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Applications of Atom Interferometry to
Fundamental Physics on Earth and in Space
Christian J. Bordé
Atomic clocks
- Measurement of the fine structure constant
Gyros, accelerometers, gravimeters
- Test of the equivalence principle

General Relativity
- Lense-Thirring effect
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E(p)
ENERGY
atom slopev
rest mass
photon slopec
p
MOMENTUM
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E(p)
p//
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E(p)
p?
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FIRST-ORDER EXCITED STATE AMPLITUDE
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REINTERPRETATION OF RAMSEY FRINGES
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RAMSEY FRINGES WITH TWO SPATIALLY SEPARATED
FIELD ZONES
a
b
b
a
a
b
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FOUNTAIN CLOCK
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Atom Interferometer
Laser beams
Atom beam
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Laser Cooling of Atoms
working horse of laser cooling
Magneto-optical trap (MOT)
MOT
BEC 1014 cm-3 10 nK 10-100 mm
density n 1011 cm-3 temperature T
100 mK size Dx 1mm

• reduction of systematic errors
• higher interaction times Tdrift ? µs ... ms
  towards 1-10 s
• new atom sources such as
• atom lasers (Bose-Einstein condensates)

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Optical clocks with cold atoms
use the working horse of laser cooling
Magneto-optical trap (MOT)

• In the future new atom sources such as atom lasers

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Time-domain Ramsey-Bordé interferences with cold
Ca atoms
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Femtosecond lasers as frequency comb generators
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Experimental Setup
Method 4 Count Ca beat 4 Count nceo 4
phase-lock frep
J. Stenger, T. Binnewies, G. Wilpers, F. Riehle,
H.R. Telle, J.K. Ranka, R.S. Windeler, A.J.
Stentz, private communication
FVC
Frequency Comb Generator
TiSa
Counter
PLL
PZT
PD
SESAM
fCa-Servo Counting
PZTs
MS Fiber
LBO
OC
?CEO-Counting
frep-Servo
100 MHz ( H - maser / Cs-clock controlled)
PD
PM
PLL
-
455 986 240 MHz from Ca-Standard (via fiber)
Counter
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a
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Interféromètres atomiques
Jets atomiques
Faisceaux laser
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RECOIL DOUBLING
E(p)
E(p)
p
p
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Measurements of a with Atom Interferometers
frequency shift due to the photon recoil in a
Ramsey-Bordé interferometer
determined by HYPER measured in ground-based
experiments, e.g. ion traps
accuracy 2?10-10 2?10-10 5?10-9
HYPER
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HYPER

• HYPER-precision
• cold atom interferometry
• in space

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The HYPER Core Team
BNM-LPTF ( A. Clairon, P. Wolf, Paris) ENS-LKB
(C. Salomon, Paris) IAMP (K. Danzmann,
Hanover) IQO (W. Ertmer E.M. Rasel, C.Jentsch,
Hanover) IOTA (P. Bouyer, Paris) LHA (N. Dimarcq,
A. Landragin , Paris) LGCR (P. Tourrenc,
Paris) LPL (C. Bordé, Paris Hanover) PTB (J.
Helmcke, Braunschweig) RAL (M.K. Sandford, R.
Bingham, M. Caldwell, B.Kent, Chilton,
Didcot) Queen Mary and Westfield College (I.
Percival, London) University Trento (S. Vitale,
Trento) University Ulm (W. Schleich,
Ulm) University Konstanz (C.Lämmerzahl, Konstanz)
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GRAVITOELECTRIC AND GRAVITOMAGNETIC
INTERACTIONS THE USUAL PICTURE
Two entries 1 - Field equations - R.L. Forward,
General Relativity for the Experimentalist
(1961) - Braginsky, Caves Thorne, Laboratory
experiments to test relativistic gravity (1977)
2 - Motion equation and Schroedinger equation
- DeWitt, Superconductors and gravitational drag
(1966) - G. Papini, Particle wave functions in
weak gravitational fields (1967)
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Atom Interferometers as Gravito-Inertial
Sensors
Analogy between gravitation and electromagnetism
Metric tensor

Newtonian potential
T
T 
T
Gravitoelectric
field
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Atom Interferometers as Gravito-Inertial
Sensors I - Gravitoelectric field case
with light Einstein red shift with neutrons COW
experiment (1975) with atoms Kasevich and Chu
(1991)
T
T 
T
Gravitational phase shift
Ratio of gravitoelectric flux to quantum of flux
Mass independent ? (time)2
Phase shift
Circulation of potential
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Atom Interferometric Gravimeter

• Performances
• Resolution 3x10-9 g after 1 minute
• Absolute accuracy ?g/glt3x10-9
• From A. Peters, K.Y. Chung and S. Chu

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Gradiometer with cold atomic clouds

• Yale university
• Sensitivity 3.10-8 s-2/?Hz 30 E/?Hz
• Potential on earth 1E/?Hz

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Atom Interferometers as Gravito-Inertial
Sensors Analogy between gravitation and
electromagnetism
Metric tensor

Pure inertial rotation
Gravitomagnetic field
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Atom Interferometers as Gravito-Inertial
Sensors II - Gravitomagnetic field case
with light Sagnac (1913) with neutrons Werner
et al.(1979) with atoms Riehle et al. (1991)

Sagnac phase shift
Ratio of gravitomagnetic flux to quantum of flux
Phase shift
Circulation of potential
ERICE 2001
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Atomic Beam Gyroscope
Interference fringes
Sensitivity 6.10-10 rad.s-1/?Hz (Yale
University)
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HYPER-precision cold atom interferometry
in space
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Atomic Sagnac Unit
Interferometer length 60 cm
Atom velocity 20 cm/s
Drift time 3 s
Area 54 cm2
109 atoms/shot
Sensitivity 2x10-12 rad/s
HYPER
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125th Anniversary of the Metre Convention
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LENSE-THIRRING FIELD
Gravitomagnetic field generated by a massive
rotating body
Field lines to magnetic dipole
Gravitomagnetic field lines
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HYPER Lense-Thirring measurement
Signal vs time
Hyper carries two atomic Sagnac interferometers,
each of them is sensitive to rotations around one
particular axis. The two units will measure the
vector components of the gravitomagnetic rotation
along the two axes perpendicular to the telescope
pointing to a guide star.
HYPER
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125th Anniversary of the Metre Convention
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The HYPER Satellite
ASU1
Cold Atom Source
Star Tracker Pointing
ASU2
ASU Reference (connected to the Raman Lasers
to the Star Tracker)
HYPER
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ONERA 2001
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Conclusion
Atomic Sagnac Unit 2
Lense-Thirring Measurement
Resolution 3x10-12rad/s /?Hz
Star Tracker
Atomic Sagnac Unit 1

• Expected Overall Performance 3x10-16rad/s over
  one year of integration i.e. a S/N100 at twice
  the orbital frequency

Raman Lasers Module
Laser Cooling Module
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The HYPER Mission Goals (1)
measurement of the fine-structure constant
improved by one or even two orders of magnitude
to test QED
a
latitudinal mapping of the general relativistic
gravito-magnetic effect of the
Earth (Lense-Thirring-effect)
HYPER
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The HYPER Mission Goals (2)
investigation of decoherence of matter-waves
for the first time cold-atom gyroscopes control
a spacecraft
HYPER
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HYPER Summary

• HYPER will investigate
• precision measurement of a (h/mat)
• gravito-inertial effects
  (Lense-Thirring-Effect)
• decoherence (effects
  of quantum gravity)
• navigation by atom interferometric sensors

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ABCDx PROPAGATOR
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GRAVITOELECTRIC AND GRAVITOMAGNETIC
INTERACTIONS THE USUAL PICTURE
Two entries 1 - Field equations - R.L. Forward,
General Relativity for the Experimentalist
(1961) - Braginsky, Caves Thorne, Laboratory
experiments to test relativistic gravity (1977)
2 - Motion equation and Schroedinger equation
- DeWitt, Superconductors and gravitational drag
(1966) - G. Papini, Particle wave functions in
weak gravitational fields (1967)
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A new analogy between electromagnetic and
gravitational interactions
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RELATIVISTIC PHASE SHIFTS