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

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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…

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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)

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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

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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

3. 1064 nm 500mW Laser, 200 μm waistProvides transverse confinement

4. 2 counter-propagating Raman beamsAllows for coherent superposition of wave packets,suitable for interferometry

vacuumchamber

latticelattice

k1

k2 k1

MOT 3D MixTrap Detection

up to 3 s

π/2 π/2

time

Measuring the Bloch Frequency νB

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Coherent superposition of states on site m and m+Δm

Verified with Rabi oscillations.

Interferometric fringes within an enveloppe. We locate the

central fringe.

U = 1.8 ErΔm = +6

νCF = Δm ∙ νB

Tramsey = 100ms↔ 1 fringe every 10Hz

Today : 𝜎𝑔

𝑔=𝜎𝜈

𝐵

𝜈𝐵= 2.2 10−6 @ 1𝑠

Corresponds to 0.1 mHzin 100 seconds

Integration time !

Phenomenology in the vicinity of a conducting surface

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Gravitationnal Potential g

We have an interferometer that measures g locally

Utot = Ugrav + UCP + UYukawa

Deviation (the quest…)

New constraints on range λ and amplitude α

By precisely calculating and measuring those 2 effects :

Casimir-Polder Interaction

L

𝑈𝐶 = −𝐴ℏ𝑐𝜋2

240𝐿3

Casimir, surf-surf

LSurface

Atom𝑈𝐶𝑃 = −

3ℏ𝑐𝛼0

8𝜋𝐿4

Casimir-Polder, surf-dipole

Utot =Utot = UgravUtot = Ugrav + UCP

Consequence of CP on energy levelsin the vicinity of a mirror.

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Energy

Position

MIR

RO

R, M

νB

|e>

|g>

νB+νCP

Numerical Calculations of theCasimir Polder potential

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Pelisson,PRA 86, 013614 (2012)

Δν C

P (

x 3

.77

kH

z)

z atom distance from mirror(in site units)

“Naïve” C-P Potential

Real C-P Potential

Energy Shift due to Casimir-Polder Interaction

ΔE = ~2 Hz !4 orders of magnitude higherthan our resolution @100s !

A quick break !

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What we have :

A trapped interferometer capable of measuring local potentials, with enough resolution to probe with great accuracy

the CP potential.

What we need :

The vertical lattice reflection mirror, which is currently outside the vacuum chamber needs to be placed inside !

The means to transport atoms close to the surface, in a well controlled manner.

Mirror inside (coming soon…)

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At the moment, we have one ultra low pressure vacuum chamber

(10-10 mbar)

The mirror is outside

The “naked” vacuum cell

MIRROR

532 nm

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

Moving the atoms fromone vacuum cell to the other, the idea.

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Atom elevator (aka Bloch lift)

By controlling the frequency differencebetween 2 laser beams, we effectivelycreate a moving lattice, accelerating

and decelerating the Rb Atoms.

Parameters : 40 GHz detuning100 mW/beamU = 100 Era = 120 g

Moving the atoms from one vacuum cell to the other.

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Test on atoms from an optical molasse

Efficiency limited by • Size of beam < size molasse• Temperature of atoms• Spontaneous emission

Ben Dahan, PRL 76, 4508 (1996)Cadoret, PRL 101, 230801 (2008)

Is loading the MixTrap from a Magneto-Optical Trap enough ?

• 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)

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The Problem:

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:

Reaching our goal through evaporative cooling

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+1 order

AOM

AOM

-1 order

f2=100mm

f1=300mm

Vacuum chamber

110mm

f=150mm

f=150mm

f=150mm

f=150mm

150mm

300mm

100+150mm

150mm

300mm

300+150mm

196µm

35.5µm

172x48.5µm

100 W 1064nm laser2 AOM to control beam power

Create a cigar shaped trapping dipolar

potential:Width ~ 30 um

Length ~ 150 um

EVAPORATIVECOOLING

Benefits of evaporative cooling

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Within a few seconds, we increase phase-space density by :

Lower temperatureFewer states populated in transverse confinement→ Better contrast at longer Ramsey time

↘Better resolution on the Bloch Frequency νB

Better space density

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 20

Atoms per site 30 2000

Preparation time 500 ms to 1s 3 seconds

The unsuspected benefit of higher densities.

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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)

What we see for Δm = 0 :

“Identical Spin Rotation Effect”Deutsch, PRL 105, 020401 (2010)

Collision induced spin rephasing :

Discerning CP from a possible deviation to Newton’s law

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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 permittivityneeds to be well characterized. A. Lambrecht and collegues (LKB)

Experimentally:

Calculated CP potential is then substracted from measurement → deviation(?)

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 with87Rb & 85Rb, then

‘87’ - ’85’

We have 4 mirrors slots : we have control over the test masses !

« What we have left ‘should’ behave like gravitational force »

At the end of the day…

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By inserting a mirror inside and properly controlling our site populations close to this mirror we can conservatively expect :

Explore the λ ≈ 10 μm rangeWhere CP < 10-2 Hz

Explore the λ ≈ 0,2 - 1 μm rangeWith differential measurements

Conclusion and perspectives

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Short term prospects:

• Insert mirror in vacuum• Transport atoms close to the mirror surface• Perform interferometric potential

measurement at short ranges

• 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.

Thank you for your attention !

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Franck Pereira Cyrille Solaro Peter Wolf Astrid Lambrecht

The Atomic Interferometryand Inertial Sensors

@ SYRTE, Paris Observatory