1. WK14
22 June 2016, International Symposium on Molecular Spectroscopy, Champaign-Urbana, Illinois
OBSERVATION OF ORTHO-PARA DEPENDENCE OF PRESSURE SHIFT AND BROADENING COEFFICIENT IN ACETYLENE ν1+ν3 VIBRATION BAND USING DUAL-COMB SPECTROSCOPY
Kana Iwakuni,1,2,5 , Sho Okubo,2,5 Koichi M. T. Yamada,3 Hajime Inaba,2,5 Atsushi Onae,2,5 Feng-Lei Hong,2,4,5 Hiroyuki Sasada1,5
1. Keio Univ., 2. NMIJ AIST, 3. EMRI AIST, 4. Yokohama National Univ., 5. JST ERATO “MINOSHIMA Intelligent Optical Synthesizer Project”

2. Pressure effects in molecular spectrum
Pressure effects due to collisions
Line broadening
Center frequency shift
Line Broadening
Center frequency shift

3. How to observe the pressure effects
CW laser spectroscopy
Molecular absorption
CW laser
Photo detector
Frequency sweep signal
Good
Bad
Good signal-to-noise ratio (SNR)
High resolution
Take a long time to record the spectral lines one by one
Difficult to maintain the pressure condition
Narrow tunable range

4. How to observe the pressure effects
Fourier transform IR spectroscopy (FTIR)
White light source
Delay stage
Fourier transform
Transmittance
Frequency
mirror
Good
Bad
Record all spectral lines in a band simultaneously
Low resolution and accuracy
Take a long time to obtain good SNR and high resolution

5. Spectroscopy using optical frequency comb
frep
Frequency
Frequency step is determined by repetition rate frep. (50 MHz)
Broad spectral coverage over 1 octave.
frep
Frequency
Accurate horizontal axis guaranteed by frequency references.
H-maser, Rb clock, etc.

6. Dual-comb spectroscopy
1/Δfrep
Signal comb
(for detection)
Molecular absorption
frep,S
Local comb
(for readout)
Optical signal is converted to RF signal.
frep,L = frep,S − Δfrep
Two combs have slightly different repetition rates.
Absorption of signal comb is detected by the interference (RF) signal with local comb.
Minimum acquisition time is 1/Δfrep.

7. Setup frep: 48 MHz Δfrep: 33 or 45 Hz Signal comb C2H2 cell
(for detection)
C2H2 cell
External freq.
reference
(CW laser)
frep,S
Local comb
(for readout)
frep,L = frep,S − Δfrep
frep: 48 MHz
Δfrep: 33 or 45 Hz
Averaging: 10,000 times (222 or 303 s)

8. Observed spectrum of ν1+ν3 vibration band of 12C2H2
even J”
para
para
nuclear spin statistical weight;
3 : 1 for odd J” : even J”
odd J”
ortho
ortho
ortho
𝐽 " : angular momentum quantum number
of the lower level

9. Voigt fitting to determine Lorentzian width and shift
R(9) 60 Pa
𝑉 𝜈,𝛿𝜈,Δ𝐿,Δ𝐺 : Voigt function
𝜎: Line intensity factor
𝛿𝜈: Center frequency shift
Δ𝐿: Lorentzian width
Δ𝐺: Gaussian width (fixed)
Fitting function
𝑔 𝜈 = 𝑎 0 + 𝑎 1 𝜈 exp −𝜎𝑉 𝜈,𝛿𝜈,Δ𝐿,Δ𝐺
We analyzed for from P(26) to R(29) with 6 different sample pressures.

10. Broadening coefficients
𝑚= −𝐽" (for 𝑃−branch) 𝐽"+1 (for 𝑅−branch)

11. Broadening coefficients
Broadening coefficients alternatively vary as 𝑚 (or 𝐽")
Spin statistical weight-independent part*
𝑓 0 𝑚 = 𝛼 1 + 𝛼 2 𝑚 + 𝛼 3 exp − 𝛼 4 𝑚
Fitting function
𝑏 𝑚 = 𝑓 0 𝑚 + 𝑓 1 (𝑚)
*Kusaba and Henningsen, JMS 209, 216 (2001)
Spin statistical weight-dependent part
𝑓 1 𝑚 = 𝛽 1 2𝐽"+1 𝑔 𝐼 exp − ℎ𝐵𝐽" 𝐽"+1 𝑘 B 𝑇
nuclear spin statistical weight
𝑔 𝐼 = 3 (for odd 𝐽" ) 1 (for even 𝐽")

12. Broadening coefficients
Good agreement especially in the R-branch (due to good SNR).
Spin-dependence suggests that molecules in the same 𝐽" have larger collisional cross-section.

13. Shift coefficients
𝑚= −𝐽" (for 𝑃−branch) 𝐽"+1 (for 𝑅−branch)

14. Shift coefficients 𝑠 𝑚 = 𝑑 −1 𝑚 −1 + 𝑑 0 + 𝑑 1 𝑚+ 𝑑 2 𝑚 2
Ortho/para dependence is not apparently observed because the shift is one order of magnitude smaller than the broadening.
Fitting function
𝑠 𝑚 = 𝑑 −1 𝑚 −1 + 𝑑 0 + 𝑑 1 𝑚+ 𝑑 2 𝑚 2
𝒎 −𝟏 term
Impact theory predicts that there is a gap in the pressure shift coefficient between the P(1) and R(0) transitions.*
*For example, Townes and Schawlow, “Microwave Spectroscopy” (1955).

15. Shift coefficients
The P(2)–R(1) (−2≤𝑚≤2) are not included for fitting because they have overlapping transitions and center frequency cannot be precisely determined.

16. Summary
Pressure-broadening and -shift coefficients of the ν1+ν3 band of 12C2H2 are determined by using dual-comb spectroscopy.
Ortho/para dependence of pressure broadening coefficient is observed for the first time.
Dual-comb spectroscopy is a powerful tool to carry out broadband spectroscopy with high precision and short time measurement.

17. Collaborators K. Iwakuni H. Sasada F.-L. Hong Japan Science and
Technology Agency (JST),
Exploratory Research
for Advanced Technology (ERATO)
S. Okubo
A. Onae
H. Inaba
K. M. T. Yamada

18. Comparison with the previous work*
*Kusaba and Henningsen, JMS 209, 216 (2001)

19. Frequency domain picture
frep,S
Δfrep
2Δfrep
frep,L
Signal comb
Optical
Local comb
Frequency
Beat detection
Δfrep RF
Δfrep
2Δfrep
Frequency