Analysis of strongly perturbed 1 1 P 2

Analysis of strongly perturbed 1 1 P – 2 3 S+ – b 3 P states of the KRb molecule J. T. Kim 1, Y. Lee 2, and B. Kim 3 1 Department of Photonic Engineering, Chosun University. 2 Department of Chemistry, Mokpo National University. 3 Department of Chemistry, KAIST. D. Wang Department of Physics, The Chinese University of Hong Kong. W. C. Stwalley, P. L. Gould, and E. E. Eyler Physics Department, University of Connecticut. Supported by the National Science Foundation, the Air Force Office of Scientific Research, the National Research Foundation of Korea, and KOSEF through NRL in Korea.

Motivation I: Assignment of perturbed spectra K(4 S 1/2)+Rb(5 PJ) • Initial state for ultracold molecule (UM) spectra is a 3 S+, mainly in v=20 and v=21, at low J. • Initial state for molecular beam (MB) spectra is X 1 S+, v =0 and v =1, at low J. 1 1 P 2 3 S + b 3 P K(4 S 1/2)+Rb(5 S 1/2) a 3 S+(v, J) X 1 S+(v =0, J ) • Selection rules allow only W=1 for triplet states in the MB spectra, but W=0, 1, 2 for UM spectra. • No rotational resolution due to pulsed laser linewidth, ~ 0. 1 cm− 1.

Motivation II: how to produce v =0 molecules? • To date, molecules with T < 1 m. K can be produced only by combining ultracold atoms using photoassociation (PA) or magnetoassociation (MA). • Both normally produce levels of very high v. • Transfer to low v requires either: 1. Unusual PA mechanisms (e. g. , FOPA). 2. Resonant coupling of small-R and large R levels due to electronic perturbations. 3. STIRAP-type Raman transfer. Optimal path often not obvious. The MB-UM method identifies it automatically.

Experimental scheme for UM (Storrs) Ionization Continuum 1) PA to form ultracold KRb*. REMPI e (v , J ) 1 1 P K(4 S 1/2)+Rb(5 PJ) 2) Spontaneous decay into the triplet ground state, a 3Σ+. e(v , J ) 2 3 S + b 3 P Spont. Emission K(4 S 1/2)+Rb(5 S 1/2) a 3 S+(v, J) X 1 S+(v =0, J ) PA 3) REMPI detection via intermediate states e (v , J ).

Experimental scheme for MB (Korea) Ionization Continuum MB RE 2 PI e (v , J ) 1 1 P K(4 S 1/2)+Rb(5 PJ) 2 3 S + 2) REMPI detection via intermediate states e (v , J ). b 3 P K(4 S 1/2)+Rb(5 S 1/2) a 3 S+(v, J) X 1 S+(v =0, J ) 1) Supersonic beam forms X 1 S+ with v = 0, 1.

Combined UM and MB spectra Ionization Continuum MB RE 2 PI UM RE 2 PI K(4 S 1/2)+Rb(5 PJ) e (v , J ) 1 1 P b 3 P • Intermediate states e (v , J ) can coincide. e(v , J ) 2 3 S + SR 1 PA SE SR 2 K(4 S 1/2)+Rb(5 S 1/2) a 3 S+(v, J) X 1 S+(v =0, J ) • Comparison facilitates assignments. • Multiplicative spectrum UM MB identifies Raman pathway SR 1+SR 2.

Excitation windows

Complete spectra from the MB and UM experiments

Franck-Condon factors • Calculated from the potential energy curves of Rousseau, Allouche, and Aubert-Frécon, J. Mol. Spectrosc. 203, 235 (2000). • Not shown is b 3 P X 1 S+, for which the FCFs are negligibly small. • The 1 1 P X transition has a larger electronic transition moment than 2 3 S+ X, in addition to its larger FCFs.

Central portion, with assignments Due to singlet-triplet mixing, the 1 1 P 1 and 2 3 S+1 levels are evident in both spectra. The b 3 P 1 level is weak, but nevertheless visible, in the MB spectrum.

Avoided crossing near 6. 5 Å Avoided crossings between levels of equal W cause anomalous spin-orbit splittings for large R, much smaller for the 2 3 S+ state than for b 3 P.

High-frequency portion, showing reversed fine structure for the 2 3 S+ state

Predicted and measured W splitting

Vibrational intervals DG from UM spectra • Agreement of overall trends with theory shows that the potential energy curves have the correct shape. • Some perturbations and scatter are evident, due to admixture between states • Agreement with prior experiments for 1 1 P is excellent, with just one level in disagreement. Prior experiments: 1. N. Okada, S. Kasahara, T. Ebi, M. Baba, and H. Kato, J. Chem. Phys. 105, 3458 (1996). 2. S. Kasahara, C. Fujiwara, N. Okada, H. Kato, and M. Baba, J. Chem. Phys. 111, 8857 (1999).

MB UM product spectra: interpretation e (v , J ) SR 2 SR 1 a 3 S+ (v=21) X 1 S+ (v =0, J =0) For Raman transfer from a 3 S+ (v=21) X 1 S+ (v =0), need an upper state in common between both spectra Ultracold Molecule intensity: Molecular Beam intensity: Stimulated Raman rate:

MB UM product spectra: results Largest amplitude is via v =7 of the 1 1 P 1 state. This level is also noticeably perturbed on the DG plot (expanded below.

Summary • Numerous new assignments to the perturbed 1 1 P – 2 3 S+ – b 3 P states of 39 K 85 Rb are made by comparing UM and MB spectra. • Good agreement with previous experiments (where available) and with potential curves from Rousseau, et al. • The MB UM product spectrum automatically selects optimal pathways for STIRAP transfer of ultracold molecules to X 1 S+, v=0. • To be published in PCCP special issue (spectra) and JPC Letters (Raman pathway via MB UM product. )