Atom interferometry test of short range gravity : recent progress in the ForCa-G experiment Experiment : Matthias Lopez, Obs Cyrille Solaro, Obs Franck Pereira, Obs Theory : Astrid Lambrecht, LKB Axel Maury, LKB Gabriel Dufour, LKB Marie-Christine Angonin, Obs Peter Wolf, Obs 1
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Atom interferometry test of short range gravity : recent progress
in the ForCa-G experiment
Experiment : Matthias Lopez, Obs
Cyrille Solaro, ObsFranck Pereira, Obs
Theory : Astrid Lambrecht, LKB
Axel Maury, LKBGabriel Dufour, LKBMarie-Christine Angonin, ObsPeter Wolf, Obs
1
Outline
• IntroductionInertial sensors with cold atoms,
Why gravity needs testing…
• State of the art in our labVertical lattice, Wannier Stark ladder, Bloch frequency &
local gravimetry. Experimental Setup.
• The next stepCasimir-Polder potential probing, Mirrors in vacuum,
Manipulation of atoms in the surface vicinity…
2
Inertial sensors with cold atoms@ SYRTE, in the IACI group.
• Gyrometer (Remi Geiger)
• Gradiometer (Franck Pereira & Sebastien Merlet)
• Gyrometer on chip (Carlos Guerrida)
• Trapped atomic clock on chip (P. Rosenbusch)
• MIGA (GW) (Geiger and collaborators @ LP2N, LBB… and more)
• Gravimeter (Franck Pereira & Sebastien Merlet)
3
σ𝑔𝑔= 5.7 × 10−9 @ 1𝑠
Gravitation, why does it need testing ?
These two theories are fundamentally incompatible.
Standard Model :Electromagnetic, weak
and strong
General Relativity:Gravitation.
Two powerful theories :
&
Unifying models with higher dimensionality predict that gravitational force should differ at short range.
(Adelberg, Ann. Rev. Part. Sci 53, 77, 2003)
They predict neither range, nor magnitude… merely constraints.
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𝜕𝜇𝜕𝜇 +
𝑚2𝑐2
ℏ2𝑈 = 0
Constraints
Klein-Gordon equation Yukawa type potential:
𝑈(𝑟) = 𝐶 𝑟 𝑒−𝑚𝑐ℏ𝑟
This formalism is used to parameterize the deviation, it yields no physical content but range λ and amplitude α
𝑈𝑁𝑒𝑤𝑡𝑜𝑛 =𝐺𝑀𝑚
𝑟1 + 𝛼𝑒
−𝑟λ
5
Gravitation, measurements atdifferent scales
Long range (103 to 1011 m):Telemetry (satellite or lunar) (Ciufolini, Science 279, 2100 (1998))Planetary Orbitography (Kolosnitsyn, Gen. Rel. Grav. 36, 1619 (2004))Pulsars (Will, Astrophysics and Space Science 63, 731 (2004))
Medium range ( ~ meters):Free fall tower (Eckhart, Phys. Rev. Lett., 60, 2567 (1988))
Short range ( < meter):Torsion pendulum (Hoskins, Phys. Rev. D., 32, 3084 (1985))Optical interferometry (Smullin, Phys. Rev. D 72, 122001 (2005))Casimir effect (Decca, Phys. Rev. Lett. 78, 5(1997))
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A. Geraci et al., Phys Rev D 78, 022002 (2008)
log 1
0a
log10l (m)
Lab
Satellite
LLR
Orbitometry
E. Fischbach, R. Hellings, & al. (2003)
Large Scale Small Scale
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Some visual insight on constraints
Principle of the experiment, Hamiltonian.“A vertical trapped atomic interferometer close to a surface”
Energy
z
g
B
2/ll
2
1 cos 22 2
latticelattice a
a
UPH k z m gz
m
Kinetic energy Trapping potential Gravity
ℎν𝐵 = 𝑚𝑎𝑔λ𝑙2= ℎ × 568.05 𝐻𝑧Bloch Frequency :
Mirror
Site mRbAtoms
λl/2 = 266 nm
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Principle of the experiment, solutions.
Eigenstates : Wannier Stark states
∀𝑚 , |𝜑𝑚 > =
Eigenvalues Em,With the following property :
𝐸𝑚 − 𝐸𝑚+∆𝑚 = ∆𝑚 × ℎν𝐵
“Wannier-Stark ladder”
Knowledge of νB yieldsknowledge on the local field (gravitationnal and
more…) !
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Principle of the experiment, interferometry.
MIRROR MIRROR MIRROR
m
m+Δm
m
RamseyTime T
π/2 π/2
m m+Δm
νHFS
Δm∙νB
g
t
Two counter-propagating Raman beams couple :• Internal degrees of freedom : Rb hyperfine structure• External degrees of freedom : position on lattice
𝑃𝑒
𝑃𝑒 + 𝑃𝑔=𝐶
21 + cos Δϕ
Δϕ =𝑈𝑚+Δ𝑚 − 𝑈𝑚
ℏ× 𝑇
We then measure populationsin both hyperfine states
where
Which yields the Bloch frequency νB !10
Current experimental setup
MOT 3D
1. Cold atoms in a 3D Magneto Optical Trap 3D107 atoms in 500ms @ 2μK
(Bonus step : Evaporative cooling)
2. 532nm 7W Laser, 800 μm waistProvides the vertical lattice