Direct Determination of the Boltzmann Constant by an Optical Method

We have recorded the Doppler profile of a well-isolated rovibrational line in the ${\nu }_2$ band of ${}^{14}\mathrm{NH}_3$. 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 $2\times {10}^{-4}$ has been obtained. The present determination should be significantly improved in the near future and contribute to a new definition of the kelvin.

Figure 1

Experimental setup. $f=8\mathrm{kHz}$, $f_1=17\mathrm{kHz}$, $f_2=1.7\mathrm{kHz}$, $f_3=2.2\mathrm{kHz}$. Only the sideband ${\nu }_{\mathrm{SB}}$ from the EOM is kept after filtering for recording the ${\mathrm{NH}}_3$ absorption profile.

Figure 2

Series of absorption spectra at different pressures.

Figure 3

Linear regression of the $1/e$ half-width of the absorption line which gives an extrapolated value at zero pressure: 49.883 1(47) MHz.