1. Hyperfine-Changing Collisions of Cold Molecules J. Aldegunde, Piotr Żuchowski and Jeremy M. Hutson University of Durham EuroQUAM meeting Durham 18th April 2009 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A AAA A AAAA A A A AAAAA A A A A A A A

2. Contents 1.Hyperfine molecular levels (QUDIPMOL). 2.Hyperfine changing collisions (CoPoMol).

3. Fine and hyperfine structure Hyperfine molecular levels Atomic physics: Gross spectra: the spectra predicted by considering non- relativistic electrons and neglecting the effect of the spin. Fine structure: energy shifts and spectral lines splittings due to relativistic corrections (including the interaction of the electronic spin with the orbital angular momentum). Hyperfine structure: energy shifts and splittings due to the interaction of the nuclear spin with the rest of the system. This classification can be extended into the molecular realm. Molecular fine and hyperfine levels Stability. Bose-Einstein condensate formation. Gross structure >> Fine structure >> Hyperfine structure

4. Atomic hyperfine structure Hyperfine splitting ≈ GHz ≈ 10 -1 K S → Electronic spin L → Orbital angular momentum I → Nuclear spin Alkali atoms → L =0, S =1/2 F=S+I Ĥ hf = A I Rb ∙ S Rb Hyperfine molecular levels Ĥ z = g s μ B B∙S Rb - g Rb μ N B∙I Rb

5. 1 Σ diatomic molecules 1 Σ molecules 7 Li 133 Cs ( M. Weidemüller (Freiburg)) 133 Cs 2 (Hanns-Christoph Nägerl (Innsbruck)) 40 K 87 Rb (Jun Ye, D. Jin (JILA)) S =0 (no fine structure) Two sources of angular momentum: N → Rotational angular momentum (L in atom-atom collisions). I 1, I 2 → Nuclear spins of nucleus 1 and 2. Hyperfine molecular levels

6. 1 Σ diatomic molecules Hyperfine molecular levels

7. 1 Σ diatomic molecules Hyperfine molecular levels

8. 1 Σ diatomic molecules Hyperfine molecular levels

9. 1 Σ diatomic molecules Hyperfine molecular levels

10. 1 Σ diatomic molecules Hyperfine molecular levels

11. 1 Σ diatomic molecules Hyperfine molecular levels

12. 1 Σ(N=0) diatomic molecules. Zero field splittings. Zero field splittings dominated by the scalar spin-spin interaction (c 4 I 1 ·I 2 ). c 4 ( 133 Cs 2 ) ≈ 13 kHzc 4 ( 40 K 87 Rb) ≈ -2 kHz Hyperfine splitting ≈ tens to hundreds of kHz ≈ 1 to 10 μK Hyperfine molecular levels

13. 1 Σ (N≠0) diatomic molecules. Zero field splittings. The ratio |c 4 /(eQq)| ratio determines the zero field splitting partner: Large |c 4 /(eQq)| values → the splitting is determined by the scalar spin- spin Interaction and coincides with that for N=0. Small |c 4 /(eQq)| values → the splitting is determined by the electric quadrupole interaction. eQq( 85 Rb 2 ) ≈ 2 MHz 85 Rb 2 (N=1) Hyperfine splitting ≈ hundreds to thousands of kHZ ≈ 10 to 100 μK Hyperfine molecular levels

14. 1 Σ diatomic molecules. Zeeman splitting. (2 I +1) components ( N =0). Each level splits into (2 F +1) components ( N ≠0). The slope of the energy levels and the corresponding splittings are determined by the nuclear g-factors. Hyperfine molecular levels

15. 1 Σ diatomic molecules. Zeeman splitting. Energy levels with the same value of M I display avoided crossings (the red lines correspond to M I =-3) I remains a good quantum number for values of the magnetic field below those for which the avoided crossings appear. For large values of the magnetic field the individual projections of the nuclear spins become good quantum numbers.

16. Hyperfine molecular levels 1 Σ diatomic molecules. Zeeman splitting. Energy levels with the same value of M I display avoided crossings (the red lines correspond to M I =-3) I remains a good quantum number for values of the magnetic field below those for which the avoided crossings appear. For large values of the magnetic field the individual projections of the nuclear spins become good quantum numbers.

17. 1 Σ diatomic molecules. Stark splitting. Hyperfine molecular levels Mixing between rotational levels is very important and increases with the electric field. The number of rotational levels required for convergence becomes larger with field. For the levels correlating with N=0, the Stark effect is quadratic at low fields and becomes linear at high fields.

18. 1 Σ diatomic molecules. Stark splitting. Hyperfine molecular levels Energy levels correlating with N =0 referred to their field-dependent average value: Each level splits into I +1 components labelled by | M I |. At large fields the splitting approach a limiting value and the individual projections of the nuclear spins become well defined.

19. Hyperfine changing collisions Rb + OH( 2 Π 3/2 ) collisions Rb + OH( 2 Π 3/2 ) M.Lara et al studied these collisions (Phys. Rev. A 75, 012704 (2007)). Rb, OH or both of them undergo fast collisions into high-field-seeking states. Sympathetic cooling is not going to work unless both species are trapped in their absolute ground states.

20. Hyperfine changing collisions Cs + Cs collisions

21. Hyperfine changing collisions

22. Rb + CO( 1 Σ) collisions Hyperfine changing collisions

23. Rb + CO( 1 Σ) collisions Hyperfine changing collisions

24. Rb + CO( 1 Σ) collisions Hyperfine changing collisions

25. Rb + ND 3 collisions Hyperfine changing collisions

26. Rb + ND 3 collisions Hyperfine changing collisions

27. Rb + ND 3 collisions Hyperfine changing collisions

28. Conclusions The rotational levels of 1 Σ alkali metal dimers split into many hyperfine components. For nonrotating states, the zero-field splitting is due to the scalar spin-spin interaction and amounts to a few μK. For N≠1 dimers, the zero-field splitting is dominated by the electric quadrupole interaction and amounts to a few tens of μK. External fields cause additional splittings and can produce avoided crossings. For molecules in closed shell single states colliding with alkali atoms, the atomic spin degrees of freedom are almost independent of the molecular degrees of freedom and the collisions will not change the atomic state even if the potential is highly anisotropic. Prospects for sympathetic cooling of ND 3 /NH 3 molecules with cold Rb atoms: 1.Poor for ND 3 /NH 3 low-field-seeking states. 2.Good for ND 3 /NH 3 high-field-seeking states. ND 3 better than NH 3. Quantitative calculations are necessary.

30. Hyperfine changing collisions Rb + OH( 2 Π 3/2 ) collisions M. Lara et al, Phys. Rev. A 75, 012704 (2007)

31. Hyperfine changing collisions Rb + OH( 2 Π 3/2 ) collisions

32. Conclusions Molecular energy levels split into many fine and hyperfine components. 1 Σ alkali dimers only display hyperfine splittings. For nonrotating states, the zero-field splitting is due to the scalar spin-spin interaction and amounts to a few μK. For N≠1 dimers, the zero-field splitting is dominated by the electric quadrupole interaction and amounts to a few tens of μK. Except for short range terms, the system Hamiltonian for collisions between 2 s atoms and singlet molecules can be factorised. The collisions will not cause fast atomic inelasticity. This factorization will not be possible when the 2 s atoms collides with doublet or triplet molecules. In this case, the potential operator will drive fast atomic Inelastic collisions. Prospects for sympathetic cooling of ND 3 /NH 3 molecules with cold Rb atoms: 1.Poor for ND 3 /NH 3 low-field-seeking states. 2.Good for ND 3 /NH 3 high-field-seeking states. ND 3 better than NH 3. Quantitative calculations are necessary.