1. Frequency Comb Velocity-Modulation Spectroscopy of HfF + Kevin Cossel Laura Sinclair, Tyler Coffey, Jun Ye, and Eric Cornell OSU 2011 Acknowledgements: Huanqian Loh, Matt Grau (JILA) John Bohn, Ed Meyer (JILA) A. Petrov, A. Titov (Petersburg Nuc Phys Inst) Bob Field (MIT) Funding: NSF and the W.M. Keck Foundation

2. Electron Electric Dipole Moment (eEDM) search Predicted HfF + Structure 3  1 metastable state of HfF + and ThF + provides high sensitivity (Hf 6s 1 5d 1 ) Use multiple excited states for state preparation and spin readout Very little spectroscopic data exists for either species A. Petrov, et al. Phys. Rev. A 76, 030501 (2007) A. Petrov, et al. Phys. Rev. A 79, 012505 (2009) 1+1+ 3131 3232 3333 1212 3030 3131 1111 E. Meyer, et. al. Phys. Rev. A 73, 062108 (2006) Need broadband survey spectroscopy of molecular ions! Up to 2000 cm -1 uncertainty Recently measured with PFI-ZEKE Barker, et al. J Chem. Phys. 134 201102 (2011)

3. Velocity-Modulation Spectroscopy Discharge produces and modulates the ions Lock-in Detector Doppler shift of transition frequency changes sign each half cycle laser Review of VMS: Stephenson and Saykally, Chem Rev. 105 (2005) 10 kHz, 1 kW t signal Ion selectivity!

4. Frequency Combs and Cavities Frequency combs provide narrow lines over a wide spectral bandwidth.... Cavity Enhancement with a Frequency Comb: Match Spacing of Frequency Comb Modes to Cavity’s Free Spectral Rang e f rep Cavity FSR Adler et al. Annu. Rev. Anal. Chem. 3 (2010)

5. 10 kHz, 1 kW (250 mA) Ring cavity Finesse ~ 100 FSR ~ 120 MHz VIPA Etalon Grating Vertical dispersion 3 GHz comb Horizontal dispersion Heliotis Lock-in Camera S. Beer, P. Seitz, Research in Microelectronics and Electronics, 2005 PhD, 2 135 (2005) Frequency comb + velocity modulation + cavity Lock-in detection on every comb tooth (1500 simultaneous channels)! Artwork: B. Baxley/JILA

6. Image of comb teeth on lock-in camera DC Intensity ~3 GHz ~100 GHz

7. Data Analysis: Fit comb teeth positions DC Intensity

8. Data Analysis: Demodulating Each Comb Mode Signal at 10 kHz

9. 28 images x1500 simultaneous channels of lock-in detection Data Analysis: Scanning

10. Putting it all together: HfF + ! 1  1  1  + (0,1) 3  1  1  + (2,0) 1  1  1  + (1,2) >500 cm -1 currently covered 150 cm -1 in under an hour 3 x 10 -7 fractional sensitivity 3 bands (over 1000 lines) + still unidentified lines

11. More HfF + ! Fit for 1  1  1  + (0,1) band

12. Summary of 180 HfF + Fits 1  1  1  + (0,1) 3  1  1  + (2,0) 1  1  1  + (1,2) T 0 [cm -1 ]12217.388 (2)12304.369 (3)12133.977 (5) B” [cm -1 ]0.30335 (3)0.30481 (4)*0.30100 (50) B’ [cm -1 ]0.28115 (3)0.28096 (4)0.27890 (40) D” [10 -7 cm -1 ]1.88 (8)1.78 (12)4.3 (4) D’ [10 -7 cm -1 ]1.81 (8)1.78 (11)4.2 (4) k‘ [10 -4 cm -1 ]3.69 (2)-3.82 (1)3.6 (5) k D ’ [10 -9 cm -1 ]9.7 (0.7)-0.3 (1.0)14 (15) E(J”,J’) = T 0 + (B’ – P*k’/2)J’(J’+1) - (D’ – P*k D ’/2)J’ 2 (J’+1) 2 - B”J”(J”+1) + D”J” 2 (J”+1) 2 For  J = 0, P = -1; For  J = ±1, P = 1 Lambda doubling (k’) switches sign between 1  1 and 3  1 Need lambda doubling proportional to J 4 (k D ’) only for 1  1 * Measured by Barker, et.al. 0.304(10)

13. Theory: A. Petrov, N. Mosyagin, A. Titov, Phys. Rev. A 79 012505 (2009) 1+1+ 3131 1111 13002.229 cm -1 12217.388 cm -1 12133.977 cm -1 12304.369 cm -1 784.84 cm -1 consistent with Barker, et al. 785.8(10) cm -1 700 cm -1 Measured HfF + Electronic Structure 1  1 shifted by 1700 cm -1 from theory 1  1 - 3  1 fine structure splitting = 2100 cm -1 (theory = 2100 cm -1 ) 1  1 & 3  1 oscillator strength to 1  + equal to ~30%

14. Conclusions  Demonstrated frequency comb velocity-modulation spectroscopy with: 4 x 10 -8 Hz -1/2 (spectral element) -1/2 fractional absorption sensitivity 150 cm -1 spectral coverage with 1500 simultaneous measurements 30 MHz absolute frequency accuracy  700 cm -1 covered so far for HfF + (ThF + coming soon)  This is a very general technique which given the current frequency comb technology could be extended across wavelengths from the UV to the IR  Other applications: physical chemistry (H 3 +, CH 5 + ), astrochemistry (diffuse interstellar bands)

15. f laser = f 0 +  f Doppler f laser = f 0 -  f Doppler 12179.312179.5