Measurement of the Boltzmann constant by the Doppler broadening technique at a 3.8 × 10 − 5 accuracy level

Abstract

In this article, we describe an experiment performed at the Laboratoire de physique des lasers and dedicated to an optical measurement of the Boltzmann constant k B . With the proposed innovative technique, determining k B comes down to an ordinary frequency measurement. The method consists in measuring as accurately as possible the Doppler absorption profile of a rovibrational line of ammonia in thermal equilibrium. This profile is related to the Maxwell–Boltzmann molecular velocity distribution along the laser beam. A fit of the absorption line shape leads to a determination of the Doppler width proportional to k B T and thus to a determination of the Boltzmann constant. The laser source is an ultra-stable CO 2 laser with a wavelength λ ≈ 10 μm . The absorption cell is placed in a thermostat, keeping the temperature at 273.15 K within 1.4 mK. We were able to measure k B with a relative uncertainty as small as 3.8 × 10 − 5 , which represents an improvement of an order of magnitude for an integration time comparable to our previous measurement published in 2007.

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