1. Nicolaus Copernicus University, Institute of Physics, Toruń, Poland
Cavity-enhanced spectroscopy of molecular hydrogen with absolute frequency axis
Daniel Lisak
Nicolaus Copernicus University, Institute of Physics, Toruń, Poland

2. Motivation High-accuracy unperturbed H2, HD, D2 transition frequencies
Testing QED calculations of molecular energy levels
Searching for new physics beyond Standard Model
Testing spectral line shape models & potential energy surfaces

3. Motivation
Various approaches to measure very weak (ro)vibrational transitions in H2, HD, D2
Combination of electronic transitions, Doppler-free
Cavity-enhanced spectroscopy of rovibrational transitions
Doppler-free saturation dip spectroscopy – not done yet, potentially most accurate
Doppler-broadened spectroscopy – signal-to-noise ratio vs collisional line shape effects
low pressure – Doppler regime, Voigt profile
high pressure – collisional line-shape effects, high signal-to-noise ratio
molecular beam
two-photon transitions

4. Doppler-broadened line shape of molecular hydrogen
Zero-pressure line position cannot be determined as a simple linear extrapolation from measurements at higher pressures
Proper line shape is critical for Doppler-limited spectroscopy of H2 at level of accuracy below cm-1
speed-dependence of collisional width and shift
proper model of velocity-changing collisions
standard semi-classical models e.g. partially correlated speed-dependent hard-collision PCSDNGP (HTP) can reproduce H2 spectra to ~2% accuracy
Nonlinear behavior of the line position with pressure for the H2 Q(1) fundamental line caused by collisional line shape effects. Red – symmetric profile, blue –SDBBP peaks
line position different by 10-3 cm-1, depending on line shape model

5. Doppler-broadened line shape of molecular hydrogen
(2002)
Speed-dependent biliard-ball profile (SDBBP)
ab initio speed-dependence of collisional broadening and shifting
collaboration with Franck Thibault
method
γ(v)
δ(v)
fM (v)
g(v) & d(v) for S(2) line from (2 – 0) band for D2 - D2 collisions
PES: R.J. Hinde, J. Chem. Phys. 128, (2008)

6. Doppler-broadened line shape of molecular hydrogen
applicability of rigid sphere potential (BBP) for velocity-changing collisions verified by classical molecular dynamics simulations
anisotropy of potential neglected for velocity-changing collisions
good agreement of collisional kernels from BB model and CMDS
hard-collision model can’t properly descibe velocity-changing collisions – no angle dependence
speed-dependence of collisional width and shift calculated from ab initio PES
collision energy
collisional kernels - rate of the molecule velocity change from vi before collision to vj after collision, for angle θk between vi and vj = 36°, 90°, and 144°
grey – hard-collision model
(a) - Maxwell-Boltzmann collision energy distribution
(b) - Lennard-Jones potential for H2-H2 approximated by rigid sphere repulsion

7. Cavity ring-down spectroscopy (FS-CRDS)
absorption from decay time
empty cavity
with absorber
Advantages of cavity enhanced spectroscopy
long optical path in the cavity  high sensitivity
high spectral resolution  limited by mode width
in CRDS - insensitivity to laser power variations  absorption from time measurement
1/(ct) = a0 + a(n)
Frequency-Stabilized CRDS (FS-CRDS)
 active control of the cavity length drift
Frequency reference
J. T. Hodges, et al., Rev. Sci. Instrum. 75, 849 (2004)
laser phase-locked to the cavity
(laser linewidth reduction)
PDH lock
low-bandwidth lock
PDH-locked FS-CRDS
A. Cygan, et al., Rev. Sci. Instrum. 82, (2011)
TEM00 modes only
increase of power
increase of RD
repetition rate
decrease of systematic errors
caused by cavity drift
resolution limited by stability
of the frequency reference

8. Very accurate line shape measurements
Sources of systematic errors in CRDS absorption axis
spectrum with signal-to-noise ratio =
Nonlinearity of detection system
High SNR spectra for testing advanced line-shape models
© R. Ciuryło
quality of the fit
QF = (amax – amin)/SR
SDNGP: QF =
Speed-Dependent Billiard-Ball Profile*
Incomplete light extinction in cw-CRDS
distortion and phase noise on the decay
QF =
FS-CRDS, SNR = (NIST)
P8 (3←0) 12C16O
at  cm−1
SDNGP fit
Even higher SNR demonstrated recently at NIST:
H. Lin, et al, JQSRT 161, 11 (2015)
Etalon fringes
A. Cygan, et al., Phys. Rev. A 85, (2012);
P. Wcisło, et al., Phys. Rev. A 88, (2013)
S. Wójtewicz, et al., Phys. Rev. A 84, (2011)
D. A. Long et al., Proc. SPIE 8726, (2013)

9. Cavity-enhanced spectroscopy methods
With absorber in the cavity, its modes are spectrally broadened due to the absorption and shifted due to dispersion. t

10. Frequency-stabilized cavity ring-down spectroscopy (FS-CRDS)
active control of the cavity length
dual-beam – continuous lock
PDH-locked probe laser
CRDS, CMWS, CMDS spectra
linked to optical frequency comb
referenced to primary frequency standard (UTC-AOS)
A. Cygan et al., Meas. Sci. Technol. 27 (2016)

11. Evaluation of experimental line shape distortion
Complex (absorption, dispersion) line shape fits enable CRDS spectra validation
line center for R24 line, CO (3 – 0) band
u(v0) = 55 kHz
Differences between line centers from 3 methods, FS-CRDS, CMWS, 1D-CMDS, provide estimation of systematic instrumental uncertainty
line shape distortion error u(v0) = 47 kHz (1.6 x 10-6 cm-1)
A. Cygan et al. J. Chem. Phys. 144, (2016)
A. Cygan et al., Meas. Sci. Technol. 27 (2016)

12. Frequency-stabilized cavity ring-down spectroscopy (FS-CRDS)
Stability and accuracy of absolute frequency measurements < 1 kHz
pressure gauge uncertainty 0.05%
laser linewidth < 40 Hz
Active temperature control of the cavity:
T stability < 10 mK
T gradient < 20 mK
A. Cygan et al. J. Chem. Phys. 144, (2016)

13. Frequency references for spectroscopy
Sr optical lattice clock: stability ~ 10-17
( 1 s)
P7 P7 line of O2 B-band
very symmetric line shape
National Lab. FAMO, Toruń
molecular spectroscopy with Hz-level uncertainty of absolute frequency axis
line position of Doppler broadened line shape with kHz-level uncertainty – if the line shape model is known
Coordinated universal time UTC(AOS)
stability ~ 10-15
( < 1 s)
P7 P7 line of O2 B-band
line center frequency
GHz
st. uncertainty = 8.5 kHz
relative st. uncert. < 2 × 10-11
Astrogeodynamic Observatory of Space Research Center, Borowiec
P. Morzyński et al., Sci. Rep. 5, (2015)
K. Bielska et al., J. Phys. Conf. Ser. 810 (2017);

14. Results for D2 S(2) line from (2 – 0) band
Comparison of CRDS spectra fitted with:
ab initio line shape – SDBBP
phenomenological line shape – PCSDHCP with quadratic SD (HTP)
multi-specrum fit with similar number of fitted parameters
SDBBP – more than order of magnitude lower fit residuals

15. Results for D2 S(2) line from (2 – 0) band
Comparison of our line position with available experimental and theoretical data
unperturbed line position:
v0 = (391) MHz
Uncertainty budget for the line position
type
value
A: statistical (1σ)
132 kHz
Optical frequency comb (A+B)
< 1 kHz
line-shape analysis (B) 10%-uncertainty of fixed parameters
365 kHz
Instrumental systematic shift (B)
47 kHz
Relativistic asymmetry (B)
3 kHz
Combined A & B
391 kHz
M. Gupta, et al, Chem. Phys. Lett. 441 (2007) 204
S. Kassi, et al, J. Chem. Phys. 136 (2012)
D. Mondelain et al. J. Molec. Spectrosc. 326 (2016) 5–8
M. Puchalski, J. Komasa, K. Pachucki, arXiv: v1

16. Prospects for future
D. Mondelain et al., J Mol. Spec. 326 (2016) 5
mirror reflectivity R = ,
cavity length Lcav = 1.4 m
effective optical path = 170 km
Our cavity:
mirror reflectivity R = ,
cavity length Lcav = 0.7 m
effective optical path = 8.8 km (20 x lower)
We have already 391 kHz combined standard uncertainty
Further room for improvements:
Lcav R
higher finesse = longer optical path → lower pressure → ab initio line shape will give even lower v0 uncertainty
improved ab initio calculation of speed dependence with new PES
other experimental methods (CMWS, 1D-CMDS) for spectra validation
Positions and half-widths of the cavity modes measured with uncertainty < 1 Hz

17. Co-authors & collaborators
Toruń, Poland
Co-authors & collaborators
Nicolaus Copernicus University, Toruń
Piotr Wcisło
Mikołaj Zaborowski
Szymon Wojtewicz
Agata Cygan
Grzegorz Kowzan
Piotr Masłowski
Daniel Lisak
Roman Ciuryło
Franck Thibault, Universite de Rennes
Financial support:
National Science Centre, Poland, Projects Nos.
2015/19/D/ST2/02195, DEC-2013/11/D/ST2/02663, 2015/17/B/ST2/02115 and DEC-2012/05/D/ST2/01914
COST Action CM1405 MOLIM
French-Polish "Programm Hubert Curien" POLONIUM
Foundation for Polish Science HOMING PLUS