Direct Determination of the Boltzmann Constant by an Optical Method

Laboratoire de Physique des Lasers, UMR CNRS 7538, Institut Galilée, Université Paris 13, 99, avenue J.-B. Clément, 93430 Villetaneuse, France.
Physical Review Letters (Impact Factor: 7.51). 07/2007; 98(25):250801. DOI: 10.1103/PhysRevLett.98.250801
Source: PubMed


We have recorded the Doppler profile of a well-isolated rovibrational line in the nu(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 x 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 latter problem is typical for auto-balancing photocurrent attenuators[18, 20]. This loss in accuracy is not critical if the ultimate goal is to achieve extraordinary sensitivity; however, in many areas, accuracy is just as important as precision[21] [22]. "
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    ABSTRACT: Here, we report a measurement scheme for determining an absorption profile with an accuracy imposed solely by photon shot noise. We demonstrate the power of this technique by measuring the absorption of cesium vapor with an uncertainty at the 2-ppm level. This extremely high signal-to-noise ratio allows us to directly observe the homogeneous line-shape component of the spectral profile, even in the presence of Doppler broadening, by measuring the spectral profile at a frequency detuning more than 200 natural linewidths from the line center. We then use this tool to discover an optically induced broadening process that is quite distinct from the well-known power broadening phenomenon.
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    • "Rb NH3 [11] CO2 [12] "
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    ABSTRACT: Quantitative spectroscopy has been used to measure accurately the Doppler-broadening of atomic transitions in $^{85}$Rb vapor. By using a conventional platinum resistance thermometer and the Doppler thermometry technique, we were able to determine $k_B$ with a relative uncertainty of $4.1\times 10^{-4}$, and with a deviation of $2.7\times 10^{-4}$ from the expected value. Our experiment, using an effusive vapour, departs significantly from other Doppler-broadened thermometry (DBT) techniques, which rely on weakly absorbing molecules in a diffusive regime. In these circumstances, very different systematic effects such as magnetic sensitivity and optical pumping are dominant. Using the model developed recently by Stace and Luiten, we estimate the perturbation due to optical pumping of the measured $k_B$ value was less than $4\times 10^{-6}$. The effects of optical pumping on atomic and molecular DBT experiments is mapped over a wide range of beam size and saturation intensity, indicating possible avenues for improvement. We also compare the line-broadening mechanisms, windows of operation and detection limits of some recent DBT experiments.
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    • "Three of these are presented in this volume [1] [2] [3] but at least three others are in preparation. This possibility was suggested by the author on the occasion of the 125th anniversary of the meter convention [4] [5] [6] [7] [8] [9]. In order to extract this Doppler width from the absorption profile, a detailed knowledge of the E-mail address: "
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    ABSTRACT: A detailed theory of the line shape in linear absorption spectroscopy of low-pressure gases is developed. The goal is to take into account all effects that come into play in the determination of Boltzmann's constant from measurements of the Doppler width. We demonstrate that there is no additional broadening from finite transit time across the laser beams. The molecular recoil and the second-order Doppler effect are included in the line shape thanks to a complete quantum treatment. The Mössbauer–Lamb–Dicke narrowing of Doppler lines by collisions is also included and the special cases of Galatry and Nelkin–Ghatak profiles are presented. To cite this article: C.J. Bordé, C. R. Physique 10 (2009).RésuméUne théorie détaillée de la forme des raies d'absorption linéaire des gaz à basse pression est développée. L'objectif est de mieux cerner tous les effets susceptibles d'intervenir dans la détermination de la constante de Boltzmann à partir d'une mesure de la largeur Doppler. On démontre en particulier qu'il n'y a pas d'élargissement supplémentaire lié au temps fini de traversée du faisceau laser par les molécules. Les effets de recul et Doppler du deuxième ordre sont intégrés dans la forme de raie grâce à un traitement quantique complet. L'effet Mössbauer–Lamb–Dicke de rétrécissement des raies Doppler par les collisions est lui aussi incorporé dans la théorie avec comme cas particuliers les profils de Galatry et de Nelkin–Ghatak. Pour citer cet article : C.J. Bordé, C. R. Physique 10 (2009).
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