Progress towards an accurate determination of the Boltzmann constant by Doppler spectroscopy

Abstract

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.

Accurate determination of the Boltzmann constant by Doppler spectroscopy: Towards a new definition of the kelvin

“…Until recently, the main source of uncertainty on determining k B was the lack of knowledge of the correct collisional model for the gas, and therefore the correct lineshape to use for fitting to our experimental data. It for instance, constituted 97% of the 144 ppm standard uncertainty published in [29]. The influence of the lineshape model on the spectroscopic determination of the Boltzmann constant has been raised by us and other groups working with O 2 and H 2 O [29,32,[40][41][42][43][44][45].…”

“…It for instance, constituted 97% of the 144 ppm standard uncertainty published in [29]. The influence of the lineshape model on the spectroscopic determination of the Boltzmann constant has been raised by us and other groups working with O 2 and H 2 O [29,32,[40][41][42][43][44][45]. We recently carried out an extensive lineshape study at relatively high pressure in SPC, in order to enhance collisional effects and to determine the most suitable model for our data [40].…”

“…Accurate knowledge of the HFS is required in order to apply the right correction to the Doppler width. Ultra-high resolution saturated absorption spectra of the saQ(6,3) line were measured in a 3-m long Fabry-Perot cavity [29]. A combined analysis of our infrared spectra and microwave data from the literature led to an accurate determination of the hyperfine constants of the transition.…”

“…Secondly, it demonstrates our ability to reach a statistical uncertainty below 10 ppm. The mean of the 02005-p.7 [29,31,32,[49][50][51] is illustrated in Figure 3. To our knowledge, 6.4 ppm represents the best statistical uncertainty ever obtained for the measurement of k B using the DBT.…”

Frequency-comb-calibrated Doppler broadening thermometry

“…A more versatile scheme was implemented by Yamada et al exploiting the technology of erbium-doped fiber-laser frequency comb synthesizers [7]. In their apparatus, an ECDL at 1.5 μm was phase locked to the comb, and continuous frequency scans around a given 13 C 2 H 2 line were performed by tuning the repetition rate, thus demonstrating a precision in Doppler-width retrieval of 1200 ppm. The present paper deals with the extension of this approach to the mid-infrared, taking the advantage of a new referencing scheme allowing a quantum cascade laser to be phase locked to a near-infrared frequency comb [8].…”