K. Iwakuni, H. Sera, M. Abe, and H. Sasada Department of Physics, faculty of Science and Technology, Keio University, Japan 1 70 th. International Symposium on Molecular Spectroscopy June 23, 2015 The University of Illinois TF02

Outline 1. Comb-referenced DFG spectrometer 2. Observed spectra and analysis 3. Assignment and determination of molecular constants 2

ν f rep ECLD Nd:YAG laser 1.06 μm 1.55 μm PPLN 3.4 μm ECAC InSb detector Comb-referenced DFG spectrometer OFC TAI synthesizer Rb clock Pump Signal Idler

The method of absolute frequency measurement of the DFG light 4 ν signal pump f beat2 f beat1 ν n1 = f ceo + n 1 f rep ν n2 = f ceo + n 2 f rep f rep = 67 MHz ・・・ 0 Hz f ceo ν idler Absolute frequency Narrow linewidth (250 kHz → 25 kHz) Repeatability sweep High resolution High accuracy High sensitivity ν DFG = (n 1 ‐ n 2 ) f rep + ( f beat1 – f beat2 ) Rb clock

1.55 μm Comb-referenced +Wavelength-modulation DFG spectrometer ν f rep ECLD Nd:YAG laser 1.06 μm PPLN 3.4 μm ECAC InSb detector synthesizer absolute frequency signal lock in amp. modulation 3 kHz demodulation 3 kHz 21.4 MHz Rb clock

Sub-Doppler resolution spectrum of H 35 Cl R(0) the fundamental vibration band v = 1, J’ = 1 v = 0, J ”= 0 F’ = 1/2 F’ = 5/2 F’ = 3/2 F” = 3/2 R(0) measurement conditions ● sweep step; 0.01 Hz/step (13.1 kHz/step in the mid-infrared frequency) ● averaged over 20 frequency sweeps ● sweep time; 20 ms/step ● pressure; a few mTorr ● measurement time; 20 min. ● linewidth (HWHM); 230 kHz measurement conditions ● sweep step; 0.01 Hz/step (13.1 kHz/step in the mid-infrared frequency) ● averaged over 20 frequency sweeps ● sweep time; 20 ms/step ● pressure; a few mTorr ● measurement time; 20 min. ● linewidth (HWHM); 230 kHz F’ = 3/2 F’ = 5/2 F’ = 1/2 * * * *cross-over resonance Spin of Cl nuclear

* *cross-over resonance * ×2 * * * * * ☆ ΔF ＝ ＋1, ☆ ΔF ＝ 0 ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆☆ ☆ Observed spectra of H 35 Cl * * * ×2 R(1) R(2) ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ ☆ * ×2 * * * * R(3) R(4)

Hamiltonian 8 Vibration energy Rotation energy Electric quadrupole hyperfine interaction Magnetic hyperfine interaction v: vibrational quantum number J: rotational quantum number Bv: rotational constant Dv: centrifugal distortion Hv, Lv: high order centrifugal distortion I: nuclear spin quantum number F: total angular momentum vibrational term value quadrupole coupling constant magnetic coupling constant

Hamiltonian 9 Vibration energy Rotation energy Electric quadrupole hyperfine interaction Magnetic hyperfine interaction vibrational term value quadrupole coupling constant magnetic coupling constant 0 Relative Freq. (reference) f1f1 f2f2

10 Determined molecular constants Analysis: Least-squares method DATA: H 35 Cl; 42 hyperfine-resolved transitions of R(0) to R(4) H 37 Cl; 35 hyperfine-resolved transitions of R(0) to R(3) The ground state constants are fixed at the values determined by Cazzoli*. L 1 is fixed at zero. The weight is taken 1 for all hyperfine-resolved transitions and 0 for unresolved lines. * G. Cazzoli, et. al, JMS 266, 161 (2004) v = 0 (sub-milli- meter data) v = 1

11 H 35 Cl: R(0) transition : Upper level : Lower level The difference of the comb mode number is determined from HITRAN2008. The uncertainly is typically 10 kHz for the lines with S/N higher than 4. The pressure shift is less than the measurement uncertainty. All ΔF = ±1, 0 transitions are observed.,,

: Upper level : Lower level H 35 Cl: R(1) transition All ΔF = +1, 0 transitions are observed. Any ΔF = – 1 transitions are not observed, but the frequencies can be experimentally determined. : weight 0 *,,

H 35 Cl: R(2) transition All ΔF = +1, 0 transitions are observed. Any ΔF = – 1 transitions are not observed, but the frequencies can be experimentally determined. : weight 0 * : Upper level : Lower level,,

H 35 Cl: R(3) transition All ΔF = +1, 0 transitions are observed. Any ΔF = – 1 transitions are not observed, but the frequencies can be experimentally determined. : weight 0 * : Upper level : Lower level,,

15 H 35 Cl: R(4) transition All ΔF = +1 transitions are observed. The frequencies of ΔF = 0 transitions are determined from that of the cross-over resonances. The frequencies of ΔF = – 1 transitions can be calculated. : weight 0 * : Upper level : Lower level,,

16 Determined molecular constants * G. Cazzoli, et. al, JMS 266, 161 (2004) *. The standard deviation: 10.1 kHz

Summary Transition frequencies of ΔF = ±1, 0 of R(0)-R(4) for H 35 Cl and R(0)- R(3) for H 37 Cl are determined with a typical uncertainty of 10 kHz using the comb-referenced DFG spectrometer. Six molecular constants are determined with a standard deviation of 10.1 kHz. The absolute frequency measurements and the assignment of absorption lines are consistent, and the model Hamiltonian is accurate enough to reproduce the measured transition frequencies. 17 Acknowledgments This research is financially supported by Grand-in-Aid for Scientific Research (A), the Photon Frontier Network Program of the Ministry of Education, Culture, Sports, Science and Technology, and JST, ERATO, MINOSHIMA Intelligent Optical Synthesizer Project Japan. Kana Iwakuni et. al, JMS 306 (2014) 19-25, Hyperfine-resolved transition frequency list of fundamental vibration bands of H 35 Cl and H 37 Cl