1. Assignment Methods for High N Rydberg States of CaF Vladimir S. Petrovi ć, Emily E. Fenn, and Robert W. Field Massachusetts Institute of Technology International Symposium on Molecular Spectroscopy Ohio State University, June 2006

2. Rydberg States of CaF Need additional diagnostics to recover dynamics from the spectrum Exchange of energy and angular momentum between electron and the ion One electron outside the doubly closed shell  Six core-penetrating series; core-nonpenetrating series ( l  3) Large multipole moments (µ = 3.52 a.u.; Q = 8.96 a.u.)  l -mixing As N increases  l -uncoupling Intermediate n*, high N: both effects present Interference effects dominate spectrum  Combination differences alone are not enough

3. Ionization-detected optical-optical double resonance in a He beam (T rot  30K) Experimental Scheme Energy level diagram for double resonance spectroscopy of CaF Pulsed ablation of Ca and subsequent reaction with CHF 3 First laser selects a single parity rotational level of D 2  + (0  N  38) Second laser scanned (18.5  n*  20.5) Autoionization formed ions collected using pulsed extraction field (E = 200 V, 200 ns after the laser excitation)

4. How Do We Make Assignments? Two sorts of stacked plots: Spectra vs. probe energy Spectra vs. total term energy Stark effect MQDT fitter (H eff does not help) Intensity patterns Polarization effects Time Domain Terahertz Spectroscopy

5. Stacked spectra vs. probe energy  visual clustering tells us pattern-forming quantum number CaF DR spectra for N = 10-15 ploted vs. the probe energy N  =10 N  =11 N  =12 N  =13 N  =14 N  =15 Stacked Plots

6. Core-penetrating states: Pattern forming quantum number is N Core-nonpenetrating states: Pattern forming quantum number is N + so branches are clustered according to (N + -N  ) Stacked Plots

7. CaF DR spectra for N = 15-19 plotted vs. total term energy N  =19 N  =18 N  =17 N  =16 N  =15 Stacked spectra vs. total term energy  combination differences tell us N Mostly useful at low N and for core-penetrating states

8. Polarization Effects Are Useful Distinguishing Q branches from P and R branches (M. Chevalier and A. de Martino; Chem. Phys. Lett. 1987, 135, 446) Transition intensity ratio (parallel to perpendicular) for lower R transition followed by upper P, Q and R transition

9. probe wavelength in nm (not calibrated) blue: perpendicular red: parallel Polarization Effects Are Useful CaF DR Spectrum (N  =3) recorded in parallel (blue) and perpendicular (red) polarization arrangement Q Q

10. l R Intensity Patterns Are Useful Too Transition intensity into different l R components in a f  2   2  transition. (lower transition R in all three cases; relative polarization perpendicular) P for f( l R = -3) Q for f( l R = -2) R for f( l R = -1) Useful for distinguishing branches within a cluster of same N + -N  l R = N-N + J intensity Applicability limited by l mixing and interference effects

11. Most features assigned up to N = 20; still working on higher N Use Stark effect to check the assignments Stark Effect

12. Exceptionally large  n*  1 transition dipole moments Double resonance spectra recorded in presence of external electric field (N  =13, d=1.27 cm); plotted vs. probe energy (cm -1 ) Energy shifts Dark states lit up by mixing with bright states  n l  r  n l-1  = 3/2 an(n 2 -l 2 ) 1/2 For n*=19, µ>1000 D

13. Stark Effect 1 Example 1: Bright state 19.14  - (N = 13) switches on P transition for 19.36  - (N = 12) Polarization analysis explains observed patterns (z-x-z polarization arrangement leads to mixing between states of the same Kronig symmetry*) * reflection symmetry of the electronic part of the wavefunction Double resonance spectra recorded in presence of external electric field (N  =13, d=1.27 cm); plotted vs. probe energy (cm -1 )

14. Stark Effect 2 Example 2: f(-2) gives intensity to higher l states Double resonance spectra recorded in presence of external electric field (N  =13, d=1.27 cm); plotted vs. probe energy (cm -1 )

15. ns THz D2+D2+ Rydberg X2+X2+ ≈16 000 cm -1 ≈6.6 cm -1 ≈1.5 cm -1 ≈30 000 cm -1 Time Domain Terahertz Spectroscopy Exceptionally large intracomplex transition dipole moments  electronic transitions strong; vibrational and rotational transitions de facto forbidden Transmitted THz pulse is modified due to the absorption and deexcitation of the excited l R ( ) components Energy level scheme for Optical- Optical-THz experiment on CaF As l increases, transition energy decreases fast Spacings are multiples of a common factor in both case b (in terms of ) and case d (in terms of l R ) THz pulse broad enough to excite several l R or components

16. Experimental Scheme THz pulses generated in z-cut LiNbO 3 by optical rectification of  150 fs pulses centered around 800 nm Scheme of the THz Spectrometer Spitfire LiA LiNbO 3 sample /4 Balanced photodiodes ITO ZnTe Absorption coefficient recovered from the transfer function It is the electric field that is detected Detection is coherent Detection by Free Space Electro Optic Sampling in 500 µm thick  110  ZnTe

17. TD THz Rotational Spectroscopy of Small Molecules Recorded rotational spectrum in the ground state of methyl fluoride (B≈0.025 THz) in a sample cell Rotational spectrum of CH 3 F, 200 Torr, 19.5 cm cell length

18. TD THz Rotational Spectroscopy of Small Molecules Work in progress: optical- THz double resonance spectroscopy of formaldehyde Calculated modifications to the rotational spectrum of H 2 CO; electronic transition into 4 1 0 J=9, K=1 of à 1 A 2 from J=9, K=0 of X 1 A 1  Large population differences in both ground and excited electronic states lead to new features in the spectrum Resonant UV transition into a selected level of à 1 A 2 depopulates one ground state rotational level

19. Next steps: Single shot detection Narrowband THz pulses using PPLN Experiment in the molecular beam TD THz Rotational Spectroscopy of Small Molecules

20. Summary Complexity in high N intermediate n* spectra of CaF Diagnostic tools (combination differences, clustering, polarization, intensity patterns, Stark effect, MQDT fitter) Assigned and fitted most of the levels up to N = 20 Work on higher N in progress Time Domain Terahertz Spectroscopy

21. Acknowledgements Robert W. Field Emily Fenn Serhan Altunata Jeff Kay (work with MQDT Fitter) Stephen Coy Thomas Hornung Joshua Vaughan Thomas Feurer Philip Lichtor Séverine Boyé-Péronne R. W. Field Research Group NSF