In this paper, we present significant progress performed on an experiment dedicated to the determination of the Boltzmann constant, B k , by accurately measuring the Doppler absorption profile of a line in a gas of ammonia at thermal equilibrium. This optical method based on the first principles of statistical mechanics is an alternative to the acoustical method which has led to the unique determination of B k published by the CODATA with a relative accuracy of 6 1 7 10 . − × . We report on the first measurement of the Boltzmann constant by laser spectroscopy with a statistical uncertainty below 10 ppm, more specifically 6.4 ppm. This progress results from improvements in the detection method and in the statistical treatment of the data. In addition, we have recorded the hyperfine structure of the probed ν2 saQ(6,3) rovibrational line of ammonia by saturation spectroscopy and thus determine very precisely the induced 4.36 (2) ppm broadening of the absorption linewidth. We also show that, in our well chosen experimental conditions, saturation effects have a negligible impact on the linewidth. Finally, we draw the route to future developments for an absolute determination of B k with an accuracy of a few ppm.

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 we present an accurate analysis of the shape of an isolated rovibrational ammonia line from the strong 2 band around 10 µm, recorded by laser absorption spectroscopy. Experimental spectra obtained under controlled temperature and pressure, are confronted to various models that take into account Dicke narrowing or speed-dependent effects. Our results show clear evidence for speed-dependent broadening and shifting, which had never been demonstrated so far in NH 3 . Accurate lineshape parameters of the ν 2 saQ(6,3) line are obtained. Our current project aiming at measuring the Boltzmann constant, k B , by laser spectroscopy will straight away benefit from such knowledge. We anticipate that a first optical determination of k B with a competitive uncertainty of a few ppm is now reachable.

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.

We report on our on-going effort to measure the Boltzmann constant, k B , using the Doppler Broadening Technique. The main systematic effects affecting the measurement are discussed. A revised error budget is presented in which the global uncertainty on systematic effects is reduced to 2.3 ppm. This corresponds to a reduction of more than one order of magnitude compared to our previous Boltzmann constant measurement. Means to reach a determination of k B at the part per million accuracy level are outlined.

No abstract

Abstract. Accurate molecular spectroscopy in the mid-infrared region allows precision measurements of fundamental constants. For instance, measuring the linewidth of an isolated Doppler-broadened absorption line of ammonia around 10 m enables a determination of the Boltzmann constant k B . We report on our latest measurements. By fitting this lineshape to several models which include Dicke narrowing or speeddependent collisional effects, we find that a determination of k B with an uncertainty of a few ppm is reachable. This is comparable to the best current uncertainty obtained using acoustic methods and would make a significant contribution to any new value of k B determined by the CODATA. Furthermore, having multiple independent measurements at these accuracies opens the possibility of defining the kelvin by fixing k B , an exciting prospect considering the upcoming redefinition of the International System of Units.