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

In this paper, we present the significant progress made by an experiment dedicated to the determination of the Boltzmann constant, k_B, by accurately measuring the Doppler absorption profile of a line in ammonia gas 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 k_B published by the Committee on Data for Science and Technology with a relative accuracy of 1.7×10⁻⁶. We report on the first measurement of the Boltzmann constant carried out by using laser spectroscopy with a statistical uncertainty below 10 p.p.m., more specifically 6.4 p.p.m. This progress results from the improvement 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) p.p.m. broadening of the absorption linewidth. We also show that in our well-chosen experimental conditions, saturation effects have negligible impact on the linewidth. Finally, we suggest directions for future work to achieve an absolute determination of k_B with an accuracy of a few p.p.m.