Condensate of Fermionic Lithium Dimers

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Condensate of Fermionic Lithium Dimers
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
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Outline

• 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

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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

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How to detect dimer formation ?
For the probe laser to be on resonance, the
magnetic field needs to be turned off. The
unbrocken dimers are not detected.
Double ramp method
Importance of the ramp speed Adiabaticity
Ancienne figure
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Temperature effects
The cooler, the more molecules, Independant of
ramp speed
The molecules are likely to be in thermal and
chemical equilibrium with the atoms
Creating molecules is heating
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Evaporative cooling to condensation ?

• Very high collision rates
• Elastic collision rate
• Three body recombinaison rate
• Long Lifetimes close to resonance
• Evaporation with alt0 (D. Jin)
• or with agt0 (R. Grimm, W. Ketterle)

t 0.5 s
t 20 ms
a 78 nm
a 35 nm
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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 B0

Detection at low field
Compensation coils off
Optical trap off
0.2 ms
0.2 ms
Pinch coils off
0.8 ms
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Fermion evaporation
TOF0.35ms N105 w4 kHz
TOF0.35 ms N7.104 w2.7 kHz
TOF1 ms N5.104 w1.6 kHz
TOF1 ms N5.104 w1.1 kHz
TG10.5 mK TF 12 mK TG/TF 0.87
TG3.1 mK TF 5.7 mK TG/TF 0.54
TG1.7 mK TF 3.7 mK TG/TF 0.46
TG1 mK TF 2.5 mK TG/TF 0.4
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Double structure
N4.5 104 atoms w1.1 kHz
Gaussian fit on the wings in X Tat0.55 mK,
Tmol1.1 mK Gaussian fit in Y Tat0.55 mK,
Tmol1.1 mK m1.4 mK, for amm120 nm, and 2 103
condensed molecules Tc1.2 mK for 1.5 104
molecules
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2 dimension bimodal fit
No structure in Y direction
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Proof of condensation
TOF0.8 ms (with field)0.2 ms (B up)0.2 ms (B
off)
Fermions _at_ 950 G Evaporation to 0.1
AtomsMol _at_ 770 G Evaporation to 0.1 Molecular
Fractiongt0.5
Atoms Mol _at_ 770 G Evaporation to 0.2
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Condensates of molecules

• D. Jin (JILA)
• R. Grimm (Innsbruck)
• W. Ketterle (MIT)
• ENS

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Very anisotropic trap _at_ 770 G
Evaporation only on vertical Frequencies 5 kHz,
650 Hz w2p2.5 kHz Fit RF31 mm Calcul RF20
mm
Evaporation only on horizontal Frequencies 1.25
kHz, 2.4 kHz w2.0 kHz
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Ellipticity study as a fonction of field
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Double structures ?
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Double structures ?
795 G
770 G
848 G
874 G
808 G
770 G
954 G
822 G
782 G
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Conclusions

• 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

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High 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.
1.5 105 atomes
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Thermodynamics of atom-molecule mixture

• 3 relevant energy scales Eb, T, m , 2 parameters
• Equilibrium
• mmol2 matEb
• Tat Tmol
• Simple Formulas

Condensat to be added when mmol0
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Thermodynamic results
Eb/Tcst
5
0
T/Tc
10
0
T/Tc
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Optical 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.

Images apres transfer, apres augmentation du
champ, apres Ze transfert
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Condensat avec a réglable
Evaporation à a 2.5 nm en baissant profondeur
du piège optique en 250 ms
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Breaking 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

Binding energy released
Molecules can be trapped!
EB
EB lt Etrap
Particles stay in trap
EB gt Etrap
Trap loss
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Notre terrain de jeux
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Le piège dipolaire
Cols 25mm Fréquences 2.5 kHz
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La résonance de Feshbach
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Mesure du gaz en interaction
Énergie du gaz piégé

• Images en temps de vol
• Expansion sans champ
• b) Expansion avec champ

Eintlt 0
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Résonance entre les états 1/2, 1/2 gt, 1/2,
-1/2 gt
M. Houbiers, H. Stoof, V. Venturi, C. Williams,
S. Kokkelmans
a 0 at 530(3) Gauss mauvaise évaporation Univ.In
nsbruck S. Jochim et al. Duke Univ. OHara et
al. Pertes à 680Gauss MIT, K. Dieckmann et
al. Résonnance Feshbach très fine à 550 G.
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Au delà de résonance
Mélange de fermions préparé à 1060 Gauss à T/TF
0.6 105 atoms a lt 0 no atom loss
B0 Expansion isotrope
B?0 Asymétrie de lexpansion, maximum à B 800
Gauss
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La résonance ??
Chauffage
Mélange préparé à 560 Gauss à T/TF0.6 7 104
atomes a gt 0 Pertes liées à un chauffage
Le plus anisotrope vers 800 G
Perte maximum 720 Gauss i.e 120 Gauss en dessous
de la position de la résonance prédite!
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Énergie dinteraction
Effet des molécules ?