Measurement of atom-surface interactions by atom

interferometry Matthias Büchner

Laboratoire Collision, Agrégats, Réactivité UMR 5589

IRSAMC

Outline

Introduction: Principle of an Mach-Zehnder interferometerAtom diffraction by a standing laser wave in the Bragg regime

Our atom interferometer

Measurement of the van der Waals interactionnon-Newtonian gravitation

ConclusionOutlook

Mach-Zehnder interferometers

beam splittermirror

mirror

light wave

beam splitterDétecteur

optic:

Atoms:optics:

• propagation in atmosphere• velocity : c= 300 000 km/s • wavelength : λλλλopt= 633 nm • time of flight (L= 1 m): T= 3 ns

• beam splitter/miroirs: standard

↔

↔

↔

↔

↔

in vacuumv= 1 km/s (thermal lithium beam)de Broglie: λλλλdB=h/(mv) ≈ 54 pmT= 1 ms extreme sensitivity to inertial effects

???

Détecteur sortie1

(0)

~λdB/a

(1)

(-1)

(2)

Atom interferometer with separated pathsCoherent manipulation of atomic waves

grating

a

Atom beam

(λdB) L L

Beam splitter

Mirrors recombining beam splitter

Mach-Zehnder atom interferometer with amplitude grating s

λdB.L/a

The mirrors and beam-splitters of the Mach-Zehnder optical interferometers are replaced by nanograting diffraction

1991-2004 group of David E. Pritchard at MIT2004 - group of A. Cronin at Univ. of Arizona

for Sodium waves

+ versatile instrument+ many experiments were carried out- low transmission- low visibility due to multiple diffraction orders

Period = 100 nmFront View

Mach-Zehnder interferometers

Lithium waveDiffracting gratings

pmmv

hdeBroglie 54≈=λ

Grating period 100 nm ⇒ diffraction angle ≈ 540 µrad ⇒ L=1 m : arm separation ≈ 0. 5 mm

The mirrors and beam-splitters of the Mach-Zehnder optical interferometers are replaced by Bragg diffraction on laser standing waves

In the Bragg regime, diffraction of order p>1 can be used.

Atom diffraction by light waves

The process

ω, kL

ω,kL|a>

|c>

keff= 2kL

Probability of the process:∝∝∝∝ laser detuning ∆∆∆∆-1

∝∝∝∝ laser power∝∝∝∝ interaction time

The photon wavelength should not be resonant with an atomic transition If not : decoherence by spontaneous emission (population of state |c>)

effect ∝∝∝∝ detuning ∆∆∆∆-2

h∆∆∆∆

⇒⇒ need of a powerful single frequency cw laser need of a powerful single frequency cw laser with a wavelength close to an atomic transitionwith a wavelength close to an atomic transition

⇒⇒⇒⇒⇒⇒⇒⇒ Selective for atoms and their isotopesSelective for atoms and their isotopes

energy

katom

Bragg diffraction

|k, a>

kL

Thick light wave : ∆y →uncertainty principle ⇒∆ky=0 : k || xθB kL

|k+2k L, a>

Condition of Bragg diffraction : BRAGG angle

λL= 671 nmλde Broglie = 54 pm

θB = p λdB/ λL

= 80 µrad (p=1)

p = diffraction order|k, a>

∞

x

y

mirror

|k+4k L, a

>

p=1|k, a>

|k, a>

p=2

2θB

θB = p λdB/ λL

= 160 µrad (p=2)

Only diffracted beam : no loss of atoms !!

Bragg diffraction

transmitted wave: order 0

Diffracted wave : order 1

Rabi oscillation - laser power- laser detuning from an atomic

resonance- laser waist (interaction time)

0 20 40 60 80 100 120 140 160 1800

5k

10k

15k

20k

25k

30k

35k

40k

45k

50k

55k

intensity of 1st order diffraction (c/s)

laser power (mW)

mirror

beam splitter

+ no stray beams+ choice of diffraction order+ choice of diffraction amplitude

|k+2p >kL

|k>

p=1

Three grating atom interferometerStanding laser waves

M1 M2 M3

•

x

z

y

Alignment condition : k+2kL(1) - 2kL

(2) = k+2kL(2) - 2kL

(3)

phase related to diffraction: ϕ= 2kL (2 x2 – x1 – x3 ) scan the fringes

∆x3 = 53 nm ↔ ∆ ϕ = 1 rad

I=I0·[1+V ·cos(ϕmirror)]V: visibilityI0: mean flux

+2kL(1)

+2kL(2)

-2kL(2)

-2kL(3)

k

Our atom interferometer

Ionization detector(hot wire)

Standing laser waves

pθB

18 µm18 µm

source Collimation slits

lithium+ rare gas

Detection slit

0,6m

M1 M2 M3

800 °C

0,6m

krypton hélium750 m/s <vLi < 3500 m/s

∆x

∆∆∆∆x∝∝∝∝p/vLi typ. 100µm for 1000 m/s, p=1200 µm, p=2 ..

0,8m

Critical alignment: collimation, Bragg angle, mirror positions Critical alignment: collimation, Bragg angle, mirror positions

≈ 30 µm

≈ 50 µm

Strong collimation of the atom beamStrong collimation of the atom beam

Our interferometer fringes

p = 1

visibilityV = 84.5 ±±±± 1%

mean fluxI0 = 23700 c/s

0.0 335.5 671.0 1006.5 1342.00

5k

10k

15k

20k

25k

30k

35k

40k

45k

Signal (c/s)

x - position du miroir M3 (nm)

I=I0·[1+V ·cos(ϕmirror)]

sensitivity around15 mrad/√Hz

Interferometric measurements

We applied our atom interferometer for the mesure of theWe applied our atom interferometer for the mesure of the

- electric polarisability of 7Li- refraction index of rare gases for lithium matter waver- atom surface interaction (van der Waals interaction) and we are mesuring now a topological phase

Perturbation U

with T ≈ 100 µµµµs

1 second mesure:∆Φ∆Φ∆Φ∆Φmin = 15 mrad

1000 m/s 10 cm

ηη

/)(1

UTdttU ≈=∆ ∫φ

Umin = 1.5 ××××10-32 J= 10-13 eV = 20 Hz

Our measurement of the vdW interaction

Motivation Motivation work of Perreault, J. D. and Cronin, A. D., PRL 95, 133201 (2005)

Several diffraction orders exist→But only order « 0 » contributes to the dephasing

Test of atom-surface interaction For distances between 0 and 26 nm over a length of 110 nm

window

Nanograting :Surface of silicon nitride covered by Au/Pd

period : (100±0.1) nm, width of the window: (53±1) nm,

Thickness: (110±5) nm

Our measurement of the vdW interaction

A collaboration between the Arizona and Toulouse groups was created

Why using our interferometer?

• low phase noise

• only two atom beams interfereinterpretation is far more easier

• another atom: Li instead of Na (group of arizona)

Our measurement of the vdW interaction

window

C: the 2 beams go through the window

CB A

B: one beam goes through the grating

A: both beams go through the grating

Our measurement of the vdW interaction

⇒⇒⇒⇒dephasing ∝∝∝∝ v-0.49

We changed the atom velocity (750 – 3300 m/s)

2nd order diffractionError bar of ±100 mrad

Perreault, and Cronin, PRL 95, 133201 (2005) our results

Li

Velocity dispersion of the vdW phase

∫⋅= dzwzV

v vdW ),,(1

)( ξξδφη

33

33

2/2/),,(

ξξξ

−−+

+−=

w

C

w

CwzVvdW

>ξ

w VvdW

Integration over the trajectories ξFourier optics:Diffraction amplitude of 0th order: ∫∝Φ ξξδφ dwieA i )];(exp[0

0

We measure this phase

X

Dispersion de la phase vdW en vitesse

dephasing:One area contributes the mostThis area depends on the velocity

X

X

vLi= 750 m/svLi= 3500 m/s

Origin of the interaction

C3/r3

C3 = (3.25 ± 0.2) meV·nm3

χ2(p)

⇒⇒⇒⇒ Signature of the van der Waals interaction

Model potential : Cp/rp

Test of non Newtonnian gravitation

Modified potential:

Amplitude Portée

correction type « Yukawa »

Constraints over α and λ :

(α,λ) adjust C3 for Φ0(v) Comparing theresiduals

rejection

acceptation

MotivationMotivation : research of a 5th force

Newton

Sonde de la gravitation non Newtonienne

Our resultats : (λ,αλ,αλ,αλ,α)

(α,λ) = (<1028,1 nm) (α,λ) = (<1026,2 nm) (α,λ) = (<1023,10 nm)

Our data points

excluded regionEderth

vdW

neutron (a)

neutron (b )

Figure : extracted from Fischbach et al. PRD 64, 075010 (2001)and H. Abele (2008)Progress in Particle and Nuclear Physics 60, 1 (2008)

Neutron a,b : Limits from neutron–nucleus scattering and neutron optics dataH. Leeb, J. Schmiedmayer, PRL 68 (1992) 1472.

Ederth: V.M. Mostepanenko and M. Novello, Phys. Rev. D 63, 115003 (2001),T. Ederth, Phys. Rev. A 62, 062104 ~2000!.

vdW: M. Bordag, V.M. Mostepanenko, and I.Yu. Sokolov, Phys. Lett. A 187, 35 (1994) Y.N. Israelachvili and D. Tabor, Proc. R. Soc. London A331, 19 (1972)

-We are actually measuring the He-McKellar-Wilkens eff ecttopological phase resulting from (induced) dipoles m oving in magnetic

fields

-Measurement of dephasing/decoherence of matter waves b y radiation

-Construction of a 2 nd generation atom interferometeratoms with v=10-1500 m/s, slowed by radiation forcesbrilliant lithium atom beam, high flux, small veloci ty distribution

active stabilized interferometer bench

-Measurement of the retarded van der Waals interaction (Casmir-Polder interaction)

-matter neutrality …..

-

Outlook

in collaboration with

V.P.A Lonji A.D. Cronin

University of Tuscon, Arizona, USA

Funding from ANR, MENRT, CNRS, Université P. Sabatier, IRSAMC, Région Midi-Pyrénées

From left to right:Steven LepoutreJacques ViguéMatthias BüchnerGérard TrénecHaikel JelassiGilles Dolfo (not present)

Toulouse group

S. Dimopoulos and A. Geraci (PRD 2003)

(extracted from Fischbach et al.PRD, 64, 075010)

Our measurement ( λ,αλ,αλ,αλ,α)

Constraint on α and λ :

(α,λ)Fit C3 for Φ0(v) Comparaiso

n of residuals

Acceptation

Rejection

(α,λ) = (<1028,1 nm) (α,λ) = (<1026,2 nm)

(α,λ) = (<1023,10 nm)

vdW : Y.N. Israelachvili and D. Tabor, Proc. R. Soc. London A331, 19 (1972)Ederth ,: T. Ederth Thomas PRA 62 062104 (2000)

|α||α||α||α|

Calcul de (7Li) :

soit

(forces d’oscillateurs des transitions)

C3 = 3,12 meV.nm 3 cohérent avec C3 = 3,25 +/- 0,2 meV.nm 3

(exp)

Transition de résonance (2s →

2p)

Autres transitions

Force d’oscillateur

0.746 0.254

Polarisabilitéstatique α0

(164,111 u.a. Z.-C. Yan,

PRA 1996)

99% (αres=161,945 u.a.)

1,32% (2,166 u.a.)

Projet I : mesure d’une phase topologique

Le premier exemple d’une phase topologique :

la phase d’Aharonov-BohmY. Aharonov and D. Bohm, Phys. Rev. 115p 485 (1959)

déphasage des franges d’interférences

La famille des effets topologiques

>µµµµ

e+e+e+e+e+>

e+

µµµµ

µµµµ

µµµµ

Aharonov-Bohme+ : particule chargéeµµµµ : dipôle magnétiqueg+ : monopôle magnétique d : dipôle électrique

>g+

d

d

d

Aharonov-Bohmdual

>d

g+g+g+g+

g+

E ↔↔↔↔ Be+ ↔↔↔↔ g+

d ↔↔↔↔ µ

Aharonov-Casher

He-McKellar-Wilkens

L’effet HeMcKellar-Wilkens

>d

g+g+g+g+

g+·

E

Li

50 mm

B

B

Ed=αE

U=½ α α α α E’ 2=½ α α α α (E+v××××B)2 =½ ααααE2 +ααααE·((((v××××B)+α ()+α ()+α ()+α (v××××B)))) 2

- 3 µrad- Identique pour chaque brasB= 112 Gauss

E= 0.85 MV/m24 mrad

-450 rad, mais- identique pour les 2 bras

ExpExpéérience en coursrience en cours

·

Projet II: Un interféromètre de 2 ème génération

•• Construction dConstruction d’’ une source de lithiumune source de lithium

- flux élevé

- accordable vers 100 m/s

- faible dispersion en vitesse (1%)

•• CrCrééation dation d’’ un banc dun banc d’’ interfinterfééromromèètre suspendu et stabilistre suspendu et stabiliséémméécaniquement caniquement Pourquoi ? Pourquoi ?

ϕ= 2pkL (2 x2 – x1 – x3 )

M1M3M1 M2

Rotation : ϕSagnac= 4pkL Ω(y) L T, T : temps de vol

Accélération : ϕacc = pkL a(x) T2

grâce à des méthodes d’optique atomique

p=5100 m/s

L

∆∆∆∆x=5 mm

Projet : Neutralité

Neutralité de la matière : charge du neutron=0 ?charge de l’électron= - charge du proton ?

Pourquoi une telle symétrie entre leptons et quarks ?

Incertitudes actuelles:charge du neutron : qn=(0.4 ±1.1) 10-21 qe

neutralité e- - p : ≈ 10-21 qe

EstEst--ce que lce que l’’ interfinterfééromroméétrie atomique est capable de trie atomique est capable de repousser ces limites ?repousser ces limites ?

Projet : Neutralité

PeutPeut--être oui être oui ……..

Publications:

• C. Champenois et al., dans The Hydrogen Atom: Precision Physics of Simple Atomic Systems, Springer Berlin / Heidelberg, 554-563 (2001) Matter Neutrality Test Using a Mach-Zehnder Interferometer

• R. Delhuille et al., AIP Conf. Proc.-- April 26, 2001 -- Volume 564, pp. 192-199QUANTUM ELECTRODYNAMICS AND PHYSICS OF THE VACUUM: QED 2000,

Atom interferometry: Principles and applications to fundamental physics

• A. Arvanitaki et al. PRL 100, p. 120407 (2008)

How to Test Atom and Neutron Neutrality with Atom Interferometry

Projet : NeutralitéPrincipe de montage expérimental :

E= ± 5MV/m, vLi= 50 m/s∆∆∆∆x (max) = 2 mm, LC= 0.5 mSensibilité actuelle :15 mrad Hz-1/2 ⇒⇒⇒⇒

Tacq ≈ 17 min pour qresi/nucléon < 10-21 e

∫Γ

= λλη dVqresivLi)(1φ

Défis: inhomogénéités du champ E (φpol ≈3·106 rad)Possibilité: hacher le jet et pulser E

A. Arvanitaki et al. PRL 100, p. 120407 (2008) :Fontaine atomiqued’hauteur 10 m : 106 lancements ⇒⇒⇒⇒ qresi/nucléon < 10-28 e