This document summarizes a talk on calculating properties of the LiYb molecule to aid in creating ultracold LiYb molecules via photoassociation spectroscopy. It describes: 1) Calculating potential energy curves and transition dipole moments of LiYb using relativistic methods to identify excited states for photoassociation. 2) Transition dipole moments between ground and excited states indicate possible routes for creating ultracold molecules. 3) Future work will calculate photoassociation intensities and spontaneous emission rates to transfer molecules to the ground or metastable excited states.

1. Relativistic calculations of ground and excited states of LiYb molecule for ultracold photo association spectroscopy studies Geetha Gopakumar1, Minori Abe1, BhanuPratap Das2, Masahiko Hada1 and Kimihiko Hirao3 1Department of Chemistry, Tokyo Metropolitan University 2Non Accelerator Particle Physics Group, Indian Institute of Astrophysics 3 Next-generation Molecular Theory Unit, RIKEN (Talk given at Tokyo Institute of Technology for the 10th Symposium on Molecular Spectroscopy on 14-15th May 2010) 2010/5/15 1

3. Experimental process of creating ultracoldLiYb molecule

4. Theoretical process of creating ultracoldLiYb molecule

5. Calculation details

6. Spin-free and Spin-orbit potential energy curves and their accuracy

7. Spin-free and Spin-orbit transition dipole moments and their accuracy

9. How do we make molecules via Photo association (PA) of cold atoms –collision associated with light Cs2: Orsay, PRL, 80, 4402 (1998); Rb2: Pisa, PRL, 84, 2814 (2000) A pair of ultra cold ground-state atoms absorbs a photon, creating a molecule in an excited ro-vibrational electronic state. Another photon thro stimulated emission transfers this to highest vibrational state of the ground state. Single species trap – PA laser is chosen in such a way that its frequency is detuned to the S-P transition and the excited state has a R-3 long range dipole –dipole interaction Mixed species trap – atoms interact thro the short range Vander Waals interaction R-6 . 4

10. Experimental process of generating ultracoldLiYb molecule (M.Okano et al,Appl Phys B (2010) 98:691-696)(Takahashi sensei’s Lab at Kyoto University) 2010/5/15 5 Li and Yb atomic beams from an atomic oven are decelerated by the Zeeman slowing method and the cooled atoms are loaded to a MOT. These trapped atoms are transferred to a optical trap and evaporatively cooled with sympathetic cooling of atoms Using magnetically tunable Feshback resonances the cooled Li and Yb atoms are adiabatically associated to form weakly bound LiYb molecules Finally weakly bound molecules are coherently transferred to the ro-vibrational ground state of the electronic ground molecular state by employing a step of STIRAP(STImulated Raman Adiabatic Passage)

11. Theoretical process of coherently transferring weakly bound LiYb molecule to the ro-vibrational ground state of the electronic ground molecular state 2010/5/15 6 High accuracy ab initio potential energy calculations of the ground and the excited states of LiYb molecule over a large inter nuclear distances. High accuracy transition moment calculations from ground to possible excited states over a large inter nuclear distances. Photo association intensities from the vibrational continuum of the ground electronic state to the bound vibrational levels of the excited state Spontaneous emission coefficients from the bound vibrational levels of the excited state to the lowest bound vibrational level of the ground electronic state.

14. Method : Spin free 3rd Order Douglas-Kroll Hamiltonian Correlation : Spin free multi-state CASPT2 followed by first order Spin-Orbit effect using RASSI (RAS State Interaction Program) – SO-MS-CASPT2

15. Symmetry : C2v

16. Active Space for CASSCF : 3 electrons in 8 orbitals(6s and 6p of Yb and 2s and 2p of Li)

17. Frozen core : 23 orbitals (1s to 4d of Yb (en ~7.561 au)

18. Active orbitals in CASPT2: 5s,6s,5p,4f (Yb) and 1s(Li)

20. 2010/5/15 9 Spin-free potential energy curves of LiYb molecule Red full lines(2Σ), Blue dotted lines (2Π), green full lines (4Σ) and green dotted lines(4Π) BSSE using CPC method for ground state is found to be ~ 100cm-1 for CASPT2

22. 2010/5/15 11 Excitation energy at R= 100 a.u. Excitations of the kind 4f-5d and 6s-5d lying below 1P1 of Yb asymptote is disregarded

24. In molecular binding regions, transitions to all 2Σ and 2Πstates are non-zero

26. 2010/5/15 14 Selection rules at the atomic limit <Li(2S1/2)+Yb(1S0)|D|Li(2P1/2,3/2)+Yb(1S0)> Ground state J – 1/2 Excited states J – 1/2 and 3/2 Selection rules: ΔJ = 0, ±1 Hence 3 possibilities… J= 1/2 to 1/2 J= 1/2 to 3/2 J= 1/2 to 1/2 M quantum number follows the selection rules of CG coefficient (3j symbol) Theory : 2.3624 a.u. Expt: Li(2s) - Li(2p) – 2.36 a.u*. ΔM= 0, ±1 * H Partridge, et al, J.Chem. Phys. 74 (1981) 2361

29. 2010/5/15 17 Atomic limit calculations Theory :0.310 a.u. Expt :0.315 a.u. CI + MBPT – 0.54 (Theory) – S. G. Prosev etal, Phys. Rev. A, 60, 2781 (1999) Ref (a) - 0.44 (Theory) –J.Mogdalek et al, J. Phys B 24, L99 (1991) Ref (c) – 0.549 (Expt) – C.J.Bowers, D. Budker et al, Lawrence Berkeley National Laboratory Report No. 42454(1998) (unpublished) Ref (d) - 0.553 (Expt) – M. Baumann and G. Wandel, Phys. Letts. 22,283(1966) This calc: 0.14 (a.u.) Fixing J’ to be 0 (ground state), J to be 1 and q to be 0,1,-1, we get 3j value to be 0.57735 This calc: 0.14 (a.u.) 3j symbol (http://www.svengato.com/threej.html)

30. 2010/5/15 18 TDMs at spin-orbit level considering states dissociating to Yb(1P) + Li(2S) CCSD(T) – 4.40(Theory) – S. G. Prosev etal, Phys. Rev. A, 60, 2781 (1999) Ref (a) - 4.44 (Theory) –J.Mogdalek et al, J. Phys B 24, L99 (1991) Ref (b) – 4.89 (Theory) – Kunisz, Acta Phys. Polon. A 62,285(1982) Ref (d) - 4.13 (Expt) – M. Baumann and G. Wandel, Phys. Letts. 22,283(1966) Ref(e) – 4.02 (Expt) – N.P.Penkin et al, Atomic Physics VI (Riga 1978) Ref(f) – 4.26 (Expt) – T. Andersen et al, Solar Physics 44,257 (1975) Theory.2.54 a.u. Expt: 2.32 a.u. This calc. 2.99 a.u.

31. 2010/5/15 19 Criterion for the formation of cold molecules Spontaneous emission by the Excited photo associated molecules Branching ratio – bound-free (leads to dissociation) and Bound-bound (leads to formation Of cold molecules) Single well molecular potential BR is small (as atoms are far - spontaneous emission to occur at small internucleardistances is small. Outer well of a double well potential (atoms are slowed down due to potential bump) (Condon point) – large BR.

32. Possible routes for PA (qualitative) 2010/5/15 20

33. Permanent Dipole moment (PDM) 2010/5/15 21 KRb molecule – 1Σ PDM is 0.30 a.u. (Kotochigava et al, Phys. Rev.A, 68,022501 (2003) RbCs molecule – 1Σ PDM is -1.25 a.u. (Kotochigava et al,JCP, 123,174304 (2005) Metastable states with large Permanent dipole moment for the formation of ultracold molecule

35. Photo association intensities from the vibrational continuum of the ground state to the bound vibrational levels of the excited state

36. Spontaneous emission coefficients from the bound vibrational levels of the excited states to the lowest bound vibrational levels of the ground state or any other metastable excited states.Thank you