We have recorded the Doppler profile of a well-isolated rovibrational line in the ν 2 band of 14 NH 3 . Ammonia gas was placed in an absorption cell thermalized by a water-ice bath. By extrapolating to zero pressure, we have deduced the Doppler width which gives a first measurement of the Boltzmann constant, k B , by laser spectroscopy. A relative uncertainty of 2×10 -4 has been obtained. The present determination should be significantly improved in the near future and contribute to a new definition of the kelvin.

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The thermodynamic temperature of the point of inflection of the melting transition of Re-C, Pt-C and Co-C eutectics has been determined to be 2747.84 ± 0.35 K, 2011.43 ± 0.18 K and 1597.39 ± 0.13 K, respectively, and the thermodynamic temperature of the freezing transition of Cu has been determined to be 1357.80 ± 0.08 K, where the ± symbol represents 95% coverage. These results are the best consensus estimates obtained from measurements made using various spectroradiometric primary thermometry techniques by nine different national metrology institutes. The good agreement between the institutes suggests that spectroradiometric thermometry techniques are sufficiently mature (at least in those institutes) to allow the direct realization of thermodynamic temperature above 1234 K (rather than the use of a temperature scale) and that metal-carbon eutectics can be used as high-temperature fixed points for thermodynamic temperature dissemination. The results directly support the developing mise en pratique for the definition of the kelvin to include direct measurement of thermodynamic temperature.

Single light beam transmission spectroscopy in an ultrathin dilute vapor cell ͑10-100 m͒ reveals sub-Doppler features. Indeed, atoms with fast ͑normal͒ velocity undergo a short interaction between the cell walls, and are shown to be less absorbing because they have not reached their steady state of interaction with light. The effect is observed in the linear-response regime with a simple two-level system, as ensured from the ultralow level of light irradiation ͑р1 W/cm 2 for the Cs D 2 line͒. The effect, known for a long time in the microwave domain, is demonstrated here in the optical domain, and is extended to cell thicknesses large relative to the optical wavelength.

We report on high-resolution single-light-beam transmission spectroscopy through an ultra thin vapor cell (thickness 10-100 mm). In addition to the expected Doppler-broadened absorption, a novel sub-Doppler structure is observed under normal incidence irradiation. This structure originates from the optical response of atoms with very small velocity components perpendicular to the cell walls, and is connected with the transient atom excitation regime during the wall-to-wall time of flight. In experiments performed in Cs vapor, the slow mechanism of optical pumping leads, for weak light intensities (10-100 mW/cm 2 ) and a 10 mm cell, to a velocity selection equivalent to an effective 1D temperature in the sub-mK range.

In this article, we describe an experiment performed at the Laboratoire de physique des lasers and dedicated to an optical measurement of the Boltzmann constant k B . With the proposed innovative technique, determining k B comes down to an ordinary frequency measurement. The method consists in measuring as accurately as possible the Doppler absorption profile of a rovibrational line of ammonia in thermal equilibrium. This profile is related to the Maxwell-Boltzmann molecular velocity distribution along the laser beam. A fit of the absorption line shape leads to a determination of the Doppler width proportional to √ k B T and thus to a determination of the Boltzmann constant. The laser source is an ultra-stable CO 2 laser with a wavelength λ ≈ 10 µm. The absorption cell is placed in a thermostat, keeping the temperature at 273.15 K within 1.4 mK. We were able to measure k B with a relative uncertainty as small as 3.8 × 10 −5 , which represents an improvement of an order of magnitude for an integration time comparable to our previous measurement published in 2007. To cite this article: K. Djerroud et al., C. R. Physique 10 (2009). RésuméMesure de la constante de Boltzmann utilisant l'élargissement Doppler avec une incertitude relative de 3,8 × 10 −5 . Dans cet article, nous présentons l'expérience développée au Laboratoire de physique des lasers pour la mesure optique de la constante de Boltzmann k B . Cette nouvelle approche ramène la détermination de k B à une mesure de fréquence. L'expérience consiste à mesurer le plus exactement possible le profil d'absorption Doppler d'une raie de vibration-rotation de l'ammoniac à l'équilibre thermodynamique. Ce profil reflète la distribution de Maxwell-Boltzmann des vitesses moléculaires le long du faisceau laser. Une analyse de la forme de la raie d'absorption conduit à une détermination de l'élargissement Doppler, proportionnel à √ k B T , et donc à une mesure de la constante de Boltzmann. La mesure spectroscopique est réalisée à l'aide d'un laser à CO 2 ultra-stable de longueur d'onde λ ≈ 10 µm. La cellule d'absorption est placée dans un thermostat qui permet de contrôler la température autour de 273,15 K avec une incertitude de 1,4 mK. Ces mesures nous ont conduit récemment à une détermination de k B avec une incertitude relative de 3,8 × 10 −5 . Cela représente, pour des temps de mesure comparables, un gain d'un ordre de grandeur par rapport à notre précédente mesure publiée en . Pour citer cet article : K. Djerroud et al., C. R. Physique 10 (2009).

In this paper, the latest results on the measurement of the Boltzmann constant k B , by laser spectroscopy of ammonia at 10 µm are presented. The Doppler absorption profile of a rovibrational line of an NH 3 gas sample at thermal and pressure equilibrium is measured as accurately as possible. The absorption cell is placed inside a large 1 m 3 thermostat filled with an ice-water mixture, which sets the temperature very close to 273.15 K. Analyzing this profile, which is related to the Maxwell-Boltzmann molecular speed distribution, leads to a determination of the Boltzmann constant via a measurement of the Doppler width (proportional to √ k B T ). A spectroscopic determination of the Boltzmann constant with an uncertainty as low as 37 ppm is obtained. Recent improvements with a new passive thermostat lead to a temperature accuracy, stability, and homogeneity of the absorption cell of 1 ppm over a day.

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