracold atoms (nK temperature)

New applications

GW, quantum gravity, etc.

∆φ = kgT ²

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Compact AI sensors

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Compact AI sensors

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Conclusions

New atomic quantum devices can be developped with

unprecedented sensitivity using ultracold atoms and

atom optics

Applications: Fundamental physics, Earth science,

Space research

Well developped laboratory prototypes

Work in progress for transportable/space-compatible

systems

need for input from geophysics community (i.e.

applications of simultaneous absolute gravity

acceleration/gradient measurement)

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Thank you for your attention

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Space-based geodesy

Accelerometer sensitivity: 10^-13 g/Hz^1/2 _ Long free-fall times in orbit

Measurement baseline

_ 100 m (Space station)

_ 100 km (Satellite constellation) Sensitivity:

_ 10^-4 E/Hz^1/2 (Space Station)

_ 10^-7 E/Hz^1/2 (Satellite constellation)

300 km 100 m – 100 km

Earth Accelerometers

http://www.esa.int/export/esaLP/goce.html

GOCE mission, 4x10^-3 E

Earthquake prediction; Water table monitoring

(1 E = 10^-9 s^-2)

from M. Kasevich, Talk at the International Workshop on Advances in Precision

Tests and Experimental Gravitation in Space, Firenze, September 2006

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Other possible applications of AI

Earth observations

ground

airborne

satellite

Fundamental physics

testing equivalence principle

atom neutrality

GW detection

quantum gravity

Metrology

definition of mass unit through Watt balance

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Raman interferometry

in a ⁸⁷ Rb atomic fountain

t

R1kr ^R1kr ^R1kr

R2kr ^R2kr ^R2kr

T T

∂2 ∂ ∂2

z(t)

Phase difference between the paths:

∆Φ = k

_c

[z(0)]2z(T )] + Φ

_e

k

_e

= k

₁

− k

²

with z(t) = −gt

²

/2 + v

₀

t + z

₀

& Φ

_e

= 0

→ ∆Φ = k

^e

gT

²

Final population:

N

_a

= N/2(1 + cos[∆Φ])

A. Peters et al., Nature 400, 849 (1999)

T = 150 ms → 2π = 10

⁻⁶

g

S/N=1000 → Sensitivity 10

⁻⁹

g/shot

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Present limitations of AI

shot-noise limit to sensitivity ~

atomic flux ~ 10

¹⁸

s

^-1

with H (~ 10

¹¹

s

^-1

with alkali)

in a 100 mW laser the photon flux is > 10

¹⁸

s

^-1

much lower path difference than in optical interferometers

better beam splitters, optical cavities

nevertheless AI inertial sensors are already competitive

long term stability (bias & scale factor) and accuracy

future developments to improve sensitivity

high momentum beam splitters

high flux atomic sources

sub-shot noise detection (quantum degenerate gases, etc.)

large size AI, µ-gravity, ultracold atoms

1/ !

N ˙

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Possible applications of AI

Already achieved:

inertial sensing (accelerations, gravity gradients, rotations)

measuring fundamental constants ( , G)

Proposed:

tests of GR (equiv. principle, limits on PPN parameters, Lense-

Thirring, etc. )

GW detection

atom neutrality

testing Newton’s 1/r

²

law at short distance

realization of mass unit (Watt balance)

α

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Gravity measurements with atom interferometry