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Thomas Bourdel, Julien Cubizolles, Lev Khaykovich, Frédéric Chevy, Jing Zhang, Martin Teichmann, Servaas Kokkelmans, Christophe Salomon Laboratoire Kastler.

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Présentation au sujet: "Thomas Bourdel, Julien Cubizolles, Lev Khaykovich, Frédéric Chevy, Jing Zhang, Martin Teichmann, Servaas Kokkelmans, Christophe Salomon Laboratoire Kastler."— Transcription de la présentation:

1 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 Dimers

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 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. Importance of the ramp speed Adiabaticity: Ancienne figure a>0 a<0

5 Temperature 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

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)  = 0.5 s  = 20 ms a = 78 nma = 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 Optical trap off Compensation coils off Pinch coils off Detection at low field 0.8 ms 0.2 ms

8 Fermion evaporation T G =10.5  K T F =12  K T G /T F =0.87 T G =3.1  K T F =5.7  K T G /T F =0.54 T G =1.7  K T F =3.7  K T G /T F =0.46 T G =1  K T F =2.5  K T G /T F =0.4 TOF=0.35ms N=10^5  =4 kHz TOF=0.35 ms N=7.10^4  =2.7 kHz TOF=1 ms N=5.10^4  =1.6 kHz TOF=1 ms N=5.10^4  =1.1 kHz

9 Double structure Gaussian fit on the wings in X: T at =0.55  K, T mol =1.1  K Gaussian fit in Y: T at =0.55  K, T mol =1.1  K    K, for a mm =120 nm, and 2 10^3 condensed molecules Tc=1.2  K for ^4 molecules N=4.5 10^4 atoms  =1.1 kHz

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 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 770 G Evaporation only on vertical Frequencies: 5 kHz, 650 Hz  = .5 kHz Fit: RF=31  m Calcul: RF=20  m Evaporation only on horizontal Frequencies: 1.25 kHz, 2.4 kHz  =2.0 kHz

14 Ellipticity study as a fonction of field

15 Double structures ?

16 770 G 954 G 874 G 848 G 822 G 808 G 795 G 782 G 770 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 ^5 atomes

19 Thermodynamics of atom-molecule mixture 3 relevant energy scales: Eb, T, , 2 parameters Equilibrium:   mol =2  at +|Eb| T at = T mol Simple Formulas Condensat to be added when  mol =0

20 Thermodynamic results Eb/T=cst 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/T C =0.8 4

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

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

25 Le piège dipolaire Cols ~ 25  m Fréquences ~ 2.5 kHz

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

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

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

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

30 Mélange préparé à 560 Gauss à T/T F = atomes; a > 0 Pertes liées à un chauffage Perte maximum: 720 Gauss i.e 120 Gauss en dessous de la position de la résonance prédite! Chauffage Le plus anisotrope vers 800 G La résonance ??

31 Effet des molécules ? Énergie d’interaction


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