Atom Interferometry test of short range gravity : recent progress

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
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Outline
• Introduction
Inertial sensors with cold atoms,
Why gravity needs testing…
• State of the art in our lab
Vertical lattice, Wannier Stark ladder, Bloch frequency &
local gravimetry. Experimental Setup.
• The next step
Casimir-Polder potential probing, Mirrors in vacuum,
Manipulation of atoms in the surface vicinity…
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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)
σ𝑔
= 5.7 × 10−9 @ 1𝑠
𝑔
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Gravitation, why does it need testing ?
Two powerful theories :
Standard Model :
Electromagnetic, weak
and strong
&
General Relativity:
Gravitation.
These two theories are fundamentally
incompatible.
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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Constraints
Klein-Gordon equation
2𝑐2
𝑚
𝜕𝜇𝜕𝜇 + 2 𝑈 = 0
ℏ
Yukawa type potential:
𝑈(𝑟) = 𝐶 𝑟 𝑒
−
𝑚𝑐
𝑟
ℏ
This formalism is used to parameterize the deviation,
it yields no physical content but range λ and amplitude α
𝑈𝑁𝑒𝑤𝑡𝑜𝑛
𝑟
𝐺𝑀𝑚
−
=
1 + 𝛼𝑒 λ
𝑟
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Gravitation, measurements at
different 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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Some visual insight on constraints
Large Scale
Small Scale
log10a
Lab
Satellite
log10l (m)
LLR
Orbitometry
E. Fischbach, R. Hellings, & al. (2003)
A. Geraci et al., Phys Rev D 78, 022002 (2008)
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Principle of the experiment, Hamiltonian.
“A vertical trapped atomic interferometer close to a surface”
g
Energy
Mirror
B
λl/2 = 266 nm
ll / 2
z
Site m
Rb
Atoms
P 2 U lattice
H

1  cos  2klattice z    ma gz
2ma
2
Kinetic energy
Bloch Frequency :
Trapping potential
Gravity
λ𝑙
ℎν𝐵 = 𝑚𝑎𝑔 = ℎ × 568.05 𝐻𝑧
2
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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 yields
knowledge on the local
field (gravitationnal and
more…) !
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Principle of the experiment, interferometry.
Two counter-propagating Raman beams couple :
• Internal degrees of freedom : Rb hyperfine structure
• External degrees of freedom : position on lattice
π/2
νHFS
π/2
RamseyTime T
t
MIRROR
MIRROR
Δm∙νB
MIRROR
m
m+Δm
We then measure populations
in both hyperfine states
m+Δm
g
𝑃𝑒
𝐶
= 1 + cos Δϕ
𝑃𝑒 + 𝑃𝑔 2
where
m
𝑈𝑚+Δ𝑚 − 𝑈𝑚
Δϕ =
×𝑇
ℏ
m
Which yields the Bloch frequency νB !
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Current experimental setup
1. Cold atoms in a
3D Magneto Optical Trap 3D
107 atoms in 500ms @ 2μK
(Bonus step : Evaporative cooling)
2. 532nm 7W Laser, 800 μm waist
vacuum
chamber
Provides the vertical lattice
3. 1064 nm 500mW Laser, 200 μm waist
Provides transverse confinement
lattice
lattice
4. 2 counter-propagating Raman beams
Allows for coherent superposition of wave packets,
suitable for interferometry
π/2
MOT 3D
π/2
MixTrap
up to 3 s
Detection
time
k1
k2
MOT 3D
k1
Measuring the Bloch Frequency νB
Coherent superposition of
states on site m and m+Δm
Verified with Rabi oscillations.
TramseyU==100ms
1.8 Er
↔ 1 fringeΔm
every
= +610Hz
Interferometric fringes within
an enveloppe. We locate the
central fringe.
νCF = Δm ∙ νB
Today :
𝜎𝑔 𝜎𝜈𝐵
=
= 2.2 10−6 @ 1𝑠
𝑔
𝜈𝐵
Corresponds to 0.1 mHz
in 100 seconds
Integration time !
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Phenomenology in the vicinity of a
conducting surface
Utot = Ugrav + UCP + UYukawa
Gravitationnal
Potential g
We have an interferometer that measures g locally
Casimir, surf-surf
ℏ𝑐𝜋2
𝑈𝐶 = −𝐴
240𝐿3
Casimir-Polder
Interaction
Casimir-Polder, surf-dipole
Surface
L
Atom
𝑈𝐶𝑃
3ℏ𝑐𝛼0
=−
8𝜋𝐿4
L
By precisely calculating and measuring those 2 effects :
Deviation
(the quest…)
New constraints on range λ and amplitude α
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Consequence of CP on energy levels
in the vicinity of a mirror.
MIRROR, M
Energy
|e>
|g>
νB
νB+νCP
Position
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Numerical Calculations of the
Casimir Polder potential
Pelisson,PRA 86, 013614 (2012)
Energy Shift due to Casimir-Polder Interaction
ΔνCP (x 3.77 kHz)
Real
C-P Potential
“Naïve”
C-P Potential
ΔE = ~2 Hz !
z atom distance from mirror
(in site units)
4 orders of magnitude higher
than our resolution @100s !
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A quick break !
What we have :
A trapped interferometer capable of
measuring local potentials, with enough
resolution to probe with great accuracy
the CP potential.
The vertical lattice reflection mirror,
which is currently outside the vacuum
chamber needs to be placed inside !
What we need :
The means to transport atoms close to
the surface, in a well controlled manner.
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Mirror inside (coming soon…)
MIRROR
At the moment, we have one
ultra low pressure vacuum chamber
(10-10 mbar)
The mirror is outside
We will in the next months add
another science chamber on top.
• 4 mirrors (1/2 inch) on
translation stage
• Large optical access
• Electric field control
• Independant vacuum
532 nm
The “naked”
vacuum cell
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Moving the atoms from
one vacuum cell to the other, the idea.
Atom elevator (aka Bloch lift)
By controlling the frequency difference
between 2 laser beams, we effectively
create a moving lattice, accelerating
and decelerating the Rb Atoms.
Parameters :
40 GHz detuning
100 mW/beam
U = 100 Er
a = 120 g
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Moving the atoms from one vacuum
cell to the other.
Ben Dahan, PRL 76, 4508 (1996)
Cadoret, PRL 101, 230801 (2008)
Efficiency limited by
• Size of beam < size molasse
• Temperature of atoms
• Spontaneous emission
Test on atoms from an optical molasse
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Is loading the MixTrap from a
Magneto-Optical Trap enough ?
The Problem:
•
•
•
60000 atoms populate 4000 sites
15 atoms per site, covering a length of 1mm.
2 μK temperature, which implies low efficiency of
the Bloch Elevator (3 atoms per site once lifted)
The requirements:
•
•
•
•
Lots of atoms too maintain
decent signal at the detection
Populate smaller span of sites
More atoms per site
Reduce temperature
“We need to load the MixTrap
from a cooler, smaller and
denser sample”
The solution:
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Reaching our goal through
evaporative cooling
f1=300mm
300+150mm
f=150mm
100 W 1064nm laser
2 AOM to control beam power
100+150mm
f2=100mm
196µm
35.5µm
f=150mm
-1 order
+1 order
300
mm
300
mm
AOM
f=150mm
Vacuum
chamber
150mm
f=150mm
Create a cigar shaped
trapping dipolar
potential:
Width ~ 30 um
Length ~ 150 um
AOM
150mm
110
mm
172x48.5µm
EVAPORATIVE
COOLING
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Benefits of evaporative cooling
Within a few seconds, we increase phase-space density by :
Lower temperature
Better space
density
Fewer states populated in transverse confinement
→ Better contrast at longer Ramsey time
↘Better resolution on the Bloch Frequency νB
We now have 1011-1012 atoms/cm3
→ More atoms per site, less sites are populated
↘ 40000 atoms in σ = 4 sites (1 um)
↘ We can expect better site adressability close
to the surface.
Loading from Molasse
Loading from Dipolar Trap
Number of atoms
60000
40000
Sites populated
2000
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Atoms per site
30
2000
Preparation time
500 ms to 1s
3 seconds
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The unsuspected benefit of higher
densities.
What we would expect :
Different collisional shifts in different sites should
kill the contrast at long times, due to spin dephasing.
(νcoll = 0,4Hz for 1012 at/cm3)
“Identical Spin Rotation Effect”
What we see for Δm = 0 :
Deutsch, PRL 105, 020401 (2010)
Collision induced spin rephasing :
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Discerning CP from a possible
deviation to Newton’s law
Numerically:
By properly modelling the Casimir Polder potential induced
by the di-electric mirror on the atomic dipole.
Main Challenge : Mirror is not a perfect conductor, its complex permittivity
needs to be well characterized. A. Lambrecht and collegues (LKB)
Calculated CP potential is then substracted from measurement → deviation(?)
Experimentally:
It’s easy to work with alternatively with 2 Rubidium isotopes : 87Rb & 85Rb
They have the same atomic polarizability α0.
However their masses differ, m87/m85 ≈ 87/85
Same experiment with
87Rb & 85Rb, then
‘87’ - ’85’
« What we have left ‘should’ behave like gravitational force »
We have 4 mirrors slots : we have control over the test masses !
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At the end of the day…
By inserting a mirror inside and properly controlling
our site populations close to this mirror we can conservatively expect :
Explore the λ ≈ 10 μm range
Where CP < 10-2 Hz
Explore the λ ≈ 0,2 - 1 μm range
With differential measurements
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Conclusion and perspectives
• We expect our ultra-cold Rb atoms to provide us
with a great tool to probe short range forces with
great accuracy.
• A unique tool to probe Casimir forces
• The means to discern a possible 5th force… or at
least set new constraints.
Short term prospects:
• Insert mirror in vacuum
• Transport atoms close to the mirror surface
• Perform interferometric potential
measurement at short ranges
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Thank you for your attention !
Franck Pereira
Cyrille Solaro
Peter Wolf
Astrid Lambrecht
The Atomic Interferometry
and Inertial Sensors
@ SYRTE, Paris Observatory
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