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1- Introduction, overview 2- Hamiltonian of a diatomic molecule

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.

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1- Introduction, overview 2- Hamiltonian of a diatomic molecule

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  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 Cs2 B1Pu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 Cs2 B1Pu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 Cs2 B1Pu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 First discussion Ultracold molecule!!

  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)

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

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

  14. PAS of cold Cs Trap loss REMPI

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

  16. 11 years of PA observations (1993-2004) • Li2: Hulet (Rice,US), Zimmerman (Tübingen, D) • Na2: Lett(NIST, US), VanderStraten (Utrecht, NL) • K2: Gould, Stwalley (Storrs, US) • Rb2: Heinzen (Austin, US), Gabbanini (Pisa, I) • Cs2: Pillet (Orsay, F), Stwalley (Storrs, US) • H2: Walraven (Amsterdam, NL) • He2: Leduc, Cohen-Tannoudji (Paris, F) • Ca2: Tiemann, Riehle (Hannover/Braunschweig, D) • Yb2: (Tokyo, JP) • RbCs: DeMille (Yale, US) • KRb: Marcassa, Bagnato (São Carlos, BR), Stwalley (Storrs, US) • NaCs: Bigelow (Rochester, US) • Sr2: (Boulder, US) • In progress: LiCs (Freiburg, D)…. • Also: PA in condensates

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

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

  19. Le Roy-Bernstein approach LeRoy&Bernstein, J. Chem.Phys. 52, 3869 (1970) How to make the link between observed transitions and long-range behavior of the potential? (fractional) vibrational quantum number at the dissociation limit • No solution for n=2 • Limited to a single potential • Rotation (1/R2) not included

  20. Accumulated phase method: Numerical approach for higher flexibility Almost constant phase F(R0) at this point R0 for all upper lying vibrational levels Moerdjik et al, PRA 51, 4852 (1995) • If: • A single level is known • The asymptotic potential is known Inward integration of the Schrödinger equation down to R0, with limit condition on the logarithmic derivative ofF(R0) Fitting strategy: Parameters: Scattering length Crubellier etal, Eur. Phys. J. D, 6, 211 (1999)

  21. Pure long-range molecules (1)

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

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

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

  25. The 0g- pure long-range state (3) Diagonalization of the spin-orbit matrix Hund’s case (c) representation Attractive potential 1/R3 interaction 1/R3 Flat potential 1/R6

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

  27. PAS of the 0g- pure long-range state in Cs2 (1) Amiot et al, PRA 66, 052506(2002) • PAS spectrum: 75 vibrational levels, J=2 • Direct Potential Fit approach: • 9 Fitting parameters • minimization

  28. PAS of the 0g- pure long-range state in Cs2 (2) asymptotic RKR Quantum chemistry

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

  30. Cold molecule formation processes • Main requirement: stabilization of the excited population in a bound state • Solution: « R »-transfer of the probability density « not efficient » case Observed in: Na2, K2, KRb, NaCs Resonant coupling Observed in: Cs2, RbCs,KRb Double-well case Observed in: Cs2, Rb2

  31. Double-well process in Cs2 REMPI PA SE

  32. PA and cold molecule formation in Cs2

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

  34. Predicted vibrational population in the lowest 3Su+ state, after decay of 0g- PA levels in Cs2 Vibrational level Of the a3Su+ state Detuning of the 0g- PA level

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

  36. Resonant coupling process (2)

  37. Resonant coupling process (3) Next resonance

  38. 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)

  39. 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

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

  41. 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)

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