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

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

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 ? 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

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

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

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

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

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 1.5 10^4 molecules

2 dimension bimodal fit No structure in Y direction

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

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

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

Ellipticity study as a fonction of field

Double structures ?

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

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 …

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 10^5 atomes

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

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

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

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

Breaking a molecule Molecules can be trapped! Binding energy released 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 Molecules can be trapped! Binding energy released +EB EB < Etrap Particles stay in trap EB > Etrap Trap loss

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

Le piège dipolaire Cols ~ 25mm Fréquences ~ 2.5 kHz

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

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

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.

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

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!

Énergie d’interaction Effet des molécules ?