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

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

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

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 10-3 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

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, 154308 (2008)

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

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, 063107 (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

Very accurate line shape measurements Sources of systematic errors in CRDS absorption axis spectrum with signal-to-noise ratio = 220 000 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 = 75 700 Speed-Dependent Billiard-Ball Profile* Incomplete light extinction in cw-CRDS distortion and phase noise on the decay QF = 92 650 FS-CRDS, SNR = 1 500 000 (NIST) P8 (3←0) 12C16O at 6316.7509 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, 022508 (2012); P. Wcisło, et al., Phys. Rev. A 88, 012517 (2013) S. Wójtewicz, et al., Phys. Rev. A 84, 032511 (2011) D. A. Long et al., Proc. SPIE 8726, 872600 (2013)

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

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) 045501

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, 214202 (2016) A. Cygan et al., Meas. Sci. Technol. 27 (2016) 045501

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, 214202 (2016)

Frequency references for spectroscopy Sr optical lattice clock: stability ~ 10-17 ( 10-14 @ 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 ( < 10-12 @ 1 s) P7 P7 line of O2 B-band line center frequency 434 783.508 485 7 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, 17495 (2015) K. Bielska et al., J. Phys. Conf. Ser. 810 (2017); 012024

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

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 = 187 104 300.038 (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) 184309. D. Mondelain et al. J. Molec. Spectrosc. 326 (2016) 5–8 M. Puchalski, J. Komasa, K. Pachucki, arXiv:1704.07153v1

Prospects for future D. Mondelain et al., J Mol. Spec. 326 (2016) 5 mirror reflectivity R = 0.9999917, cavity length Lcav = 1.4 m effective optical path = 170 km Our cavity: mirror reflectivity R = 0.999917, 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

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