Condensate of Fermionic Lithium Dimers

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1 Condensate of Fermionic Lithium Dimers
Collège de France 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

2 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

3 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

4 How to detect dimer formation ?
1,3 2 4 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 : a>0 a<0 Importance of the ramp speed Adiabaticity: Ancienne figure

5 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

6 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) t = 0.5 s t = 20 ms a = 78 nm a = 35 nm

7 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 Detection at low field Compensation coils off Optical trap off 0.2 ms 0.2 ms 0.8 ms Pinch coils off

8 Fermion evaporation TOF=0.35ms N=10^5 w=4 kHz TOF=0.35 ms N=7.10^4
TG=10.5 mK TF =12 mK TG/TF =0.87 TG=3.1 mK TF =5.7 mK TG/TF =0.54 TG=1.7 mK TF =3.7 mK TG/TF =0.46 TG=1 mK TF =2.5 mK TG/TF =0.4

9 m=1.4 mK, for amm=120 nm, and 2 10^3 condensed molecules
Double structure N=4.5 10^4 atoms w=1.1 kHz Gaussian fit on the wings in X: Tat=0.55 mK, Tmol=1.1 mK Gaussian fit in Y: Tat=0.55 mK, Tmol=1.1 mK m=1.4 mK, for amm=120 nm, and 2 10^3 condensed molecules Tc=1.2 mK for ^4 molecules

10 2 dimension bimodal fit No structure in Y direction

11 Proof of condensation TOF=0.8 ms (with field)+0.2 ms (B up)+0.2 ms (B off) 950 G Evaporation to 0.1 770 G Evaporation to 0.1 Molecular Fraction>0.5 Atoms 770 G Evaporation to 0.2

12 Condensates of molecules
D. Jin (JILA) R. Grimm (Innsbruck) W. Ketterle (MIT) ENS                                                             

13 Very anisotropic trap @ 770 G
Evaporation only on vertical Frequencies: 5 kHz, 650 Hz w=2p*2.5 kHz Fit: RF=31 mm Calcul: RF=20 mm Evaporation only on horizontal Frequencies: 1.25 kHz, 2.4 kHz w=2.0 kHz

14 Ellipticity study as a fonction of field

15 Double structures ?

16 Double structures ? 795 G 770 G 848 G 808 G 874 G 770 G 782 G 822 G

17 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 …

18 High field imaging Which transition are we using ?
The detuning is of the order of MHz in the region of interest. A double pass AOM at 225 MHz is added on the probe beam. 1.5 10^5 atomes

19 Thermodynamics of atom-molecule mixture
3 relevant energy scales: Eb, T, m , 2 parameters Equilibrium: mmol=2 mat+|Eb| Tat = Tmol Simple Formulas Condensat to be added when mmol=0

20 Thermodynamic results
Eb/T=cst 5 T/Tc 10 T/Tc

21 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

22 Condensat avec a réglable
Evaporation à a = 2.5 nm en baissant profondeur du piège optique en 250 ms Image en temps de vol: N =4 10 T/TC=0.8 4

23 Breaking a molecule Molecules can be trapped! Binding energy released
Shift of resonance? Bpeak = Gauss unlikely! Three-body recombination [D. Petrov, PRA 67, (2003)] Molecules form efficiently in highest weakly bound state Molecules can be trapped! Binding energy released +EB EB < Etrap Particles stay in trap EB > Etrap Trap loss

24 Notre terrain de jeux Lithium bosonique (7Li)
Lithium fermionique (6Li)

25 Le piège dipolaire Cols ~ 25mm Fréquences ~ 2.5 kHz

26 La résonance de Feshbach
Évaporation Gaz idéal Longueur de diffusion a < 0

27 Mesure du gaz en interaction
Énergie du gaz piégé Images en temps de vol Expansion sans champ b) Expansion avec champ Eint< 0

28 Résonance entre les états: |1/2, +1/2 >, |1/2, -1/2 >
M. Houbiers, H. Stoof, V. Venturi, C. Williams, S. Kokkelmans a = 0 at 530(3) Gauss mauvaise évaporation Univ.Innsbruck: S. Jochim et al. Duke Univ. O’Hara et al. Pertes à 680Gauss MIT, K. Dieckmann et al. Résonnance Feshbach très fine à 550 G.

29 Au delà de résonance Mélange de fermions préparé à
1060 Gauss à T/TF = 0.6 105 atoms; a < 0 : no atom loss B=0 Expansion isotrope B≠0 Asymétrie de l’expansion, maximum à B= 800 Gauss

30 La résonance ?? Chauffage Mélange préparé à 560 Gauss à T/TF=0.6
7 104 atomes; a > 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!

31 Énergie d’interaction
Effet des molécules ?