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Ultra-cold Molecules: Formation, Trapping and Prospects

Ultra-cold Molecules: Formation, Trapping and Prospects. Pierre Pillet Laboratoire Aimé Cotton, CNRS Bât. 505, Campus d’Orsay, 91405 Orsay cedex, France pierre.pillet@lac.u-psud.fr http://www.lac.u-psud.fr. ____________________________________________

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Ultra-cold Molecules: Formation, Trapping and Prospects

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  1. Ultra-cold Molecules:Formation, Trapping and Prospects Pierre Pillet Laboratoire Aimé Cotton, CNRS Bât. 505, Campus d’Orsay, 91405 Orsay cedex, France pierre.pillet@lac.u-psud.fr http://www.lac.u-psud.fr ____________________________________________ 34th EGAS – SOFIA – 9th – 12th July 2002

  2. OUTLINE • Control of a pair of colliding atoms through photoassociation • Schemes for formation of cold ground-state molecules, temperature and formation rate • Trapping and accumulation • Photoassociative spectroscopy • Two-color photoassociation • Feshbach resonance • Conclusion

  3. L A S E R C O O L I N G

  4. F’=5 4 6p3/2 3 2 4 6s F =3 Laser cooling for molecules In molecular systems, lack of closed two-level scheme Laser cooling scheme for Cs atom and Cs2 dimer Because of the large number of ro-vibrational levels, to add repuming lasers is not a reasonable solution. If to extend laser cooling techniques to molecules is not totally impossible, it seems to be actually difficult!

  5. COLD MOLECULES Sympathetic cooling with a He buffer gas in a magnetic trap CaH, 400 mK, 108 molecules; J. Doyle, B. Friedrich, et al., (Harvard), Nature 395, 148 (1998)) Decelerator of polar molecules in a supersonic beam (ND3 , 106 cm-3, 350 mK); G. Meijer et al. (FOM), Nature 406, 491 (2000)

  6. 6p hn ~10 nm 6s ? hn’’ hn’ Dissociation Formation of cold molecules At the frontier of atomic and molecular physics:Use of cold atoms to form cold molecules

  7. C3/R3 C6/R6 Control of a Pair of Colliding Cold Atoms via PhotoassociationCs(6s,F=4)+Cs(6s,F=4)+hnL Cs2*(Wu,g(6s+6p3/2(or 1/2);v,J) level f continuum a • To form an electronically excited molecule in a selected ro-vibrational level • These excited molecules are cold but have a very short life (~ 30 ns) • Mostly they dissociate; the channel to form ground-state molecules is negligible

  8. Theory Fermi golden rule PA rate: Properties of photoassociation of cold atoms (case of a MOT) • COLD ATOMS • Resonant process: Ef(v,J)-2Ei-hnL~kBT~a few MHz • FRANCK-CONDON FACTOR • Excitation at the classical outer turning point (R0): The intensities are proportionnal to (modulation of the intensities of the spectral lines) • Excitation of long-range molecules: Efficiency decrease with v • DETECTION (trap-losses) • The photoassociated molecules dissociate by giving two « hot » atoms which escape outside the cold atomic cloud

  9. Energy (cm-1)

  10. SET-UP

  11. Absolute calibration 150 MHz

  12. Photoassociation Spectra below the 6s+6p3/2 limit Notice the modulation of the line intenities The low v correspond to shortest range excitation at the classical turning point

  13. MOT 1.9 mm 3.8 mm MOT 0.95 mm 1.9 mm 2.85 mm All the vibrational progressions are observed in the fluorescence spectrum Only the 0g- and 1u are observed in the ion spectrum below the 6s+6p3/2 limit Proof for formation of translationally cold ground-state molecules Delay of the pulsed laser Td~10ms>>Tsp~30ns Ballistic expansionand time-of-flight of the falling molecular cloud Tmol~Tat Tmol~20-5+15µK

  14. 0g- and 1u states present Condon points at intermediate distance suitable for bound-bound transition toward the singlet ground-state or the lowest triplet state 0g- excitation leads to the formation of cold molecules in a3Su+ state in vibrational levels in the « middle » of the well. 1u one leads to cold molecules in X1Sg+ state, in levels very close to the dissociation limit. These cases are quite optimum for the formation of cold molecules via photoassociation

  15. Photoassociation Spectra below the 6s+6p1/2 dissociation limit All the vibrationnal progressions are observed The excitation of 0u+ (6s + 6p1/2) permits the formation of cold molecules

  16. LAC 1997 Cs2 LAC 2000 Cs2 Stoors 2000 K2 Schemes of formation of cold molecules via photoassociationPhotoassociation: Cs(6s,F=4)+Cs(6s,F=4)+hnL->Cs2*(Wu,g(6s+6p3/2(or 1/2);v,J)Spontaneous emission and formation of cold molecules: Cs2*(Wu,g(6s1/2+6p3/2;v,J)) ->Cs2 (X1Sg+ or a3Su+ ;v,J) +hnSP 0g- and 1u (6s + 6p3/2) also Rb2 (Pisa) 0u+ (6s + 6p1/2) internal coupling between two states 0u+ (6s+6p1/2 ) and 0u+ (6s+6p3/2 ) with the same symmetry

  17. µB With gravity µA TRAPPING COLD MOLECULES DIPOLE TRAP - Nd:YAG laser does not work for the considered molecules. - CO2 laser is more promising(T. Takekoshi et al. PRL 81, 5105 (1999)Trapping of the cold molecules, present in the MOT. MAGNETIC QUADRUPOLAR TRAPWe can trap the cold molecules in the triplet state with the good magnetic momentum: the momenta of the two atoms are parallel The magnetic field gradient for trapping is comparable for atoms and molecules ~ 3 mT/cm.

  18. Accumulation and trapping in a mixed atomic MOT and molecular quadrupolar trap(magnetic field gradient 6mT/cm) (a)   Scheme : a3Su+ (b)   Trapping in the MOT zone, (b) all the lasers (MOT and PA) off, (b’) only PA laser off (c)    Lifetime: ~0.5 s (d)    Accumulation at 60ms

  19. Spatial analyzis 200 000 molecules at 40 µK

  20. DETECTIONThe photoionisation is a two-photon resonant process via the (2)3Pg vibrational levels correlated to the dissociation limit 6s+5d (REMPI)

  21. PA laser on At 14 cm-1 trap losses: 23 % MOT on Rate for photoassociation (case 0u+) Dynamic trap eq.: Measured photoassociation rates: bPAnat~ 0.1 – 5 s-1/atom The number of cold molecules is given by the branching ratio between bound-bound and bound-free molecular transition

  22. Rate for formation of cold molecules (case 0g-) Direct measurement The branching ratio for bound-bound transitions towards the ground state is 0.9 RATECM (v=6, 140 W/cm2, nat ~ 5 1010) = 0,06 s-1/atom ~106 molecules/s with 5 107 atoms

  23. Formation rate of cold molecules (a) Calculated branching ratios 0g- (6s+6p3/2), 0g- (6s+6p1/2) (b) Expected formation rates T = 140 µK, n = 1011 cm-3, I = 55 W.cm-2 0.1 molecule per atom and per second  Rate ~ a few 106 molecules per second Computed phototoassossiated rates (a) 0g-, (b) 0u+ (6s+6p3/2),(6s+6p1/2) T = 140 µK, n = 1011 cm-3, I = 55 W.cm-2

  24. FIRST CONCLUSION • A way for formation of ultra-cold ground-state molecules; a rate of 0.2 molecules per atom and per second, at 10-100 µK. For increasing the rate, increase the atomic density. • Others ways: sympathetic cooling, Stark decelerator. • Trapping: ~ 104-6 molecules at a temperature of a few 10 µK. • The use of a dipole CO2 laser trap is promising. • Role of the sensitivity of the REMPI detection (photoionization + time-of-flight). • FEW MORE WORDS • Photoassociative spectroscopy • Two color photoassociation • Use of Feshbach resonance

  25. 1u long-range molecules: at the frontier of atomic and molecular physics Adiabatic asymptotic potential including fine et hyperfine structure The exchange terms are negligible V=1 With the rotation s, p, d and f-waves Eur. Phys. J. D11, 59 (2000).

  26. The long-range spectroscopy permits to determine asymptotic long-range coefficients C3 (proportional to the atomic dipole) of the potential curves The case of the 0g- (6s+6p3/2) has so permitted to give a value for the atomic lifetime Cs(6p3/2): t=30.462+/-0.003 ns (R. Gutteres, C. Amiot, O. Dulieu, F. Masnou-Seeuws) to compare with experimental values: t=30.41(10) ns (Young et al) and t=30.50(7) ns (Rafac et al) At the frontier of the atomic and molecular physics: we use cold atoms to do molecular spectroscopy and then to determine atomic parameters

  27. TWO-COLOR PHOTOASSOCIATION J=0 2 4 Frustration of PA dark resonances Stimulated Raman PA Preparation of cold molecules in a well-defined level? Lifetime of 2: t2=t1(D/W122) Fano profiles (interference) G -L1->1 -SP-> F G -L1-> 1 -L2-> 2 -L1-> 1 -SP-> F

  28. CONTROL OF THE FORMATION OF MOLECULES THROUGH A FESCHBACH RESONANCE Cs(6s,F=3,m=3)+Cs(6s,F=3,m=3)+hnLCs2*(0g-(6s+6p3/2);v,J) v=6, J=0 and 2 Due to the Feshbach resonance, we observe an increasing of the PA rate for v<30, corresponding to an excitation at the external turning point R0< 38 a0.

  29. CONCLUSION • Applications: Molecule optics and molecule interferometry, molecule lithography, metrology, high precision measurement… • Bose-Einstein condensation of a molecular gas, molecule laser…, ensemble of ultacold dipoles, BCS… • Starting with an atomic condensate: Interest for Stimulated Raman Phototassociation (Rb2, Li2) and for Feshbach Resonance (Rb2) • Case of Cs BEC: Mixed magnetic and dipolar trap for F=3, m=3 level – LAC and Innsbruck • (R. Grimm) – in progress • - Ultra-cold photochemistry: to form more complex cold molecules? (heteronuclear dimers of alkalines, trimers)…

  30. LAC Team • Experiments:Daniel Comparat, Samuel Guibal,P.P.,Christian Lisdat, Nicolas Vanhaecke, Salah Boussen, Nathalie Hoang, Wilson de Melo Souza, Andrea Fioretti (Pisa),Cyril Drag (2000), Bruno Laburthe Tolra (2001) • Theory:Françoise Masnou-Seeuws, Olivier Dulieu,Anne Crubellier, Claude Amiot,Philippe Pellegrini, Benoît T ’Jampens,Kai Willner, Pascal Naidon, Claude Dion, Ricardo Gutteres,Mihaëla Vatacescu (1999), Viatcheslav Kokoouline (1999)

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