Hyperfine-Changing Collisions of Cold Molecules

1. Hyperfine-Changing Collisions of Cold Molecules J. Aldegunde, PiotrŻuchowski and Jeremy M. HutsonUniversity of Durham EuroQUAM meetingDurham18th April 2009 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAAAAAAAAAAAA

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

3. 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. Fine and hyperfine structure Gross structure >> Fine structure >> Hyperfine structure This classification can be extended into the molecular realm. • Stability. • Bose-Einstein condensate formation. Molecular fine and hyperfine levels

4. Hyperfine molecular levels S → Electronic spin L → Orbital angular momentum I → Nuclear spin Alkali atoms → L=0, S=1/2 Atomic hyperfine structure F=S+I Ĥhf= A IRb ∙ SRb Ĥz=gsμBB∙SRb- gRbμNB∙IRb Hyperfine splitting ≈ GHz ≈ 10-1 K

5. Hyperfine molecular levels 7Li133Cs ( M. Weidemüller (Freiburg)) 133Cs2 (Hanns-ChristophNägerl (Innsbruck)) 40K87Rb (Jun Ye, D. Jin (JILA)) 1Σ molecules 1Σ diatomic molecules • S=0 (no fine structure) • Two sources of angular momentum: • N → Rotational angular momentum (L in atom-atom collisions). • I1, I2 → Nuclear spins of nucleus 1 and 2.

6. Hyperfine molecular levels 1Σ diatomic molecules

7. Hyperfine molecular levels 1Σ diatomic molecules

8. Hyperfine molecular levels 1Σ diatomic molecules

9. Hyperfine molecular levels 1Σ diatomic molecules

10. Hyperfine molecular levels 1Σ diatomic molecules

11. Hyperfine molecular levels 1Σ diatomic molecules

12. Hyperfine molecular levels Zero field splittings dominated by the scalar spin-spin interaction (c4I1·I2). 1Σ(N=0) diatomic molecules. Zero field splittings. c4(40K87Rb) ≈ -2 kHz c4(133Cs2) ≈ 13 kHz Hyperfine splitting ≈ tens to hundreds of kHz ≈ 1 to 10 μK

13. Hyperfine molecular levels • The ratio |c4/(eQq)| ratio determines the zero field splitting partner: • Large |c4/(eQq)| values → the splitting is determined by the scalar spin-spin Interaction and coincides with that for N=0. • Small |c4/(eQq)| values → the splitting is determined by the electric quadrupole interaction. 85Rb2 (N=1) 1Σ (N≠0) diatomic molecules. Zero field splittings. Hyperfine splitting ≈ hundreds to thousands of kHZ ≈ 10 to 100 μK eQq(85Rb2) ≈ 2 MHz

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

15. Hyperfine molecular levels 1Σ diatomic molecules. Zeeman splitting. • Energy levels with the same value of MI display avoided crossings (the red lines correspond to MI =-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 1Σ diatomic molecules. Zeeman splitting. • Energy levels with the same value of MI display avoided crossings (the red lines correspond to MI =-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. Hyperfine molecular levels 1Σ diatomic molecules. Stark splitting. • 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. Hyperfine molecular levels Energy levels correlating with N=0 referred to their field-dependent average value: 1Σ diatomic molecules. Stark splitting. • Each level splits into I+1 components labelled by |MI|. • 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(2Π3/2) M.Laraet al studied these collisions (Phys. Rev. A 75, 012704 (2007)). Rb + OH(2Π3/2) collisions • 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 Cs + Cs collisions

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

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

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

25. Hyperfine changing collisions Rb + ND3 collisions

26. Hyperfine changing collisions Rb + ND3 collisions

27. Hyperfine changing collisions Rb + ND3 collisions

28. Conclusions • The rotational levels of 1Σalkali 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 ND3/NH3 molecules with cold Rb atoms: • Poor for ND3/NH3 low-field-seeking states. • Good for ND3/NH3 high-field-seeking states. ND3 better than NH3. • Quantitative calculations are necessary.

30. Hyperfine changing collisions Rb + OH(2Π3/2) collisions M. Lara et al, Phys. Rev. A 75, 012704 (2007)

31. Hyperfine changing collisions Rb + OH(2Π3/2) collisions

32. Conclusions • Molecular energy levels split into many fine and hyperfine components. • 1Σ 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 • 2s atoms and singlet molecules can be factorised. The collisions will not cause • fast atomic inelasticity. • This factorization will not be possible when the 2s atoms collides with doublet • or triplet molecules. In this case, the potential operator will drive fast atomic • Inelastic collisions. • Prospects for sympathetic cooling of ND3/NH3 molecules with cold Rb atoms: • Poor for ND3/NH3 low-field-seeking states. • Good for ND3/NH3 high-field-seeking states. ND3 better than NH3. • Quantitative calculations are necessary.