1. Resonance-enhanced Photoassociative Formation of Ground-state Rb 2 and Spectroscopy of Mixed-Character Excited States H.K. Pechkis, D. Wang, Y. Huang, E.E. Eyler, P.L. Gould, and W.C. Stwalley Physics Department, University of Connecticut Supported by the National Science Foundation

2. 1.Formation and state-selective detection. 2.Coupling of the 0 u + States. 3.Periodic enhancement of bound-state molecule formation. 4.Electronic spectroscopy and singlet - triplet mixing. 5.Future plans: Optical trapping, Dynamics, etc. Outline

3. Formation and detection of singlet states Steps: 1) PA to form ultracold Rb 2 *. 2) Radiative stabilization into the singlet ground state, X 1 Σ g +. 3) Detection using REMPI through the 2 1 Σ u + state. PA 597

4. Z axis Detection Laser Trap PA Laser CCD Channeltron Repump Experimental Scheme

5. X 1 Σ g + ground-state vibrational levels agree well with calculations using potentials from Seto, et al.* But Franck-Condon factors for decay do not— they peak near v"=119. Levels with v″>117 can be photodissociated by the PA laser, but why are 111- 114 so strong? Y. Huang et al., J. Phys. B: At. Mol. Opt. Phys. 39, S857-S869. *J. Y. Seto, R.J. Le Roy, J. Verges, and C. Amiot, J. Chem. Phys. 113, 3067 (2000). Detection Spectra for singlet Rb 2 : 2 1  u + (v') ← X (v")

6. Fine structure splitting: ~ 237cm -1 Not to scale First studied in Cs 2 by Dion et al., PRL 86, 2253 (2001). Energy levels are system- atically perturbed by spin- orbit coupling. Franck-Condon factors are greatly altered by vibra- tional wave function admixture. Resonant coupling of the 0 u + states

7. Energy level perturbations in PA spectra From T. Bergeman, et al., J. Phys. B 39, S813(2006)

8. Coupled-state vibrational Wave functions Resonant E bind = 9.39 cm -1 Non-resonant E bind = 11.27 cm -1 Singlet character: blue Triplet character: red H. K. Pechkis, et al., to be pulished. Available on www.arXiv.org.

9. Franck-Condon factors for decay

10. Detection spectra for various  PA non-resonant resonant

11. Total X-state molecules ( v  =112–116) Red diamonds: Sums of theoretical FCFs. Squares: Experimental data set 1 (normalized by PA rate). Circles: Set 2.

12. 2 1  u + ← X Spectra: 582nm to 606nm Assignments are based on potentials cal- culated by Park, et al.* Vibrational numbering is approximate. *J. Mol. Spectrosc. 207, 129 (2001).

13. Theory: S.J. Park, et al., J.Mol. Spectrosc. 207,129 (2001). Experiments: Y. Huang, et al., J. Phys. B 39, S857 (2006). ΔG  E(v+1) – E(v) Vibrational Spacings of the 2 1 Σ u + State Trough-shaped poten- tial causes a nearly semicircular profile. Small well near 5Å causes discontinuity at low v—very sensitive to details.

14. The triplet 2 3 Π u state cros- ses the 2 1 Σ u + state near R e. Low-v levels can be mixed by spin-orbit coupling. Triplet splitting in the 2 3 Π u state is not known, but only  =0 can mix with 2 1 Σ u + in lowest order. Another Complication at low v: singlet-triplet Perturbations

15. Two new vibrational progressions are observed in the blue portion of the spectrum. Both seem to match the 2 3 Π u state. Not yet clear whether the splitting is due to lambda doubling or fine structure. Singlet-triplet mixing in the 2 1  u + spectrum

16. R(Å)R(Å) Energy(cm -1 ) Production and detection is similar to the singlet scheme. We scan the detection laser from 582– 715nm. A similar scheme was used by Gabbanini’s group, * but with lower resolution. Detection of Metastable Triplet Rb 2 * A. Fioretti et al., Eur. Phys. J. D. 15, 189 (2001).

17.  G and FCFs for the 2 3  g + state ΔG  E(v+1) – E(v) Calculations via mapped Fourier grid Hamiltonian (MFGH) method. Rb 2 + (arb. units) Detection Laser Frequency (cm -1 ) 14000 14400 14800 15200 Experiment Theory v Comparison between experimental line strengths and calculated FCFs. Asterisks denote atomic transitions. Present calculations Experiment (UCONN) Energy Spacing (cm -1 ) Full description: J. Lozeille, A. Fioretti, C. Gabbanini, Y. Huang, H. K. Pechkis, D. Wang, P. L. Gould, E.E. Eyler, W.C. Stwalley, M. Aymar, and O. Dulieu, EPJD 39, 260 (2006).

18. Singlet - Triplet Mixing (again) Note the difference in lineshapes between the singlet 3 1 Σ g + state and the triplet 2 3 Σ g + state. *Park, et al., J.Mol. Spectrosc. 207,129 (2001) The triplet 2 3 Π u state crosses the singlet 2 1 Σ u + state near R e.* Low- v levels can be mixed by spin-orbit coupling. Energy (cm -1 x 1000)

19. Analysis by J. Lozeille and O. Dulieu In this region, six case (a) states are mixed! Assignments are based on MFGH calculations including spin-orbit coupling. Data from Pisa on 87 Rb 2 was analyzed simultaneously. Ion signal (arb. Units) Transition energy (cm -1 ) J. Lozeille, et al., EPJD 39, 260 (2006).

20. What’s next? Photoassociation of trapped Rb in an optical dipole trap. (Magnetic trapping of triplets already achieved.) Studies of ultracold molecular collisions, starting with vibrational quenching in Rb 2 +Rb collisions. L 2 L 1 W 1 W 2 L 3 CO 2, 10.6  m PA, ~795 nm N ~ 1 x 10 12 cm -3 N = 2.6 x10 6  ~ 1s Rb atoms in a CO 2 laser optical trap

21. Conclusions Rb 2 is produced in the X 1  g + and a 3  u + states via PA and radiative decay. State-selective detection of both states is achieved with a pulsed dye laser at 582-713 nm. Resonant coupling of the 0 u + states greatly enhances X state formation in high- v levels. We have made the first observation of the 2 1  u + state, and observed extensive mixing with the triplet 2 3  u state. We have observed and assigned extensive spectra of the 2 3  g + state and observed the 2 3  g state and several higher states for the first time. Optical trapping of Rb atoms in an optical dipole trap designed for PA and molecule trapping.

23. Detection spectra of triplet Rb 2 : Vibrational structure of the a 3 Σ g + state Three different PA detunings below the 5s+5P 1/2 atomic asymptote Intermediate state for detection: 2 3 Σ g + (v'=17) For smaller  PA, higher vibrational levels are populated.