1. A. Nishiyama a, K. Nakashima b, A. Matsuba b, and M. Misono b a The University of Electro-Communications b Fukuoka University High Resolution Spectroscopy of Naphthalene Calibrated by an Optical Frequency Comb TF04 1

2. ●Dynamics of excited states in polyatomic molecules is important ・ Basic properties of molecules ・ Chemical reaction processes Introduction ●Requirement for the spectroscopic system ・High resolution spectroscopy ・Calibration by a precise optical frequency ruler ・Wide frequency applicability Optical Frequency ●The dynamics appears in the form of minute effects in spectra in wide wavelength range ・Frequency shift ・Line broadening ・Intensity anomaly ・Zeeman splitting 2 precise optical frequency ruler

3. Precise Optical Frequency Ruler EOM Confocal Etalon Etalon marker 300 MHz cw Laser … uncertainty ～ several MHz = 10 -8 f n = nf rep + f CEO (n : mode number) Optical Frequency f CEO = Δφf rep /2π f rep Intensity fnfn GPS clock uncertainty = 10 -11 3

4. ・Resolution and Precision < natural width (～1 MHz) Aim of Our Study ●Development of high resolution spectroscopic system with an optical frequency comb ●Application to Doppler-free two photon absorption spectroscopy of naphthalene ・Wide Frequency Applicability ・Calculation of molecular constants 4

5. f dye + f AOM f beat f dye f AOM Optical frequency Optical frequency Radio frequency time f rep Radio frequency time f rep Wave meter Wave meter Ti:S comb APD PCF DG λ/2 λ/4 RF synthesizer RF synthesizer Frequency counter f AOM /2 Saturated absorption spectroscopy of I 2 Photon counting unit Photon counting unit Cw dye laser linewidth 130 kHz Cw dye laser linewidth 130 kHz PC f beat PBS Doppler-free two photon absorption spectroscopy of C 10 H 8 Experimental setup GPS clock PMT 5

6. 40.8 41.2 1.16 1.00 17352.23.24.25 Wavenumber [cm -1 ] Hyperfine spectrum of iodine ～ P(62)17-1 Scan rate : 0.8 MHz/s, Gate time of the counter : 0.1 s Wave length : 576 nm Measurement time : 22 minutes f AOM [GHz] f beat [MHz] I 2 Sat. Abs. Intensity [arb.unit] A. Nishiyama, et. al., Opt. Lett. 39, 4923 (2014). We can determine the absolute frequencies of hyperfine spectra with the uncertainty of 10s kHz 6

7. Doppler-Free Two Photon Absorption Spectroscopy f dye u f dye (1-u/c)f dye (1+u/c) Dye Laser Linewidth:130 kHz Dye Laser Linewidth:130 kHz PMT λ/2 fluorescence 596 nm 298 nm S11B1uS11B1u S01AgS01Ag Pressure : 20 Pa Finesse : 94 The cavity length was controlled to maintain a resonance. 7

8. x z D 2h S11B1uS11B1u S01Ag S01Ag v 4 (C-C stretch)=1 : b 1u ～ 33578 cm -1 ～ 32018 cm -1 ～ 35804 cm -1 S21B3uS21B3u 1560 cm -1 Two Photon Transition of Naphthalene 8

9. 335763357733578 I 2 Sat. Abs. Intensity [arb.unit] C 10 H 8 Two Photon Transition [arb.unit] f AOM [GHz] 16788.016788.516789.0 Wavenumber [cm -1 ] Band origin S 1 1 B 1u (v 4 =1 : b 1u ) ← S 0 1 A g (v=0) transition Scan rate : 2 MHz/s, Gate time : 0.2 s, Sampling rate：0.4 MHz Naphthalene spectrum ～ Q(K) Q(J) transition f beat [MHz] 40.6 41.2 1.16 1.00 9

10. Line width of naphthalene spectra 5000 0 33577.9150.9160.9155 [cm -1 ] FWHM = 2.48 MHz [count] Natural width (calculated from the life time [1] ) = 0.91 MHz [1] U. Boesl et. al. Chem. Phys. Lett, 42, 16 (1976). Transit-time broadening = 0.64 MHz (diameter of beam = 0.25 mm) Pressure broadening = 0.53 MHz (20 Pa) Laser linewidth×2 ＝ 0.26 MHz 2.48 – (0.64 + 0.53 + 0.26) = 1.05 MHz

11. Assignment We assigned 1466 lines (J = 3 - 42, K a = 0 – 27) Q(K) Q(J) transitions（ΔJ = 0, ΔK a = 0） Near the band origin (J = 3 - 18, K a = 0 - 8) 11

12. Interaction between excited states [MHz] J 0 30 10 20 K a = 0 K a = 1 K a = 2 K a = 3 K a = 4 0 200 -200 0 200 -200 0 200 -200 0 200 -200 0 200 -200 0 200 -200 K a = 5 K a + K c = J+1 K a + K c = J We observed frequency shift by Coriolis interaction ＜Differences between calculation and observation＞ 12

13. Molecular constants Least-squares fitting with 963 lines: negligible perturbation ※ O. Pirali, et al., Phys. Chem. Chem. Phys. 15, 10141 (2013). S 1 B 1u (v 4 =1 ) This work [cm -1 ] A 0.101 380 6 (3) B 0.040 434 0 (2) C 0.028 932 6 (2) D j ×10 9 1.35 (10) D jk ×10 8 -1.26 (5) D k ×10 8 1.52 (4) d j ×10 9 3.51 (8) d k ×10 7 1.03 (1) S 0 A g (v=0) ※ [cm -1 ] A0.104 051 836 (124) B0.041 127 33 (37) C0.029 483 552 (140) D j ×10 9 0.528 (49) D jk ×10 8 0.1206 (145) D k ×10 8 0.5648 (112) d j ×10 9 0.1752 d k ×10 7 0.01951 13

14. Molecular constants Standard deviation: 8 MHz >> 10s of kHz system performance Large deviations of Ground state constants 14 ※ O. Pirali, et al., Phys. Chem. Chem. Phys. 15, 10141 (2013). S 1 B 1u (v 4 =1 ) This work [cm -1 ] A 0.101 380 6 (3) B 0.040 434 0 (2) C 0.028 932 6 (2) D j ×10 9 1.35 (10) D jk ×10 8 -1.26 (5) D k ×10 8 1.52 (4) d j ×10 9 3.51 (8) d k ×10 7 1.03 (1) S 0 A g (v=0) ※ [cm -1 ] A0.104 051 836 (124) B0.041 127 33 (37) C0.029 483 552 (140) D j ×10 9 0.528 (49) D jk ×10 8 0.1206 (145) D k ×10 8 0.5648 (112) d j ×10 9 0.1752 d k ×10 7 0.01951 Least-squares fitting with 963 lines: negligible perturbation

15. Frequency marker To determined precise rotational constants of ground state, we observed other transitions. (ΔJ ≠ 0, ΔK a ≠ 0) [cm -1 ] 33581.00.01.02.03 C 10 H 8 Two Photon Transition [arb.unit] 33580 335853357533570 Band origin A. Nishiyama, et. al., J. Opt. Soc. Am. B 30, 2107 (2013). Wavenumber [cm -1 ] Frequency markers generated from beat signals between two lasers Q(K)Q(J)Q(K)Q(J) Q(K)Q(J)Q(K)Q(J) Naphthalene spectrum in wide frequency range 15 ΔJ = 0, ±2, ΔK a = 0, ±1, ±2 Q(K) S(J), S(K) Q(J), S(K) R(J)

16. 3358133582 16790.516791.5 Wavenumber [cm -1 ] 33580 I 2 Sat. Abs. Intensity [arb.unit] C 10 H 8 Two Photon Transition [arb.unit] f AOM [GHz] f beat [MHz] 40.6 41.2 1.16 1.00 3358333584 Naphthalene spectrum ～ Q(K) S(J) transition S 1 1 B 1u (v 4 =1 : b 1u ) ← S 0 1 A g (v=0) transition Scan rate : 2 MHz/s, Gate time : 0.2 s, Sampling rate：0.4 MHz 16

17. ● We developed a high resolution spectroscopic system with an optical frequency comb ・ High Precision (uncertainty < 100 kHz) ・ High Resolution (linewidth ～ 2.5 MHz) ● We determined molecular constants of the excited state ・ We determine precise rotational constants of ground and excited states. Summary Future plan 17