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: 7.73). 07/2007; 98(25):250801. DOI: 10.1103/PhysRevLett.98.250801
Source: PubMed

ABSTRACT 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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    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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    ABSTRACT: We introduce optical feedback frequency stabilized cavity ring-down spectroscopy (OFFS-CRDS), a near-shot-noise-limited technique that combines kilohertz resolution with an absorption detection sensitivity of 5×10−13 cm−1 Hz−1/2. Its distributed feedback laser source is stabilized to a highly stable V-shaped reference cavity by optical feedback and fine-tuned by means of single-sideband modulation. The stability of this narrow laser is transferred to a ring-down (RD) cavity using a new fibered Pound–Drever–Hall (PDH) locking scheme without a dedicated electro-optic phase modulator, yielding several hundred RD events per second. We demonstrate continuous coverage of more than 7 nm with a baseline noise of 5×10−12 cm−1 and a dynamic range spanning six decades. With its resonant intracavity light intensity on the order of 1 kW/cm2, the spectrometer was used for observing a Lamb dip in a transition of carbon dioxide involving four vibrational quanta. Saturating such a weak transition at 160 μW input power, OFFS-CRDS paves the way to Doppler-free molecular overtone spectroscopy for precision measurements of hyperfine structures and pressure shifts.
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