Thomas Bourdel, Julien Cubizolles , Lev Khaykovich, Frédéric Chevy, Jing Zhang, Martin Teichmann, Servaas Kokkelmans,

Christophe Salomon

Laboratoire Kastler Brossel, Ecole Normale Supérieure, Paris,Séminaire interne, Janvier, 2004

Collège de France

Condensate of Fermionic Lithium DimersCondensate of Fermionic Lithium Dimers

-0.2 -0.1 0.0 0.1

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Position [mm]

Y

OutlineOutline

• Formation and detection of molecules• Cooling to condensation• Condensates

– Double structure– Comparaison with other molecular condensates– Some more proofs of condensation– Condensates in very anisotropic traps– An ellipticity study

How to form molecules ?How to form molecules ?

• Sympathetic cooling of fermions by evaporation of bosons• Transfer into the optical trap

• Hyperfine transfer by RF adiabatic passage• Increase of the magnetic field to 1060 Gauss• Mixture: ½ Zeeman Transfer by RF sweep on

resonance• (Evaporation by lowering the trap intensity)• Slow crossing of the Feshbach resonance• (Further evaporation)• Detection

How to detect dimer formation ?How to detect dimer formation ?

0,0 0,5 1,0 1,5 2,0

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-100

0

100

200

scat

terin

g le

ngth

[nm

]Magnetic field [kG]

1,3

2

4

Double ramp method :

For the probe laser to be on resonance, the magnetic field needs to be turned off. The unbrocken dimers are not detected.

232 NNNmol

1 B B

B

dE E

E dt

Importance of the ramp speedAdiabaticity:

a>0

a<0

Temperature effectsTemperature effects

The cooler, the more molecules,Independant of ramp speed

Creating molecules is heating

The molecules are likely to be in thermal and chemical equilibrium with the atoms

Evaporative cooling to condensation ?Evaporative cooling to condensation ?

• Very high collision rates– Elastic collision rate– Three body recombinaison rate

• Long Lifetimes close to resonance

• Evaporation with a<0 (D. Jin) or with a>0 (R. Grimm, W. Ketterle)

= 0.5 s = 20 ms

a = 78 nm a = 35 nm

How to directly detect molecules ?How to directly detect molecules ?

• Low binding energy: It is possible to brake the molecules with a fast magnetic field sweep– When breaking the molecules, some extra energy is released

• High field imaging• RF dissociation of molecules during TOF

– Detection of molecules only

• Increase B during TOF before breaking molecules while going to B=0

Optical trap off Compensation coils off

Pinchcoils off

Detection at low field

0.8 ms

0.2 ms

0.2 ms

Fermion evaporationFermion evaporation

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Opt

ical

den

sity

Position [mm]-0.2 -0.1 0.0 0.1

Position [mm]

Opt

ical

den

sity

-0.3 -0.2 -0.1 0.0 0.1Position [mm]

Opt

ical

den

sity

-0.3 -0.2 -0.1 0.0 0.1Position [mm]

Op

tica

l de

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TG=10.5 K

TF =12 KTG/TF =0.87

TG=3.1 K

TF =5.7 KTG/TF =0.54

TG=1.7 K

TF =3.7 KTG/TF =0.46

TG=1 K

TF =2.5 KTG/TF =0.4

TOF=0.35msN=10^5=4 kHz

TOF=0.35 msN=7.10^4=2.7 kHz

TOF=1 msN=5.10^4=1.6 kHz

TOF=1 msN=5.10^4=1.1 kHz

Double structureDouble structure

-0.2 -0.1 0.0 0.1

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Position [mm]

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Gaussian fit on the wings in X: Tat=0.55 K, Tmol=1.1 K

Gaussian fit in Y: Tat=0.55 K, Tmol=1.1 K

K, for amm=120 nm, and 2 10^3 condensed molecules

Tc=1.2 K for 1.5 10^4 molecules

N=4.5 10^4 atoms=1.1 kHz

2 dimension bimodal fit 2 dimension bimodal fit

No structure in Y direction

Proof of condensationProof of condensation

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position [mm]

Opt

ica

l den

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Y

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Opt

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position [mm]

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Y

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position [mm]

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TOF=0.8 ms (with field)+0.2 ms (B up)+0.2 ms (B off)

Fermions @ 950 GEvaporation to 0.1

Atoms+Mol @ 770 GEvaporation to 0.1 Molecular Fraction>0.5

Atoms +Mol @ 770 GEvaporation to 0.2

Condensates of moleculesCondensates of molecules

• D. Jin (JILA)

• R. Grimm (Innsbruck)• W. Ketterle (MIT)

• ENS

                                                          

  

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Very anisotropic trap @ 770 GVery anisotropic trap @ 770 G

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X [mm]

Y

-0.10 -0.05 0.00 0.05 0.10 0.15X [mm]

Opt

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Evaporation only on verticalFrequencies: 5 kHz, 650 Hz=.5 kHz

Fit: RF=31 m

Calcul: RF=20 m

Evaporation only on horizontalFrequencies: 1.25 kHz, 2.4 kHz=2.0 kHz

Ellipticity study as a fonction of fieldEllipticity study as a fonction of field

750 800 850 900 9500.02

0.03

0.04

Clo

ud s

ize

in X

and

Y [m

m]

Magnetic field (Gauss)

sigmaX sigmaY

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sca

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(nm

)

sc. length

Double structures ?Double structures ?

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-0.2 -0.1 0.0 0.1position [mm]

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Double structures ?Double structures ?

-0.2 -0.1 0.0 0.1

-0.2 -0.1 0.0 0.1

-0.2 -0.1 0.0 0.1position [mm]

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770 G

954 G

874 G

848 G

822 G

808 G

795 G

782 G

770 G

ConclusionsConclusions

• Careful check of the number of remaining atoms• Lifetime of the condensate• Study of the value of Tc• Evaporation toward a pure condensate• Decrease B to lower value, (decrease |a|)• Coming back to the Fermion side

– Ellipticity as a function of degeneracy (a new thermometer)– BCS …

High field imagingHigh field imaging

Which transition are we using ?The detuning is of the order of 400-600 MHz in the region of interest.A double pass AOM at 225 MHz is added on the probe beam.

1.5 10^5atomes

Thermodynamics of atom-molecule mixtureThermodynamics of atom-molecule mixture

• 3 relevant energy scales: Eb, T, , 2 parameters

• Equilibrium:

mol=2 at+|Eb|

Tat = Tmol

Simple Formulas

]]Exp[ PolyLog[3,)(

13

N

]]Exp[ PolyLog[4,)(

33

E

]]Exp[ PolyLog[4,24]]Exp[ ,6PolyLog[4)(

3B

kS

Condensat to be

added when mol=0

0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 100

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0.4

0.6

0.8

1

Thermodynamic resultsThermodynamic results

-8 -6 -4 -2 00.0

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1.0

cond

ensa

te fr

actio

n (d

ashe

d)

Eb [TF

0]

mol

ecul

ar fr

actio

n (s

olid

)

-8 -6 -4 -2 00.0

0.5

1.0

1.5

2.0

TC

Eb [TF

0]

Tem

pera

ture

[TF

0 ]

Eb/T=cst

T/Tc

T/Tc

0

5

10

0

Optical trap transfer problemOptical trap transfer problem

• The three directions of the trap are decoupled in the Hamiltonian:

• With spin polarised fermions, no collision, no adiabatic transformation of the trap possible.

HzHyHxH 222

21

21 xmmvHx xx

Images apres transfer, apres augmentation du champ, apres Ze transfert

Condensat avec a réglableCondensat avec a réglable

Evaporation à a = 2.5 nm en baissant profondeur du piège optique en 250 ms

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dens

ité o

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. arb

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axial distance [mm]

Image en temps de vol:

N =4 10T/TC=0.8

4

Breaking a moleculeBreaking a molecule

• Shift of resonance? Bpeak = 855 +- 53 Gauss unlikely!

• Three-body recombination [D. Petrov, PRA 67, 010703 (2003)]– Molecules form efficiently in highest weakly bound state

2

2

maEB

Molecules can be trapped!

+EB

Binding energy released

EB < Etrap

EB > Etrap

Particles stay in trap

Trap loss

1( ) ( 2 ) exp( / )r r a r a

Notre terrain de jeuxNotre terrain de jeux

E |2,+2>

140 G B

|1 ,-1>

|1,+1>

Lithium bosonique (7Li)

|3/2,+3/2>

|1/2,-1/2>

|1/2,+1/2>

27 G B

Lithium fermionique (6Li)

a = - 1.4 nm = 1 b

{ a = + 2.1 nm6,7

= 1 b{

a = + 0.27 nm = 1/2 b

{ 6,7a = + 2.0 nm = 1/3 b

{ = -1/2 b

{

Le piège dipolaireLe piège dipolaire

Cols ~ 25mFréquences ~ 2.5 kHz

La résonance de FeshbachLa résonance de Feshbach

0 500 1000 1500-3

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-1

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[nm

]

B [Gauss]ÉvaporationGaz idéalLongueur de diffusion a < 0

x

y

z350 m

a b

intkintot l pota E EE E

kr inE E

Images en temps de vol

a) Expansion sans champ

b) Expansion avec champ

Énergie du gaz piégé

intkinrE EE Eint< 0

Mesure du gaz en interactionMesure du gaz en interaction

0.0 0.5 1.0 1.5 2.0

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[nm

]

Magnetic field [kG]

M. Houbiers, H. Stoof, V. Venturi,C. Williams, S. Kokkelmans

a = 0 at 530(3) Gaussmauvaise évaporationUniv.Innsbruck: S. Jochim et al.Duke Univ. O’Hara et al.

Pertes à 680GaussMIT, K. Dieckmann et al.

Résonnance Feshbach très fine à 550 G.

Résonance entre les états: |1/2, +1/2 >, |entre les états: |1/2, +1/2 >, |1/2, -1/2 >1/2, -1/2 >

Résonance entre les états: |1/2, +1/2 >, |entre les états: |1/2, +1/2 >, |1/2, -1/2 >1/2, -1/2 >

0.8 0.9 1.0 1.1 1.2 1.3 1.4

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ry

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auss

ian

size

[m

]

Magnetic field [kG]

a

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B=0Expansion isotrope

B≠0Asymétrie de l’expansion, maximum à B= 800 Gauss

Mélange de fermions préparé à1060 Gauss à T/TF = 0.6105 atoms; a < 0 : no atom loss

Au delà de résonanceAu delà de résonance

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m n

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[10 ]

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[m

]

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a

b

c

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550 600 650 700 750 800 850 900

12345678

550 600 650 700 750 800 850 900

12345678

magnetic field [Gauss]

Mélange préparé à560 Gauss à T/TF=0.67 104 atomes; a > 0 Pertes liées à un chauffage

Perte maximum: 720 Gaussi.e 120 Gauss en dessous de laposition de la résonance prédite!

Chauffage

Le plus anisotrope vers 800 G

La résonance ??La résonance ??

600 700 800 900 1000

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0.6E

int/E

kin

Magnetic field [G]

Effet des molécules ?

Énergie d’interactionÉnergie d’interaction