1. 1- Introduction, overview 2- Hamiltonian of a diatomic molecule 3- Molecular symmetries; Hund’s cases 4- Molecular spectroscopy 5- Photoassociation of cold atoms 6- Ultracold (elastic) collisions Olivier Dulieu Predoc’ school, Les Houches,september 2004

2. How to create ultracold molecules using laser cooling? Laser cooling of molecules: NO closed level-scheme Laser cooling of atoms: closed level-scheme

3. One proposal Based on the development of a Multiple Single Frequency Laser Sequential cooling on electronic transitions: R,T,V Simulation on Cs 2 B 1  u  X, with chirped frequencies

4. One proposal Based on the development of a Multiple Single Frequency Laser Sequential cooling on electronic transitions: R,T,V Simulation on Cs 2 B 1  u  X, with chirped frequencies

5. One proposal Based on the development of a Multiple Single Frequency Laser Sequential cooling on electronic transitions: R,T,V Simulation on Cs 2 B 1  u  X, with chirped frequencies

6. One exception? Direct laser cooling of BeH, CaH, at Los Alamos Alkaline-earth hydrides have Rydberg transitions similar to the D1, D2 lines in alkali atoms (good spectral isolation), with almost diagonal FC factors matrix (99%) BeH: theoretical benchmark for open-shell molecules CaH/CaD: degenerate quantum gases

7. One Solution: cold atom photoassociation Ultracold molecule!! First discussion

8. First steps

9. First observations Ultracold molecule!!

10. First reviews

11. PA well-known at thermal energies: diffuse bands From Stwalley&Wang, J. Mol. Spectrosc. 195, 194 (1999)

14. PA at ultracold energies Free-bound transition = quasibound-bound transition detuning Energy balance 200 cm -1 @300K 10 -4 cm -1 @100  K Ultracold Excited Short-lived molecules

15. Stwalley&Wang, J. Mol. Spectrosc. 195, 194 (1999)

16. PAS of cold Cs Trap loss REMPI

17. Detection of PA REMPI TRAP LOSS Ultracold molecules Ex: Cs Ex:Na

18. 11 years of PA observations (1993-2004) Li 2 : Hulet (Rice,US), Zimmerman (Tübingen, D) Na 2 : Lett (NIST, US), VanderStraten (Utrecht, NL) K 2 : Gould, Stwalley (Storrs, US) Rb 2 : Heinzen (Austin, US), Gabbanini (Pisa, I) Cs 2 : Pillet (Orsay, F), Stwalley (Storrs, US) H 2 : Walraven (Amsterdam, NL) He 2 : Leduc, Cohen-Tannoudji (Paris, F) Ca 2 : Tiemann, Riehle (Hannover/Braunschweig, D) Yb 2 : (Tokyo, JP) RbCs: DeMille (Yale, US) KRb: Marcassa, Bagnato (São Carlos, BR), Stwalley (Storrs, US) NaCs: Bigelow (Rochester, US) Sr 2 : (Boulder, US) In progress: LiCs (Freiburg, D)…. Also: PA in condensates

19. PA: Probe of the long-range part of molecular potentials

20. Long-range interactions between neutral atoms Multipolar expansion (in 1/R) of electrostatic interaction: Stwalley&Wang, J. Mol. Spectrosc. 195, 194 (1999)

21. Le Roy-Bernstein approach How to make the link between observed transitions and long-range behavior of the potential? LeRoy&Bernstein, J. Chem.Phys. 52, 3869 (1970) (fractional) vibrational quantum number at the dissociation limit -No solution for n=2 -Limited to a single potential -Rotation (  1/R 2 ) not included

22. Accumulated phase method: Numerical approach for higher flexibility Moerdjik et al, PRA 51, 4852 (1995) Crubellier etal, Eur. Phys. J. D, 6, 211 (1999) Almost constant phase  (R 0 ) at this point R 0 for all upper lying vibrational levels If: -A single level is known -The asymptotic potential is known Inward integration of the Schrödinger equation down to R 0, with limit condition on the logarithmic derivative of  (R 0 ) Fitting strategy: Parameters: Scattering length

23. Pure long-range molecules (1)

24. Pure long-range molecules (2) R -3 R -3 R -6, R -8 Quantum chemistry Spies, 1989 R -3 R -6, R -8 +exchange

25. The 0 g - pure long-range state (1)

26. Hund’s case (a) representation The 0 g - pure long-range state (2) At large distances: -Atomic spin-orbit X X X -Asymptotic expansion of V

27. The 0 g - pure long-range state (3) Hund’s case (c) representation Diagonalization of the spin-orbit matrix Flat potential  1/R 6 Attractive potential  1/R 3 interaction  1/R 3

28. attractive The 0 g - pure long-range state (4) repulsive Potential well

29. PAS spectrum: 75 vibrational levels, J=2 Direct Potential Fit approach: PAS of the 0 g - pure long-range state in Cs 2 (1) Amiot et al, PRA 66, 052506(2002) 9 Fitting parameters minimization

30. PAS of the 0 g - pure long-range state in Cs 2 (2) RKR asymptotic Quantum chemistry

31. Atomic radiative lifetime from PAS Amiot et al, PRA 66, 052506(2002) Non-relativistic

32. Cold molecule formation processes Main requirement: stabilization of the excited population in a bound state Solution: « R »-transfer of the probability density Double-well case Observed in: Cs 2, Rb 2 Resonant coupling Observed in: Cs 2, RbCs,KRb « not efficient » case Observed in: Na 2, K 2, KRb, NaCs

33. Double-well process in Cs 2 PA SE REMPI

34. PA and cold molecule formation in Cs 2

35. REMPI spectra Varying the PA laser frequency Varying the REMPI laser frequency Dion et al, EPJD 18, 365 (2002)

36. Predicted vibrational population in the lowest 3  u + state, after decay of 0 g - PA levels in Cs 2 Detuning of the 0 g - PA level Vibrational level Of the a 3  u + state

37. Resonant coupling process (1) C. M. Dion et al, PRL 86, 2253 (2001)

38. Resonant coupling process (2)

39. Next resonance Resonant coupling process (3)

40. PA rates, shifts, line shapes: references (non exhaustive) Thorsheim et al, PRL 58, 2420 (1987) Napolitano et al, PRA 73, 1352 (1994) Julienne, J. Research NIST 101, 487 (1996) Pillet et al, JPB 30, 2801 (1997) Côté & Dalgarno, PRA 58, 498 (1998) Javanainen & Mackie, PRA 58, R789 (1998) Bohn& Julienne, PRA 60, 414 (1999) Mackie & Javanainen, PRA 60, 3174 (1999) Jones et al, PRA 61, 012501 (1999) Drag et al, IEEE J. Quantum Electronics 36, 1378 (2001) Montalvão & Napolitano, PRA 64, 011403(R) (2001) C. M. Dion et al, PRL 86, 2253 (2001) Dion et al, EPJD 18, 365 (2002) Simoni et al, PRA 66, 063406 (2002)

41. A short tutorial on Feshbach resonances Resonance: a bound state embedded in a continuum Shape resonance, Feshbach resonance Collision in channel i with a resonance

42. Tuning the scattering length Moerdjik et al,PRA 51, 4852 (1995)

44. Bibliography « Interactions in ultracold gases: from atoms to molecules », ed. by M. Weidemüller and C. Zimmermann, Wiley VCH (2003); nice collection of tutorials and research papers from a workshop and training school held in Heidelberg in 2002, in the framework of the EU Network « Cold Molecules » J.T. Bahns, P.L. Gould, W.C. Stwalley, Adv. At. Mol. Opt. Physics 42, 171 (2000) F. Masnou-Seeuws, P. Pillet, Adv. At. Mol. Opt. Physics 47, 53 (2001) O. Dulieu, F. Masnou-Seeuws, JOSA B, (2003)