Article

# Direct Determination of the Boltzmann Constant by an Optical Method

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Laboratoire de Physique des Lasers, UMR CNRS 7538, Institut Galilée, Université Paris 13, 99, avenue J.-B. Clément, 93430 Villetaneuse, France.
(Impact Factor: 7.51). 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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• "In proof-of-principle experiments performed on NH 3 and CO 2 molecules, k B was determined with a combined uncertainty of 190 and 160 parts in 10 6 , respectively [4] [5]. The ammonia infrared spectrum was probed by a frequency-stabilized CO 2 laser, while an extended-cavity diode laser (ECDL) at 2 μm was used to interrogate a vibration–rotation transition of carbon dioxide. "
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ABSTRACT: We report on complementary tests and measurements regarding our recent determination of the Boltzmann constant, kB, by means of Doppler broadening thermometry, also providing additional information as compared to previous articles. A revised uncertainty budget is illustrated, including some new components that were ignored in previous spectroscopic experiments, and better quantifying other components that were estimated to be negligible. In particular, we consider the relativistic Doppler effect, the perturbation caused by the finite bandwidth of the detection system and the influence of the spontaneous emission content of the probe laser. These new components do not increase the global uncertainty which still amounts to 24 ppm. Our value for the Boltzmann constant is 1.380 631 (33) 10-23 J K-1, which is the best determination reported so far by using an optical method.
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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.
Physical Review A 09/2012; 86(3). DOI:10.1103/PhysRevA.86.030501 · 2.81 Impact Factor
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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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