Abstract

There is an increasing demand for precise molecular spectroscopy, in particular in the mid-infrared (MIR) fingerprint window that hosts a considerable number of vibrational signatures, whether it be for modeling our atmosphere, interpreting astrophysical spectra, or testing fundamental physics. We present a high-resolution MIR spectrometer traceable to primary frequency standards. It combines a widely tunable ultra-narrow quantum cascade laser (QCL), an optical frequency comb, and a compact multipass cell. The QCL frequency is stabilized onto a comb controlled with a remote near-infrared ultra-stable laser, transferred through a fiber link. The resulting QCL frequency stability is below 1015 from 0.1 to 10 s, and its frequency uncertainty of 4×1014 is given by the remote frequency standards. Continuous tuning over 400MHz is reported. We use the apparatus to perform saturated absorption spectroscopy of methanol in the low-pressure multipass cell and demonstrate a statistical uncertainty at the kilohertz level on transition center frequencies, confirming its potential for driving the next generation technology required for precise spectroscopic measurements.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (8)

ACME Collaboration, “Improved limit on the electric dipole moment of the electron,” Nature 562, 355–360 (2018).
[Crossref]

M. Lamperti, B. AlSaif, D. Gatti, M. Fermann, P. Laporta, A. Farooq, and M. Marangoni, “Absolute spectroscopy near 7.8  μm with a comb-locked extended-cavity quantum-cascade-laser,” Sci. Rep. 8, 1292 (2018).
[Crossref]

E. Vicentini, A. Gambetta, N. Coluccelli, E. Fasci, A. Castrillo, L. Gianfrani, V. Di Sarno, P. Maddaloni, A. Ceausu-Velcescu, P. De Natale, Y. Wang, T. T. Fernandez, P. Laporta, and G. Galzerano, “Rovibrational fine structure and transition dipole moment of CF3H by frequency-comb-assisted saturated spectroscopy at 8.6 μm,” J. Quant. Spectrosc. Radiat. Transfer 217, 373–379 (2018).
[Crossref]

D. Xu, W.-K. Lee, F. Stefani, O. Lopez, A. Amy-Klein, and P.-E. Pottie, “Studying the fundamental limit of optical fiber links to the 10-21 level,” Opt. Express 26, 9515–9527 (2018).
[Crossref]

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. A. Kocheril, C. R. Markus, A. M. Esposito, A. W. Schrader, T. S. Dieter, and B. J. McCall, “Extended sub-Doppler resolution spectroscopy of the ν3 band of methane,” J. Quant. Spectrosc. Radiat. Transfer 215, 9–12 (2018).
[Crossref]

F. Guillou-Camargo, V. Ménoret, E. Cantin, O. Lopez, N. Quintin, E. Camisard, V. Salmon, J.-M. L. Merdy, G. Santarelli, A. Amy-Klein, P.-E. Pottie, B. Desruelle, and C. Chardonnet, “First industrial-grade coherent fiber link for optical frequency standard dissemination,” Appl. Opt. 57, 7203–7210 (2018).
[Crossref]

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, 1–5 (2018).
[Crossref]

2017 (12)

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).
[Crossref]

J. Karhu, M. Vainio, M. Metsälä, and L. Halonen, “Frequency comb assisted two-photon vibrational spectroscopy,” Opt. Express 25, 4688–4699 (2017).
[Crossref]

S. K. Tokunaga, R. J. Hendricks, M. R. Tarbutt, and B. Darquié, “High-resolution mid-infrared spectroscopy of buffer-gas-cooled methyltrioxorhenium molecules,” New J. Phys. 19, 053006 (2017).
[Crossref]

S. Truppe, H. J. Williams, M. Hambach, L. Caldwell, N. J. Fitch, E. A. Hinds, B. E. Sauer, and M. R. Tarbutt, “Molecules cooled below the Doppler limit,” Nat. Phys. 13, 1173–1176 (2017).
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I. Kozyryev, L. Baum, K. Matsuda, B. L. Augenbraun, L. Anderegg, A. P. Sedlack, and J. M. Doyle, “Sisyphus laser cooling of a polyatomic molecule,” Phys. Rev. Lett. 118, 173201 (2017).
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X. Xie, R. Bouchand, D. Nicolodi, M. Lours, C. Alexandre, and Y. L. Coq, “Phase noise characterization of sub-hertz linewidth lasers via digital cross correlation,” Opt. Lett. 42, 1217–1220 (2017).
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M. Daprà, C. Henkel, S. A. Levshakov, K. M. Menten, S. Muller, H. L. Bethlem, S. Leurini, A. V. Lapinov, and W. Ubachs, “Testing the variability of the proton-to-electron mass ratio from observations of methanol in the dark cloud core L1498,” Mon. Not. R. Astron. Soc. 472, 4434–4443 (2017).
[Crossref]

W.-K. Lee, F. Stefani, A. Bercy, O. Lopez, A. Amy-Klein, and P.-E. Pottie, “Hybrid fiber links for accurate optical frequency comparison,” Appl. Phys. B 123, 161 (2017).
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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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W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119, 243601 (2017).
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G. Insero, S. Borri, D. Calonico, P. C. Pastor, C. Clivati, D. D’Ambrosio, P. 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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J. Eills, J. W. Blanchard, L. Bougas, M. G. Kozlov, A. Pines, and D. Budker, “Measuring molecular parity nonconservation using nuclear-magnetic-resonance spectroscopy,” Phys. Rev. A 96, 042119 (2017).
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2016 (5)

B. Lankhaar, G. C. Groenenboom, and A. van der Avoird, “Hyperfine interactions and internal rotation in methanol,” J. Chem. Phys. 145, 244301 (2016).
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C. Cheng, A. P. P. van der Poel, P. Jansen, M. Quintero-Pérez, T. E. Wall, W. Ubachs, and H. L. Bethlem, “Molecular fountain,” Phys. Rev. Lett. 117, 253201 (2016).
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A. Prehn, M. Ibrügger, R. Glöckner, G. Rempe, and M. Zeppenfeld, “Optoelectrical cooling of polar molecules to submillikelvin temperatures,” Phys. Rev. Lett. 116, 063005 (2016).
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T. Kobayashi, D. Akamatsu, K. Hosaka, H. Inaba, S. Okubo, T. Tanabe, M. Yasuda, A. Onae, and F.-L. Hong, “Absolute frequency measurements and hyperfine structures of the molecular iodine transitions at 578  nm,” J. Opt. Soc. Am. B 33, 725–734 (2016).
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J. Biesheuvel, J.-P. Karr, L. Hilico, K. S. E. Eikema, W. Ubachs, and J. C. J. Koelemeij, “Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD+,” Nat. Commun. 7, 10385 (2016).
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2015 (8)

F. Stefani, O. Lopez, A. Bercy, W.-K. Lee, C. Chardonnet, G. Santarelli, P.-E. Pottie, and A. Amy-Klein, “Tackling the limits of optical fiber links,” J. Opt. Soc. Am. B 32, 787–797 (2015).
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J. C. Pearson, A. M. Daly, and R. M. Lees, “Unraveling torsional bath interactions with the CO stretching state in methanol,” J. Mol. Spectrosc. 318, 70–77 (2015).
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L. H. Coudert, C. Gutlé, T. R. Huet, J. U. Grabow, and S. A. Levshakov, “Spin-torsion effects in the hyperfine structure of methanol,” J. Chem. Phys. 143, 044304 (2015).
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O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Physique 16, 531–539 (2015).
[Crossref]

B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. L. Coq, and A. Amy-Klein, “Quantum cascade laser frequency stabilization at the sub-Hz level,” Nat. Photonics 9, 456–460 (2015).
[Crossref]

M. G. Hansen, E. Magoulakis, Q.-F. Chen, I. Ernsting, and S. Schiller, “Quantum cascade laser-based mid-IR frequency metrology system with ultra-narrow linewidth and 1×10-13-level frequency instability,” Opt. Lett. 40, 2289–2292 (2015).
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S. Mejri, P. L. T. Sow, O. Kozlova, C. Ayari, S. K. Tokunaga, C. Chardonnet, S. Briaudeau, B. Darquié, F. Rohart, and C. Daussy, “Measuring the Boltzmann constant by mid-infrared laser spectroscopy of ammonia,” Metrologia 52, S314 (2015).
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P. Cancio Pastor, I. Galli, G. Giusfredi, D. Mazzotti, and P. De Natale, “Testing the validity of Bose-Einstein statistics in molecules,” Phys. Rev. A 92, 063820 (2015).
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2014 (4)

P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquié, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
[Crossref]

F. Rohart, S. Mejri, P. L. T. Sow, S. K. Tokunaga, C. Chardonnet, B. Darquié, H. Dinesan, E. Fasci, A. Castrillo, L. Gianfrani, and C. Daussy, “Absorption-line-shape recovery beyond the detection-bandwidth limit: application to the precision spectroscopic measurement of the Boltzmann constant,” Phys. Rev. A 90, 042506 (2014).
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A. Bercy, F. Stefani, O. Lopez, C. Chardonnet, P.-E. Pottie, and A. Amy-Klein, “Two-way optical frequency comparisons at 5×10-21 relative stability over 100-km telecommunication network fibers,” Phys. Rev. A 90, 061802 (2014).
[Crossref]

P. Jansen, H. L. Bethlem, and W. Ubachs, “Perspective: tipping the scales: search for drifting constants from molecular spectra,” J. Chem. Phys. 140, 010901 (2014).
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2013 (5)

B. Chanteau, O. Lopez, W. Zhang, D. Nicolodi, B. Argence, F. Auguste, M. Abgrall, C. Chardonnet, G. Santarelli, B. Darquié, Y. L. Coq, and A. Amy-Klein, “Mid-infrared laser phase-locking to a remote near-infrared frequency reference for high-precision molecular spectroscopy,” New J. Phys. 15, 073003 (2013).
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R. Le Targat, L. Lorini, Y. Le Coq, M. Zawada, J. Guéna, M. Abgrall, M. Gurov, P. Rosenbusch, D. G. Rovera, B. Nagórny, R. Gartman, P. G. Westergaard, M. E. Tobar, M. Lours, G. Santarelli, A. Clairon, S. Bize, P. Laurent, P. Lemonde, and J. Lodewyck, “Experimental realization of an optical second with Strontium lattice clocks,” Nat. Commun. 4, 2109 (2013).
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S. K. Tokunaga, C. Stoeffler, F. Auguste, A. Shelkovnikov, C. Daussy, A. Amy-Klein, C. Chardonnet, and B. Darquié, “Probing weak force induced parity violation by high resolution mid-infrared molecular spectroscopy,” Mol. Phys. 111, 2363–2373 (2013).
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S. Truppe, R. J. Hendricks, S. K. Tokunaga, H. J. Lewandowski, M. G. Kozlov, C. Henkel, E. A. Hinds, and M. R. Tarbutt, “A search for varying fundamental constants using hertz-level frequency measurements of cold CH molecules,” Nat. Commun. 4, 2600 (2013).
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I. Galli, M. Siciliani de Cumis, F. Cappelli, S. Bartalini, D. Mazzotti, S. Borri, A. Montori, N. Akikusa, M. Yamanishi, G. Giusfredi, P. Cancio, and P. De Natale, “Comb-assisted subkilohertz linewidth quantum cascade laser for high-precision mid-infrared spectroscopy,” Appl. Phys. Lett. 102, 121117 (2013).
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2012 (5)

2011 (3)

J. B. McManus, M. S. Zahniser, and D. D. Nelson, “Dual quantum cascade laser trace gas instrument with astigmatic Herriott cell at high pass number,” Appl. Opt. 50, A74–A85 (2011).
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J. J. Hudson, D. M. Kara, I. J. Smallman, B. E. Sauer, M. R. Tarbutt, and E. A. Hinds, “Improved measurement of the shape of the electron,” Nature 473, 493–496 (2011).
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J. J. Harrison, P. F. Bernath, and G. Kirchengast, “Spectroscopic requirements for ACCURATE, a microwave and infrared-laser occultation satellite mission,” J. Quant. Spectrosc. Radiat. Transfer 112, 2347–2354 (2011).
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2010 (2)

M. Guinet, D. Mondelain, C. Janssen, and C. Camy-Peyret, “Laser spectroscopic study of ozone in the 100←000 band for the SWIFT instrument,” J. Quant. Spectrosc. Radiat. Transfer 111, 961–972 (2010).
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Z. X. Jiu, D. L. Zuo, L. Miao, Z. H. Cheng, and C. C. Qi, “Pulsed CH3OH terahertz laser emission pumped by a TEA CO2 laser,” J. Infrared Millim. Terahz. Waves 31, 885–891 (2010).
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2009 (1)

E. Herbst and E. F. van Dishoeck, “Complex organic interstellar molecules,” Annu. Rev. Astron. Astrophys. 47, 427–480 (2009).
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2008 (2)

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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H. L. Bethlem, M. Kajita, B. Sartakov, G. Meijer, and W. Ubachs, “Prospects for precision measurements on ammonia molecules in a fountain,” Eur. Phys. J. Spec. Top. 163, 55–69 (2008).
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2007 (4)

F. Bielsa, A. Douillet, T. Valenzuela, J.-P. Karr, and L. Hilico, “Narrow-line phase-locked quantum cascade laser in the 9.2  μm range,” Opt. Lett. 32, 1641–1643 (2007).
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S. T. Dawkins, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918–925 (2007).
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J. C. J. Koelemeij, B. Roth, A. Wicht, I. Ernsting, and S. Schiller, “Vibrational spectroscopy of HD+ with 2-ppb accuracy,” Phys. Rev. Lett. 98, 173002 (2007).
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N. Vanhaecke and O. Dulieu, “Precision measurements with polar molecules: the role of the black body radiation,” Mol. Phys. 105, 1723–1731 (2007).
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2006 (2)

Z.-D. Sun, R. M. Lees, and L.-H. Xu, “Saturation-dip measurements for the ν8 C-O stretching band of CH3OH with a CO2-laser-microwave-sideband spectrometer,” J. Opt. Soc. Am. B 23, 2398–2417 (2006).
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E. R. Hudson, H. J. Lewandowski, B. C. Sawyer, and J. Ye, “Cold molecule spectroscopy for constraining the evolution of the fine structure constant,” Phys. Rev. Lett. 96, 143004 (2006).
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2004 (1)

L.-H. Xu, R. M. Lees, P. Wang, L. R. Brown, I. Kleiner, and J. W. C. Johns, “New assignments, line intensities, and HITRAN database for CH3OH at 10  μm,” J. Mol. Spectrosc. 228, 453–470 (2004).
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2003 (1)

Z.-D. Sun, T. Mizuochi, M. Kaneko, Y. Moriwaki, F. Matsushima, K. Takagi, Z.-D. Sun, T. Mizuochi, M. Kaneko, Y. Moriwaki, F. Matsushima, and K. Takagi, “Sub-Doppler spectroscopy by use of microwave sidebands of CO2 laser lines applied to the C-O stretching fundamental band of methanol,” Molecules 8, 92–102 (2003).
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2002 (2)

Z.-D. Sun, S. Ishikuro, Y. Moriwaki, F. Matsushima, S. Tsunekawa, and K. Takagi, “Sub-Doppler measurements of vco=1←0, K=0, A/E lines of methanol with microwave sidebands of CO2 laser lines,” J. Mol. Spectrosc. 211, 162–166 (2002).
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H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002).
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2001 (1)

H. Singh, Y. Chen, A. Staudt, D. Jacob, D. Blake, B. Heikes, and J. Snow, “Evidence from the Pacific troposphere for large global sources of oxygenated organic compounds,” Nature 410, 1078–1081 (2001).
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2000 (2)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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Z.-D. Sun, F. Matsushima, S. Tsunekawa, and K. Takagi, “Sub-Doppler spectroscopy of the C–O stretching fundamental band of methanol by use of microwave sidebands of CO2 laser lines,” J. Opt. Soc. Am. B 17, 2068–2080 (2000).
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1998 (1)

1997 (1)

O. Acef, “Metrological properties of CO2/OsO4 optical frequency standard,” Opt. Commun. 134, 479–486 (1997).
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1995 (1)

V. Bernard, P. E. Durand, T. George, H. W. Nicolaisen, A. Amy-Klein, and C. Chardonnet, “Spectral purity and long-term stability of CO2 lasers at the Hertz level,” IEEE J. Quantum Electron. 31, 1913–1918 (1995).
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1987 (1)

W. Batrla, H. E. Matthews, K. M. Menten, and C. M. Walmsley, “Detection of strong methanol masers towards galactic H II regions,” Nature 326, 49–51 (1987).
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1983 (1)

1980 (1)

R. A. Forber, J. Tenenbaum, and M. S. Feld, “Laser Stark saturation spectroscopy in methyl alcohol,” Int. J. Infrared Millim. Waves 1, 527–560 (1980).
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1976 (2)

C. J. Bordé, J. L. Hall, C. V. Kunasz, and D. G. Hummer, “Saturated absorption line shape: calculation of the transit-time broadening by a perturbation approach,” Phys. Rev. A 14, 236–263 (1976).
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J. L. Hall, C. J. Bordé, and K. Uehara, “Direct optical resolution of the recoil effect using saturated absorption spectroscopy,” Phys. Rev. Lett. 37, 1339 (1976).
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Abgrall, M.

B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. L. 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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B. Chanteau, O. Lopez, W. Zhang, D. Nicolodi, B. Argence, F. Auguste, M. Abgrall, C. Chardonnet, G. Santarelli, B. Darquié, Y. L. Coq, and A. Amy-Klein, “Mid-infrared laser phase-locking to a remote near-infrared frequency reference for high-precision molecular spectroscopy,” New J. Phys. 15, 073003 (2013).
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R. Le Targat, L. Lorini, Y. Le Coq, M. Zawada, J. Guéna, M. Abgrall, M. Gurov, P. Rosenbusch, D. G. Rovera, B. Nagórny, R. Gartman, P. G. Westergaard, M. E. Tobar, M. Lours, G. Santarelli, A. Clairon, S. Bize, P. Laurent, P. Lemonde, and J. Lodewyck, “Experimental realization of an optical second with Strontium lattice clocks,” Nat. Commun. 4, 2109 (2013).
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J. Guéna, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. Tobar, R. Li, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–410 (2012).
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Ablewski, P.

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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Acef, O.

O. Acef, “Metrological properties of CO2/OsO4 optical frequency standard,” Opt. Commun. 134, 479–486 (1997).
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A. Clairon, O. Acef, C. Chardonnet, and C. J. Bordé, “State-of-the art for high accuracy frequency standards in the 28  THz range using saturated absorption resonances of OsO4 and CO2,” in Frequency Standards and Metrology, A. deMarchi, ed. (Springer-Verlag, 1989), pp. 212–221.

Achkar, J.

O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Physique 16, 531–539 (2015).
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Akamatsu, D.

Akikusa, N.

I. Galli, M. Siciliani de Cumis, F. Cappelli, S. Bartalini, D. Mazzotti, S. Borri, A. Montori, N. Akikusa, M. Yamanishi, G. Giusfredi, P. Cancio, and P. De Natale, “Comb-assisted subkilohertz linewidth quantum cascade laser for high-precision mid-infrared spectroscopy,” Appl. Phys. Lett. 102, 121117 (2013).
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F. Cappelli, I. Galli, S. Borri, G. Giusfredi, P. Cancio, D. Mazzotti, A. Montori, N. Akikusa, M. Yamanishi, S. Bartalini, and P. D. Natale, “Subkilohertz linewidth room-temperature mid-infrared quantum cascade laser using a molecular sub-Doppler reference,” Opt. Lett. 37, 4811–4813 (2012).
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Alexandre, C.

Allen, N. D. C.

J. J. Harrison, N. D. C. Allen, and P. F. Bernath, “Infrared absorption cross sections for methanol,” J. Quant. Spectrosc. Radiat. Transfer 113, 2189–2196 (2012).
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AlSaif, B.

M. Lamperti, B. AlSaif, D. Gatti, M. Fermann, P. Laporta, A. Farooq, and M. Marangoni, “Absolute spectroscopy near 7.8  μm with a comb-locked extended-cavity quantum-cascade-laser,” Sci. Rep. 8, 1292 (2018).
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Amy-Klein, A.

D. Xu, W.-K. Lee, F. Stefani, O. Lopez, A. Amy-Klein, and P.-E. Pottie, “Studying the fundamental limit of optical fiber links to the 10-21 level,” Opt. Express 26, 9515–9527 (2018).
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F. Guillou-Camargo, V. Ménoret, E. Cantin, O. Lopez, N. Quintin, E. Camisard, V. Salmon, J.-M. L. Merdy, G. Santarelli, A. Amy-Klein, P.-E. Pottie, B. Desruelle, and C. Chardonnet, “First industrial-grade coherent fiber link for optical frequency standard dissemination,” Appl. Opt. 57, 7203–7210 (2018).
[Crossref]

W.-K. Lee, F. Stefani, A. Bercy, O. Lopez, A. Amy-Klein, and P.-E. Pottie, “Hybrid fiber links for accurate optical frequency comparison,” Appl. Phys. B 123, 161 (2017).
[Crossref]

O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Physique 16, 531–539 (2015).
[Crossref]

B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. L. Coq, and A. Amy-Klein, “Quantum cascade laser frequency stabilization at the sub-Hz level,” Nat. Photonics 9, 456–460 (2015).
[Crossref]

F. Stefani, O. Lopez, A. Bercy, W.-K. Lee, C. Chardonnet, G. Santarelli, P.-E. Pottie, and A. Amy-Klein, “Tackling the limits of optical fiber links,” J. Opt. Soc. Am. B 32, 787–797 (2015).
[Crossref]

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G. Insero, S. Borri, D. Calonico, P. C. Pastor, C. Clivati, D. D’Ambrosio, P. 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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J. Vojtěch, J. Radil, V. Smotlacha, R. Velc, P. Krehlik, Ł. Śliwczyński, M. Campanella, D. Calonico, C. Clivati, F. Levi, O. Číp, S. Rerucha, R. Holzwarth, M. Lessing, S. Saint-Jalm, F. Camargo, B. Desruelle, J. Lautier-Gaud, E. L. English, J. Kronjäger, P. Whibberley, E. Bookjans, P.-E. Pottie, P. Tuckey, T. Müller, J. Štefl, M. Šteflová, P. Nogaś, R. Urbaniak, A. Binczewski, W. Bogacki, K. Turza, G. Grosche, H. Schnatz, E. Camisard, N. Quintin, J. Diaz, E. Ros, T. García, A. Galardini, A. Seeds, Z. Yang, and A. Amy-Klein, “The H2020 European project CLONETS: clock services over optical-fibre networks in Europe,” in European Frequency and Time Forum (EFTF) (2018), p. 285.

Camargo, F.

J. Vojtěch, J. Radil, V. Smotlacha, R. Velc, P. Krehlik, Ł. Śliwczyński, M. Campanella, D. Calonico, C. Clivati, F. Levi, O. Číp, S. Rerucha, R. Holzwarth, M. Lessing, S. Saint-Jalm, F. Camargo, B. Desruelle, J. Lautier-Gaud, E. L. English, J. Kronjäger, P. Whibberley, E. Bookjans, P.-E. Pottie, P. Tuckey, T. Müller, J. Štefl, M. Šteflová, P. Nogaś, R. Urbaniak, A. Binczewski, W. Bogacki, K. Turza, G. Grosche, H. Schnatz, E. Camisard, N. Quintin, J. Diaz, E. Ros, T. García, A. Galardini, A. Seeds, Z. Yang, and A. Amy-Klein, “The H2020 European project CLONETS: clock services over optical-fibre networks in Europe,” in European Frequency and Time Forum (EFTF) (2018), p. 285.

Camisard, E.

F. Guillou-Camargo, V. Ménoret, E. Cantin, O. Lopez, N. Quintin, E. Camisard, V. Salmon, J.-M. L. Merdy, G. Santarelli, A. Amy-Klein, P.-E. Pottie, B. Desruelle, and C. Chardonnet, “First industrial-grade coherent fiber link for optical frequency standard dissemination,” Appl. Opt. 57, 7203–7210 (2018).
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J. Vojtěch, J. Radil, V. Smotlacha, R. Velc, P. Krehlik, Ł. Śliwczyński, M. Campanella, D. Calonico, C. Clivati, F. Levi, O. Číp, S. Rerucha, R. Holzwarth, M. Lessing, S. Saint-Jalm, F. Camargo, B. Desruelle, J. Lautier-Gaud, E. L. English, J. Kronjäger, P. Whibberley, E. Bookjans, P.-E. Pottie, P. Tuckey, T. Müller, J. Štefl, M. Šteflová, P. Nogaś, R. Urbaniak, A. Binczewski, W. Bogacki, K. Turza, G. Grosche, H. Schnatz, E. Camisard, N. Quintin, J. Diaz, E. Ros, T. García, A. Galardini, A. Seeds, Z. Yang, and A. Amy-Klein, “The H2020 European project CLONETS: clock services over optical-fibre networks in Europe,” in European Frequency and Time Forum (EFTF) (2018), p. 285.

Campanella, M.

J. Vojtěch, J. Radil, V. Smotlacha, R. Velc, P. Krehlik, Ł. Śliwczyński, M. Campanella, D. Calonico, C. Clivati, F. Levi, O. Číp, S. Rerucha, R. Holzwarth, M. Lessing, S. Saint-Jalm, F. Camargo, B. Desruelle, J. Lautier-Gaud, E. L. English, J. Kronjäger, P. Whibberley, E. Bookjans, P.-E. Pottie, P. Tuckey, T. Müller, J. Štefl, M. Šteflová, P. Nogaś, R. Urbaniak, A. Binczewski, W. Bogacki, K. Turza, G. Grosche, H. Schnatz, E. Camisard, N. Quintin, J. Diaz, E. Ros, T. García, A. Galardini, A. Seeds, Z. Yang, and A. Amy-Klein, “The H2020 European project CLONETS: clock services over optical-fibre networks in Europe,” in European Frequency and Time Forum (EFTF) (2018), p. 285.

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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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M. Guinet, D. Mondelain, C. Janssen, and C. Camy-Peyret, “Laser spectroscopic study of ozone in the 100←000 band for the SWIFT instrument,” J. Quant. Spectrosc. Radiat. Transfer 111, 961–972 (2010).
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Cappelli, F.

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Casado, M.

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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Castrillo, A.

E. Vicentini, A. Gambetta, N. Coluccelli, E. Fasci, A. Castrillo, L. Gianfrani, V. Di Sarno, P. Maddaloni, A. Ceausu-Velcescu, P. De Natale, Y. Wang, T. T. Fernandez, P. Laporta, and G. Galzerano, “Rovibrational fine structure and transition dipole moment of CF3H by frequency-comb-assisted saturated spectroscopy at 8.6 μm,” J. Quant. Spectrosc. Radiat. Transfer 217, 373–379 (2018).
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F. Rohart, S. Mejri, P. L. T. Sow, S. K. Tokunaga, C. Chardonnet, B. Darquié, H. Dinesan, E. Fasci, A. Castrillo, L. Gianfrani, and C. Daussy, “Absorption-line-shape recovery beyond the detection-bandwidth limit: application to the precision spectroscopic measurement of the Boltzmann constant,” Phys. Rev. A 90, 042506 (2014).
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E. Vicentini, A. Gambetta, N. Coluccelli, E. Fasci, A. Castrillo, L. Gianfrani, V. Di Sarno, P. Maddaloni, A. Ceausu-Velcescu, P. De Natale, Y. Wang, T. T. Fernandez, P. Laporta, and G. Galzerano, “Rovibrational fine structure and transition dipole moment of CF3H by frequency-comb-assisted saturated spectroscopy at 8.6 μm,” J. Quant. Spectrosc. Radiat. Transfer 217, 373–379 (2018).
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Chanteau, B.

B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. L. 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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O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Physique 16, 531–539 (2015).
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B. Chanteau, O. Lopez, W. Zhang, D. Nicolodi, B. Argence, F. Auguste, M. Abgrall, C. Chardonnet, G. Santarelli, B. Darquié, Y. L. Coq, and A. Amy-Klein, “Mid-infrared laser phase-locking to a remote near-infrared frequency reference for high-precision molecular spectroscopy,” New J. Phys. 15, 073003 (2013).
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Chardonnet, C.

F. Guillou-Camargo, V. Ménoret, E. Cantin, O. Lopez, N. Quintin, E. Camisard, V. Salmon, J.-M. L. Merdy, G. Santarelli, A. Amy-Klein, P.-E. Pottie, B. Desruelle, and C. Chardonnet, “First industrial-grade coherent fiber link for optical frequency standard dissemination,” Appl. Opt. 57, 7203–7210 (2018).
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F. Stefani, O. Lopez, A. Bercy, W.-K. Lee, C. Chardonnet, G. Santarelli, P.-E. Pottie, and A. Amy-Klein, “Tackling the limits of optical fiber links,” J. Opt. Soc. Am. B 32, 787–797 (2015).
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O. Lopez, F. Kéfélian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.-E. Pottie, A. Amy-Klein, and G. Santarelli, “Frequency and time transfer for metrology and beyond using telecommunication network fibres,” C. R. Physique 16, 531–539 (2015).
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B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. L. 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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S. Mejri, P. L. T. Sow, O. Kozlova, C. Ayari, S. K. Tokunaga, C. Chardonnet, S. Briaudeau, B. Darquié, F. Rohart, and C. Daussy, “Measuring the Boltzmann constant by mid-infrared laser spectroscopy of ammonia,” Metrologia 52, S314 (2015).
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F. Rohart, S. Mejri, P. L. T. Sow, S. K. Tokunaga, C. Chardonnet, B. Darquié, H. Dinesan, E. Fasci, A. Castrillo, L. Gianfrani, and C. Daussy, “Absorption-line-shape recovery beyond the detection-bandwidth limit: application to the precision spectroscopic measurement of the Boltzmann constant,” Phys. Rev. A 90, 042506 (2014).
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A. Bercy, F. Stefani, O. Lopez, C. Chardonnet, P.-E. Pottie, and A. Amy-Klein, “Two-way optical frequency comparisons at 5×10-21 relative stability over 100-km telecommunication network fibers,” Phys. Rev. A 90, 061802 (2014).
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P. L. T. Sow, S. Mejri, S. K. Tokunaga, O. Lopez, A. Goncharov, B. Argence, C. Chardonnet, A. Amy-Klein, C. Daussy, and B. Darquié, “A widely tunable 10-μm quantum cascade laser phase-locked to a state-of-the-art mid-infrared reference for precision molecular spectroscopy,” Appl. Phys. Lett. 104, 264101 (2014).
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S. K. Tokunaga, C. Stoeffler, F. Auguste, A. Shelkovnikov, C. Daussy, A. Amy-Klein, C. Chardonnet, and B. Darquié, “Probing weak force induced parity violation by high resolution mid-infrared molecular spectroscopy,” Mol. Phys. 111, 2363–2373 (2013).
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B. Chanteau, O. Lopez, W. Zhang, D. Nicolodi, B. Argence, F. Auguste, M. Abgrall, C. Chardonnet, G. Santarelli, B. Darquié, Y. L. Coq, and A. Amy-Klein, “Mid-infrared laser phase-locking to a remote near-infrared frequency reference for high-precision molecular spectroscopy,” New J. Phys. 15, 073003 (2013).
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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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V. Bernard, P. E. Durand, T. George, H. W. Nicolaisen, A. Amy-Klein, and C. Chardonnet, “Spectral purity and long-term stability of CO2 lasers at the Hertz level,” IEEE J. Quantum Electron. 31, 1913–1918 (1995).
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A. Clairon, O. Acef, C. Chardonnet, and C. J. Bordé, “State-of-the art for high accuracy frequency standards in the 28  THz range using saturated absorption resonances of OsO4 and CO2,” in Frequency Standards and Metrology, A. deMarchi, ed. (Springer-Verlag, 1989), pp. 212–221.

C. Chardonnet, “Spectroscopie de saturation de hautes précision et sensibilité en champ laser fort. Applications aux molécules OsO4, SF6 et CO2 et à la métrologie des fréquences,” Ph.D. thesis (Université Paris, 1989).

Chen, Q.-F.

Chen, Y.

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Cheng, Z. H.

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Chupin, B.

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J. Vojtěch, J. Radil, V. Smotlacha, R. Velc, P. Krehlik, Ł. Śliwczyński, M. Campanella, D. Calonico, C. Clivati, F. Levi, O. Číp, S. Rerucha, R. Holzwarth, M. Lessing, S. Saint-Jalm, F. Camargo, B. Desruelle, J. Lautier-Gaud, E. L. English, J. Kronjäger, P. Whibberley, E. Bookjans, P.-E. Pottie, P. Tuckey, T. Müller, J. Štefl, M. Šteflová, P. Nogaś, R. Urbaniak, A. Binczewski, W. Bogacki, K. Turza, G. Grosche, H. Schnatz, E. Camisard, N. Quintin, J. Diaz, E. Ros, T. García, A. Galardini, A. Seeds, Z. Yang, and A. Amy-Klein, “The H2020 European project CLONETS: clock services over optical-fibre networks in Europe,” in European Frequency and Time Forum (EFTF) (2018), p. 285.

Ciurylo, R.

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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J. Guéna, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. Tobar, R. Li, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–410 (2012).
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A. Clairon, O. Acef, C. Chardonnet, and C. J. Bordé, “State-of-the art for high accuracy frequency standards in the 28  THz range using saturated absorption resonances of OsO4 and CO2,” in Frequency Standards and Metrology, A. deMarchi, ed. (Springer-Verlag, 1989), pp. 212–221.

Clivati, C.

G. Insero, S. Borri, D. Calonico, P. C. Pastor, C. Clivati, D. D’Ambrosio, P. 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).
[Crossref]

J. Vojtěch, J. Radil, V. Smotlacha, R. Velc, P. Krehlik, Ł. Śliwczyński, M. Campanella, D. Calonico, C. Clivati, F. Levi, O. Číp, S. Rerucha, R. Holzwarth, M. Lessing, S. Saint-Jalm, F. Camargo, B. Desruelle, J. Lautier-Gaud, E. L. English, J. Kronjäger, P. Whibberley, E. Bookjans, P.-E. Pottie, P. Tuckey, T. Müller, J. Štefl, M. Šteflová, P. Nogaś, R. Urbaniak, A. Binczewski, W. Bogacki, K. Turza, G. Grosche, H. Schnatz, E. Camisard, N. Quintin, J. Diaz, E. Ros, T. García, A. Galardini, A. Seeds, Z. Yang, and A. Amy-Klein, “The H2020 European project CLONETS: clock services over optical-fibre networks in Europe,” in European Frequency and Time Forum (EFTF) (2018), p. 285.

Coluccelli, N.

E. Vicentini, A. Gambetta, N. Coluccelli, E. Fasci, A. Castrillo, L. Gianfrani, V. Di Sarno, P. Maddaloni, A. Ceausu-Velcescu, P. De Natale, Y. Wang, T. T. Fernandez, P. Laporta, and G. Galzerano, “Rovibrational fine structure and transition dipole moment of CF3H by frequency-comb-assisted saturated spectroscopy at 8.6 μm,” J. Quant. Spectrosc. Radiat. Transfer 217, 373–379 (2018).
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X. Xie, R. Bouchand, D. Nicolodi, M. Lours, C. Alexandre, and Y. L. Coq, “Phase noise characterization of sub-hertz linewidth lasers via digital cross correlation,” Opt. Lett. 42, 1217–1220 (2017).
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B. Argence, B. Chanteau, O. Lopez, D. Nicolodi, M. Abgrall, C. Chardonnet, C. Daussy, B. Darquié, Y. L. 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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B. Chanteau, O. Lopez, W. Zhang, D. Nicolodi, B. Argence, F. Auguste, M. Abgrall, C. Chardonnet, G. Santarelli, B. Darquié, Y. L. Coq, and A. Amy-Klein, “Mid-infrared laser phase-locking to a remote near-infrared frequency reference for high-precision molecular spectroscopy,” New J. Phys. 15, 073003 (2013).
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Coudert, L. H.

L. H. Coudert, C. Gutlé, T. R. Huet, J. U. Grabow, and S. A. Levshakov, “Spin-torsion effects in the hyperfine structure of methanol,” J. Chem. Phys. 143, 044304 (2015).
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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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Figures (6)

Fig. 1.
Fig. 1. Experimental setup. The NIR reference signal (frequency ν ref ) developed at LNE-SYRTE (Paris) is transferred to LPL (Villetaneuse) through a 43-km-long optical-fiber link with active noise compensation (not shown). At LNE-SYRTE, its absolute frequency is measured against primary frequency standards using an OFC. At LPL, a local laser diode (frequency ν OLO ) is used as an optical local oscillator (OLO). An electro-optic modulator (EOM) driven at frequency f EOM with a phase-jump-free synthesizer generates sidebands tunable over 9 GHz in the OLO signal. The beat note signal between one sideband and the reference signal provided by LNE-SYRTE is used to phase-lock the former to the latter, with an offset frequency δ 1 (using PLL1). This allows the carrier frequency to be used as a tunable ultra-stable local oscillator. The repetition rate f rep of an OFC is then phase-locked to the OLO carrier frequency after removal of the comb carrier-envelope offset frequency (via PLL2). A QCL (frequency ν QCL ) is finally phase-locked to the stabilized OFC by performing sum-frequency generation in a AgGaSe 2 crystal and processing the beat note signal between the resulting beam and the OFC (using PLL3). Tunability is thus transferred from the local reference to the OFC and finally the QCL. The stabilized and tunable QCL beam is then used to perform saturated absorption spectroscopy in a multipass cell. The QCL is frequency modulated, and the signal is recorded after detection in a lock-in amplifier. PD, photodetector; PLL, phase-lock loop; FM, frequency modulation; OC, optical coupler; OSA, optical spectrum analyzer. Padlocks symbolize phase-lock loops.
Fig. 2.
Fig. 2. Saturated absorption spectrum of the P ( E , co , 0 , 2 , 33 ) ro-vibrational line of methanol recorded using frequency modulation and first-harmonic detection. Experimental conditions: pressure, 1 Pa; modulation frequency, 20 kHz; frequency modulation excursion, 50 kHz; frequency step, 15 kHz ; average of five pairs of up and down scans; total integration time per point, 1 s; whole spectrum measurement time, 935 s. The P ( E , co , 0 , 2 , 33 ) line frequency position reported in the HITRAN database [51] at 971.76295 cm 1 is also shown as a blue stick.
Fig. 3.
Fig. 3. Saturated absorption spectrum of methanol spanning 400 MHz recorded using frequency modulation and first-harmonic detection (black line). The gray solid line is a fit to the data. The oscillations in the baseline result from Doppler broadening. The observed lines are labeled with the transition assignments as detailed in Appendix B. Blue sticks indicate the line frequency positions reported in the HITRAN database [51]. The inset is a zoom on the small ( A , sb , 0 , 1 , 10 ) ( A , gr , 2 , 1 , 11 ). Experimental conditions: pressure, 1 Pa; modulation frequency, 20 kHz; frequency modulation excursion; 50 kHz; frequency step, 15 kHz ; average of one pair of up and down scans; total integration time per point, 200 ms; whole spectrum measurement time, 5400 s.
Fig. 4.
Fig. 4. Spectral range coverage. Gray solid sticks, spectrum of methanol simulated using HITRAN’s data [51]. Blue dashed sticks, methanol lines recorded by us so far labeled with their spectroscopic assignment (see Appendix A). The spectral range covered is of 90 GHz . The red asterisks pinpoint the data shown in Fig. 2 (thin stick around 971.75 cm 1 ) and Fig. 3 (thick stick around 971.56 cm 1 ) above, where their assignments have been introduced.
Fig. 5.
Fig. 5. Saturated absorption spectrum of the P ( E , co , 0 , 2 , 33 ) ro-vibrational line of methanol, with fit and residuals. The data (black dots) are recorded using frequency modulation and first-harmonic detection. The orange solid line is a fit to the data resulting in a reduced chi-squared of 1.27. Residuals are shown on the bottom graph. Experimental conditions: pressure, 1 Pa; modulation frequency, 20 kHz; frequency modulation excursion; 50 kHz; frequency step, 15 kHz ; average of one pair of up and down scans (corresponding to one of the five pairs contributing to Fig. 2); total integration time per point, 200 ms; whole spectrum measurement time, 80.2 s.
Fig. 6.
Fig. 6. Frequency measurements of the P ( E , co , 0 , 2 , 33 ) ro-vibrational methanol line. Twenty measurements carried out at a pressure of 1 Pa in June and October 2017 are displayed after correction of a power-dependent frequency shift. The transition frequency resulting from the weighted mean of all June (respectively October) data is indicated at the bottom with the associated 1 σ weighted standard errors. The overall weighted mean and its 1 σ weighted standard error is indicated at the top and symbolized by the gray rectangle. The red asterisk pinpoints the measurement corresponding to Figs. 2 and 5.

Tables (1)

Tables Icon

Table 1. Uncertainty Budget Table for Frequency Measurements in June and October 2017, all Recorded at 1 Pa and Displayed in Fig. 6

Equations (9)

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δ 1 = ν ref ν OLO f EOM .
δ 2 = ν OLO N f rep ,
δ 3 = n f rep ν QCL .
ν OLO 0 = ν ref f EOM 0 δ 1 .
N = [ ν OLO 0 δ 2 f rep 0 ] ,
n = [ ν QCL 0 + δ 3 f rep 0 ] .
ν QCL = n N ( ν ref f EOM δ 1 δ 2 ) δ 3 .
ν g ( ν ) + i = 0 N s i ( ν ν 0 ) i , with g ( ν ) = A [ B ( ν ν 0 ) + 1 ] × L ( ν ) and L ( ν ) = 1 π γ ( ν ν 0 ) 2 + γ 2 .
ν QCL = n f rep δ 3 ,

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