Abstract

Accurate and spectroscopic measurements of molecular transition frequencies are increasingly being employed in a variety of rigorous tests of physics, including the validity of quantum electrodynamics, the proton–electron mass ratio, and the dipole moment of the electron. Near-infrared molecular transitions may also underpin secondary frequency standards for length metrology and provide convenient wavelength standards for telecommunication and spectroscopy. To report progress in this field, we describe measurements of near-infrared Doppler-broadened carbon dioxide line positions. Our experiment uses cavity ring-down spectroscopy in the linear domain and provides an accurate International System of Units (SI)-traceable frequency axis via active locking of the probe laser and ring-down cavity to a Cs-clock-referenced optical frequency comb. The approach has several key attributes: the ability to rapidly scan the probe laser while maintaining a phase lock to the optical frequency comb, continuously tunable spectrum frequency axes that are not limited by the cavity mode spacing, and high signal-to-noise-ratio spectra resulting in stationary statistics amenable to long-term averaging. This performance is achieved by phase locking a single-mode probe laser to the optical frequency comb, coherent electro-optical phase modulation for rapid cavity mode-to-mode shifting of the probe laser, and sub-kilohertz-level frequency stabilization of the ring-down cavity relative to the probe laser. We report vacuum transition frequencies of five transitions in the $({{30012}}) \leftarrow ({{00001}})$ vibrational band of $^{12}{{\rm{C}}^{16}}{{\rm{O}}_2}$ near 1.57 µm and achieve combined standard uncertainties as low as 212 Hz, corresponding to a relative combined standard uncertainty near ${{10}^{- 12}}$.

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2020 (2)

H. Wu, C.-L. Hu, J. Wang, Y. R. Sun, Y. Tan, A.-W. Liu, and S.-M. Hu, “A well-isolated vibrational state of CO2 verified by near-infrared saturated spectroscopy with kHz accuracy,” Phys. Chem. Chem. Phys. 22, 2841–2848 (2020).
[Crossref]

D. A. Long, Z. D. Reed, A. J. Fleisher, J. Mendonca, S. Roche, and J. T. Hodges, “High accuracy near-infrared carbon dioxide intensity measurements to support remote sensing,” Geophys. Res. Lett. 47, e2019GL086344 (2020).
[Crossref]

2019 (6)

2018 (11)

G. E. Marti, R. B. Hutson, A. Goban, S. L. Campbell, N. Poli, and J. Ye, “Imaging optical frequencies with 100 µHz precision and 1.1 µm resolution,” Phys. Rev. Lett. 120, 103201 (2018).
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F. M. J. Cozijn, P. Dupré, E. J. Salumbides, K. S. E. Eikema, and W. Ubachs, “Sub-Doppler frequency metrology in HD for tests of fundamental physics,” Phys. Rev. Lett. 120, 153002 (2018).
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L. G. Tao, A. W. Liu, K. Pachucki, J. Komasa, Y. R. Sun, J. Wang, and S. M. Hu, “Toward a determination of the proton–electron mass ratio from the lamb-dip measurement of HD,” Phys. Rev. Lett. 120, 153001 (2018).
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V. Andreev, D. G. Ang, D. DeMille, J. M. Doyle, G. Gabrielse, J. Haefner, N. R. Hutzler, Z. Lasner, C. Meisenhelder, B. R. O’Leary, C. D. Panda, A. D. West, E. P. West, X. Wu, and A. Collaboration, “Improved limit on the electric dipole moment of the electron,” Nature 562, 355–360 (2018).
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F. Riehle, P. Gill, F. Arias, and L. Robertsson, “The CIPM list of recommended frequency standard values: guidelines and procedures,” Metrologia 55, 188–200 (2018).
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R. Gotti, M. Prevedelli, S. Kassi, M. Marangoni, and D. Romanini, “Feed-forward coherent link from a comb to a diode laser: application to widely tunable cavity ring-down spectroscopy,” J. Chem. Phys. 148, 054202 (2018).
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J.-M. Hartmann, H. Tran, R. Armante, C. Boulet, A. Campargue, F. Forget, L. Gianfrani, I. Gordon, S. Guerlet, M. Gustafsson, J. T. Hodges, S. Kassi, D. Lisak, F. Thibault, and G. C. Toon, “Recent advances in collisional effects on spectra of molecular gases and their practical consequences,” J. Quant. Spectrosc. Radiat. Transfer 213, 178–227 (2018).
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S. Kassi, T. Stoltmann, M. Casado, M. Daëron, and A. Campargue, “Lamb dip CRDS of highly saturated transitions of water near 1.4 µm,” J. Chem. Phys. 148, 054201 (2018).
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P. Guay, J. Genest, and A. J. Fleisher, “Precision spectroscopy of H13CN using a free-running, all-fiber dual electro-optic frequency comb system,” Opt. Lett. 43, 1407–1410 (2018).
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G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 µm,” Nat. Photonics 12, 202–208 (2018).
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L. Rutkowski, P. Masłowski, A. C. Johansson, A. Khodabakhsh, and A. Foltynowicz, “Optical frequency comb Fourier transform spectroscopy with sub-nominal resolution and precision beyond the Voigt profile,” J. Quant. Spectrosc. Radiat. Transfer 204, 63–73 (2018).
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2017 (11)

I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. F. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J. M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M. A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J. M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. V. Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN2016 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 203, 3–69 (2017).
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E. M. Waxman, K. C. Cossel, G. W. Truong, F. R. Giorgetta, W. C. Swann, S. Coburn, R. J. Wright, G. B. Rieker, I. Coddington, and N. R. Newbury, “Intercomparison of open-path trace gas measurements with two dual-frequency-comb spectrometers,” Atmos. Meas. Tech. 10, 3295–3311 (2017).
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K. Bielska, S. Wójtewicz, P. Morzyński, P. Ablewski, A. Cygan, M. Bober, J. Domysławska, M. Zawada, R. Ciuryło, P. Masłowski, and D. Lisak, “Absolute frequency determination of molecular transition in the Doppler regime at kHz level of accuracy,” J. Quant. Spectrosc. Radiat. Transfer 201, 156–160 (2017).
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G. Insero, S. Borri, D. Calonico, P. C. Pastor, C. Clivati, D. D’Ambrosio, P. De Natale, M. Inguscio, F. Levi, and G. Santambrogio, “Measuring molecular frequencies in the 1–10 µm range at 11-digits accuracy,” Sci. Rep. 7, 12780 (2017).
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R. Gotti, D. Gatti, P. Masłowski, M. Lamperti, M. Belmonte, P. Laporta, and M. Marangoni, “Conjugating precision and acquisition time in a Doppler broadening regime by interleaved frequency-agile rapid-scanning cavity ring-down spectroscopy,” J. Chem. Phys. 147, 134201 (2017).
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B. J. Drouin, “Practical uses of SPFIT,” J. Mol. Spectrosc. 340, 1–15 (2017).
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A. Gambetta, E. Vicentini, Y. Wang, N. Coluccelli, E. Fasci, L. Gianfrani, A. Castrillo, V. Di Sarno, L. Santamaria, P. Maddaloni, P. De Natale, P. Laporta, and G. Galzerano, “Absolute frequency measurements of CHF3 Doppler-free ro-vibrational transitions at 8.6µm,” Opt. Lett. 42, 1911–1914 (2017).
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J. Wang, Y. R. Sun, L.-G. Tao, A.-W. Liu, T.-P. Hua, F. Meng, and S.-M. Hu, “Comb-locked cavity ring-down saturation spectroscopy,” Rev. Sci. Instumr. 88, 043108 (2017).
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J. Wang, Y. R. Sun, L.-G. Tao, A.-W. Liu, and S.-M. Hu, “Communication: molecular near-infrared transitions determined with sub-kHz accuracy,” J. Chem. Phys. 147, 091103 (2017).
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W. B. Cairncross, D. N. Gresh, M. Grau, K. C. Cossel, T. S. Roussy, Y. Ni, Y. Zhou, J. Ye, and E. A. Cornell, “Precision measurement of the electron’s electric dipole moment using trapped molecular ions,” Phys. Rev. Lett. 119, 153001 (2017).
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J. L. Bohn, A. M. Rey, and J. Ye, “Cold molecules: progress in quantum engineering of chemistry and quantum matter,” Science 357, 1002–1010 (2017).
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2016 (6)

S. Borri and G. Santambrogio, “Laser spectroscopy of cold molecules,” Adv. Phys.: X 1, 368–386 (2016).
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L. Santamaria, V. D. Sarno, P. D. Natale, M. D. Rosa, M. Inguscio, S. Mosca, I. Ricciardi, D. Calonico, F. Levi, and P. Maddaloni, “Comb-assisted cavity ring-down spectroscopy of a buffer-gas-cooled molecular beam,” Phys. Chem. Chem. Phys. 18, 16715–16720 (2016).
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N. Nemitz, T. Ohkubo, M. Takamoto, I. Ushijima, M. Das, N. Ohmae, and H. Katori, “Frequency ratio of Yb and Sr clocks with 5 × 10−17 uncertainty at 150 seconds averaging time,” Nat. Photonics 10, 258–261 (2016).
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D. Gatti, R. Gotti, A. Gambetta, M. Belmonte, G. Galzerano, P. Laporta, and M. Marangoni, “Comb-locked Lamb-dip spectrometer,” Sci. Rep. 6, 27183 (2016).
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N. Coluccelli, M. Cassinerio, B. Redding, H. Cao, P. Laporta, and G. Galzerano, “The optical frequency comb fibre spectrometer,” Nat. Commun. 7, 12995 (2016).
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E. Zak, J. Tennyson, O. L. Polyansky, L. Lodi, N. F. Zobov, S. A. Tashkun, and V. I. Perevalov, “A room temperature CO2 line list with ab initio computed intensities,” J. Quant. Spectrosc. Radiat. Transfer 177, 31–42 (2016).
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2015 (9)

J. Burkart, T. Sala, S. Kassi, D. Romanini, and M. Marangoni, “Optical phase cloning by an integrated dual-parallel Mach–Zehnder modulator,” Opt. Lett. 40, 816–819 (2015).
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D. A. Long, S. Wójtewicz, C. E. Miller, and J. T. Hodges, “Frequency-agile, rapid scanning cavity ring-down spectroscopy (FARS-CRDS) measurements of the (30012)←(00001) near-infrared carbon dioxide band,” J. Quant. Spectrosc. Radiat. Transfer 161, 35–40 (2015).
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D. Mondelain, T. Sala, S. Kassi, D. Romanini, M. Marangoni, and A. Campargue, “Broadband and highly sensitive comb-assisted cavity ring down spectroscopy of CO near 1.57µm with sub-MHz frequency accuracy,” J. Quant. Spectrosc. Radiat. Transfer 154, 35–43 (2015).
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H. Lin, Z. D. Reed, V. T. Sironneau, and J. T. Hodges, “Cavity ring-down spectrometer for high-fidelity molecular absorption measurements,” J. Quant. Spectrosc. Radiat. Transfer 161, 11–20 (2015).
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J. Burkart, T. Sala, D. Romanini, M. Marangoni, A. Campargue, and S. Kassi, “Communication: saturated CO2 absorption near 1.6 µm for kilohertz-accuracy transition frequencies,” J. Chem. Phys. 142, 191103 (2015).
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S. A. Tashkun, V. I. Perevalov, R. R. Gamache, and J. Lamouroux, “CDSD-296, high resolution carbon dioxide spectroscopic databank: version for atmospheric applications,” J. Quant. Spectrosc. Radiat. Transfer 152, 45–73 (2015).
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D. Gatti, T. Sala, R. Gotti, L. Cocola, L. Poletto, M. Prevedelli, P. Laporta, and M. Marangoni, “Comb-locked cavity ring-down spectrometer,” J. Chem. Phys. 142, 074201 (2015).
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T. L. Nicholson, S. L. Campbell, R. B. Hutson, G. E. Marti, B. J. Bloom, R. L. McNally, W. Zhang, M. D. Barrett, M. S. Safronova, G. F. Strouse, W. L. Tew, and J. Ye, “Systematic evaluation of an atomic clock at 2 × 10−18 total uncertainty,” Nat. Commun. 6, 6896 (2015).
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B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. Le Coq, and A. Amy-Klein, “Quantum cascade laser frequency stabilization at the sub-Hz level,” Nat. Photonics 9, 456–460 (2015).
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2014 (1)

J. Baron, W. C. Campbell, D. DeMille, J. M. Doyle, G. Gabrielse, Y. V. Gurevich, P. W. Hess, N. R. Hutzler, E. Kirilov, I. Kozyryev, B. R. O’Leary, C. D. Panda, M. F. Parsons, E. S. Petrik, B. Spaun, A. C. Vutha, and A. D. West, “Order of magnitude smaller limit on the electric dipole moment of the electron,” Science 343, 269–272 (2014).
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2013 (4)

A. Cygan, S. Wójtewicz, J. Domysławska, P. Masłowski, K. Bielska, M. Piwiński, K. Stec, R. S. Trawiński, F. Ozimek, C. Radzewicz, H. Abe, T. Ido, J. T. Hodges, D. Lisak, and R. Ciuryło, “Spectral line-shapes investigation with Pound–Drever–Hall-locked frequency-stabilized cavity ring-down spectroscopy,” Eur. Phys. J. 222, 2119–2142 (2013).
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D. A. Long, G. W. Truong, J. T. Hodges, and C. E. Miller, “Absolute 12C16O2 transition frequencies at the kHz-level from 1.6 to 7.8µm,” J. Quant. Spectrosc. Radiat. Transfer 130, 112–115 (2013).
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G.-W. Truong, D. A. Long, A. Cygan, D. Lisak, R. D. V. Zee, and J. T. Hodges, “Comb-linked, cavity ring-down spectroscopy for measurements of molecular transition frequencies at the kHz-level,” J. Chem. Phys. 138, 094201 (2013).
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G. W. Truong, K. O. Douglass, S. E. Maxwell, R. D. van Zee, D. F. Plusquellic, J. T. Hodges, and D. A. Long, “Frequency-agile, rapid scanning spectroscopy,” Nat. Photonics 7, 532 (2013).
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2012 (2)

T. Sala, D. Gatti, A. Gambetta, N. Coluccelli, G. Galzerano, P. Laporta, and M. Marangoni, “Wide-bandwidth phase lock between a CW laser and a frequency comb based on a feed-forward configuration,” Opt. Lett. 37, 2592–2594 (2012).
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X. Huang, D. W. Schwenke, S. A. Tashkun, and T. J. Lee, “An isotopic-independent highly accurate potential energy surface for CO2 isotopologues and an initial 12C16O2 infrared line list,” J. Chem. Phys. 136, 124311 (2012).
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2011 (1)

A. Foltynowicz, P. Maslowski, T. Ban, F. Adler, K. C. Cossel, T. C. Briles, and J. Ye, “Optical frequency comb spectroscopy,” Faraday Discuss. 150, 23–31 (2011).
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2010 (4)

F. Adler, M. J. Thorpe, K. C. Cossel, and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy: technology and applications,” Annu. Rev. Anal. Chem. 3, 175–205 (2010).
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S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus B: Chem. Phys. Meteorol. 62, 759–769 (2010).
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G. Giusfredi, S. Bartalini, S. Borri, P. Cancio, I. Galli, D. Mazzotti, and P. De Natale, “Saturated-absorption cavity ring-down spectroscopy,” Phys. Rev. Lett. 104, 110801 (2010).
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A. Predoi-Cross, W. Liu, R. Murphy, C. Povey, R. R. Gamache, A. L. Laraia, A. R. W. McKellar, D. R. Hurtmans, and V. Malathy Devi, “Measurement and computations for temperature dependences of self-broadened carbon dioxide transitions in the 30012←00001 and 30013←00001 bands,” J. Quant. Spectrosc. Radiat. Transfer 111, 1065–1079 (2010).
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2009 (1)

A. Predoi-Cross, A. R. W. McKellar, D. C. Benner, V. M. Devi, R. R. Gamache, C. E. Miller, R. A. Toth, and L. R. Brown, “Temperature dependences for air-broadened Lorentz half-width and pressure shift coefficients in the 30013←00001 and 30012←00001 bands of CO2 near 1600 nm,” Can. J. Phys. 87, 517–535 (2009).
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2008 (1)

A. Shelkovnikov, R. J. Butcher, C. Chardonnet, and A. Amy-Klein, “Stability of the proton-to-electron mass ratio,” Phys. Rev. Lett. 100, 150801 (2008).
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2007 (2)

V. Malathy Devi, D. C. Benner, L. R. Brown, C. E. Miller, and R. A. Toth, “Line mixing and speed dependence in CO2 at 6348cm−1: positions, intensities, and air- and self-broadening derived with constrained multispectrum analysis,” J. Mol. Spectrosc. 242, 90–117 (2007).
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T. Furtenbacher, A. G. Császár, and J. Tennyson, “MARVEL: measured active rotational–vibrational energy levels,” J. Mol. Spectrosc. 245, 115–125 (2007).
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2006 (2)

J. L. Hall, “Nobel Lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78, 1279–1295 (2006).
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M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595–1599 (2006).
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2005 (4)

D. Jacquemart, R. Gamache, and L. S. Rothman, “Semi-empirical calculation of air-broadened half-widths and air pressure-induced frequency shifts of water-vapor absorption lines,” J. Quant. Spectrosc. Radiat. Transfer 96, 205–239 (2005).
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C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10−17,” Phys. Rev. Lett. 94, 203904 (2005).
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A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30, 3320–3322 (2005).
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J. T. Hodges and R. Ciuryło, “Automated high-resolution frequency-stabilized cavity ring-down absorption spectrometer,” Rev. Sci. Instrum. 76, 023112 (2005).
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2004 (2)

J. T. Hodges, H. P. Layer, W. W. Miller, and G. E. Scace, “Frequency stabilized single mode cavity ringdown apparatus for high resolution absorption spectroscopy,” Rev. Sci. Instrum. 75, 849–863 (2004).
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A. Amy-Klein, H. Vigué, and C. Chardonnet, “Absolute frequency measurement of 12C16O2 laser lines with a femtosecond laser comb and new determination of the 12C16O2 molecular constants and frequency grid,” J. Mol. Spectrosc. 228, 206–212 (2004).
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2002 (2)

2000 (1)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,” Phys. Rev. Lett. 84, 5102–5105 (2000).
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1999 (2)

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the cesium D1 line with a mode-locked laser,” Phys. Rev. Lett. 82, 3568–3571 (1999).
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O. Acef, F. Michaud, and G. D. Rovera, “Accurate determination of OsO4 absolute frequency grid at 28/29 THz,” IEEE Trans. Instrum. Meas. 48, 567–570 (1999).
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1997 (2)

M. A. Gubin and E. D. Protsenko, “Laser frequency standards based on saturated-dispersion lines of methane,” Quantum Electron. 27, 1048–1062 (1997).
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1996 (1)

K. K. Lehmann and D. Romanini, “The superposition principle and cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
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1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
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1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16, 630–631 (1980).
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1976 (1)

J. M. Flaud, C. Camy-Peyret, and J. P. Maillard, “Higher ro-vibrational levels of H2O deduced from high resolution oxygen-hydrogen flame spectra between 2800–6200 cm−1,” Mol. Phys. 32, 499–521 (1976).
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A. Cygan, S. Wójtewicz, J. Domysławska, P. Masłowski, K. Bielska, M. Piwiński, K. Stec, R. S. Trawiński, F. Ozimek, C. Radzewicz, H. Abe, T. Ido, J. T. Hodges, D. Lisak, and R. Ciuryło, “Spectral line-shapes investigation with Pound–Drever–Hall-locked frequency-stabilized cavity ring-down spectroscopy,” Eur. Phys. J. 222, 2119–2142 (2013).
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Abgrall, M.

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K. Bielska, S. Wójtewicz, P. Morzyński, P. Ablewski, A. Cygan, M. Bober, J. Domysławska, M. Zawada, R. Ciuryło, P. Masłowski, and D. Lisak, “Absolute frequency determination of molecular transition in the Doppler regime at kHz level of accuracy,” J. Quant. Spectrosc. Radiat. Transfer 201, 156–160 (2017).
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Abshire, J. B.

S. R. Kawa, J. Mao, J. B. Abshire, G. J. Collatz, X. Sun, and C. J. Weaver, “Simulation studies for a space-based CO2 lidar mission,” Tellus B: Chem. Phys. Meteorol. 62, 759–769 (2010).
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O. Acef, F. Michaud, and G. D. Rovera, “Accurate determination of OsO4 absolute frequency grid at 28/29 THz,” IEEE Trans. Instrum. Meas. 48, 567–570 (1999).
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A. Foltynowicz, P. Maslowski, T. Ban, F. Adler, K. C. Cossel, T. C. Briles, and J. Ye, “Optical frequency comb spectroscopy,” Faraday Discuss. 150, 23–31 (2011).
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B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. Le Coq, and A. Amy-Klein, “Quantum cascade laser frequency stabilization at the sub-Hz level,” Nat. Photonics 9, 456–460 (2015).
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A. Shelkovnikov, R. J. Butcher, C. Chardonnet, and A. Amy-Klein, “Stability of the proton-to-electron mass ratio,” Phys. Rev. Lett. 100, 150801 (2008).
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A. Amy-Klein, A. Goncharov, M. Guinet, C. Daussy, O. Lopez, A. Shelkovnikov, and C. Chardonnet, “Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation,” Opt. Lett. 30, 3320–3322 (2005).
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A. Amy-Klein, H. Vigué, and C. Chardonnet, “Absolute frequency measurement of 12C16O2 laser lines with a femtosecond laser comb and new determination of the 12C16O2 molecular constants and frequency grid,” J. Mol. Spectrosc. 228, 206–212 (2004).
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V. Andreev, D. G. Ang, D. DeMille, J. M. Doyle, G. Gabrielse, J. Haefner, N. R. Hutzler, Z. Lasner, C. Meisenhelder, B. R. O’Leary, C. D. Panda, A. D. West, E. P. West, X. Wu, and A. Collaboration, “Improved limit on the electric dipole moment of the electron,” Nature 562, 355–360 (2018).
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Figures (7)

Fig. 1.
Fig. 1. Overview of the frequency chain realized in the present experiment. The indicated relative uncertainties are those arising from random effects (Type A) and correspond to averaging over the 60-s-long time scale of a single spectrum acquisition. All reported Allan deviations and averaging times throughout the text are based on this averaging time scale. Here, ${f_{\rm{RF}}}$ is the 10 MHz reference frequency provided by the Cs clock, ${f_{{\rm OFC},k}} = \pm$${f\!}$ceo $+ k$ ${f_{\rm{rep}}}$, where ${f\!}$ceo and ${f_{\rm{rep}}}$ are the OFC carrier-envelope offset frequency and repetition rate, ${f_{\rm{ECDL}}}$ is the probe laser, which is frequency-offset locked to OFC comb tooth $k$, and ${f_{{\rm RDC},q}}$ is the frequency of mode-order $q$ of the ring-down cavity, which is locked to the probe laser frequency ${f_{\rm{ECDL}}}$. Adding all terms in the quadrature, the contribution of these effects to the relative combined standard uncertainty in the average cavity mode frequency is ${4.5} \times {{10}^{- 13}}$. For simplicity, we have not shown the contributions of the phase-lock local oscillator frequency ${f_{\rm{LO}}}$ and the shift frequency ${f_{\rm{EO}}}$ of the EOM discussed in the text.
Fig. 2.
Fig. 2. Schematic drawing of the apparatus, showing the comb-locking servo, optical cavity length servo, and electro-optical tuning scheme. PSD, phase-sensitive detector; PD, photodiode; LO, local oscillator; FC, fiber combiner; EOM, electro-optic phase modulator; DAQ, data acquisition.
Fig. 3.
Fig. 3. Time dependence of the open-loop ring-down cavity locking error signal (yellow dots) for linear drift (yellow dashed line) of the cavity length. The triangle wave shows the induced modulation (${\pm}{7.5}\;{\rm{kHz}}$) of the cavity mode frequency caused by translation of the ring-down cavity mirror. The green clusters are triggers induced by bursts of transmitted light from the probe laser and produced by a gate and delay generator. Each trigger cluster has a centroid indicated by the blue dashed lines, which gives the detuning of the cavity mode position during each half-cycle of the length modulation. With the loop closed, the servo feedback signal to the PZT actuator is proportional to the indicated error signal.
Fig. 4.
Fig. 4. Scheme for locking the mean cavity mode position to the excitation laser frequency. The blue curve represents the efficiency with which the excitation laser couples into the ring-down cavity as a function of the frequency detuning between a single-frequency laser and cavity mode, ${{\Delta}}\!f$, as described in the text. We assumed a linewidth of ${{\Gamma}}\!/\!(2\pi) = 1\;{\rm{kHz}}$, corresponding to when the absorption losses equal the cavity base losses. The calculated coupling efficiency neglects the effect of cavity motion on the dynamics of buildup in the cavity field: an appropriate assumption given that, in the present experiment, the cavity time constant (80 µs) is about 40 times smaller than the time to sweep the cavity mode frequency by one halfwidth. The set of triggered transmission bursts (see Fig. 3) for the unlocked case spans a frequency detuning range that is set by the modulation amplitude of the cavity mirror displacement. The burst threshold can be adjusted upward to reduce the frequency span of sampled bursts, at the expense of reducing the capture range of the servo. With the servo engaged, the distribution in frequency detuning of triggered bursts becomes narrower because fluctuations in the cavity length about the sinusoidal length modulation are reduced by the active stabilization. The symmetry of the coupling spectrum combined with the equal probability of triggered bursts above a given threshold ensure that the average frequency detuning $\to 0$ when the cavity lock is engaged. We note that this description can be generalized to a laser source of non-zero bandwidth by convolving the indicated transmission curve with the laser spectrum, leading to a broadening of the former quantity. Provided the excitation spectrum is symmetric about the center frequency and interrogates a single-cavity mode, the locking scheme will be qualitatively the same as depicted.
Fig. 5.
Fig. 5. (Left panel) Relative frequencies ${{\Delta}}\!{f_0} = {f_0} - {\bar f_0}$ (in kHz) determined for approximately 2300 measurements of the R16e transition of the $^{12}{{\rm{C}}^{16}}{{\rm{O}}_2}$ $({{30012}}) \leftarrow ({{00001}})$ vibrational band, measured at nominally 1.6 Pa and 297.0 K. ${{1}}\sigma$ uncertainty bounds are also present as dashed red lines. (Right panel) Histogram of counts of relative position measurements in 2.5 kHz bins, with overlaid normal distribution.
Fig. 6.
Fig. 6. Typical CL-CRDS single-spectrum at a pressure of $p = {1.6}\;{\rm{Pa}}$ and nominally $T = {296.6}\;{\rm{K}}$ of the R16e $^{12}{{\rm{C}}^{16}}{{\rm{O}}_2}$ $({{30012}}) \leftarrow ({{00001}})$ transition, with a spectrum sampling density of 107 MHz. Lower panel, spectral residuals of Voigt profile fit.
Fig. 7.
Fig. 7. Comparison of line center uncertainty, $u({f_0})$, versus signal-to-noise ratio (SNR), determined experimentally (open circles) and by Monte Carlo modeling (red line).

Tables (1)

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Table 1. Uncertainty Budget for the Unperturbed Line Positions k B of the C O 2 ) f 0 Vibrational Band

Equations (2)

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f ¯ q = Δ f ¯ ± f C E O + k f r e p ± f L O ± f E O ,
R ( n σ D / Δ ν s ) 1 / 2 S N R p ( Δ f p / σ D ) e x p ( ( Δ f p / σ D ) 2 / 4 ) ,