Abstract:
Accurate molecular spectroscopy in the mid-infrared region allows precision measurements of fundamental constants. For instance, measuring the linewidth of an isolated Doppler-broadened absorption line of ammonia around 10 $\mu$m enables a determination of the Boltzmann constant k B. We report on our latest measurements. By fitting this lineshape to several models which include Dicke narrowing or speed-dependent collisional effects, we find that a determination of k B with an uncertainty of a few ppm is reachable. This is comparable to the best current uncertainty obtained using acoustic methods and would make a significant contribution to any new value of k B determined by the CODATA. Furthermore, having multiple independent measurements at these accuracies opens the possibility of defining the kelvin by fixing k B, an exciting prospect considering the upcoming redefinition of the International System of Units.

Abstract:
We report on our on-going effort to measure the Boltzmann constant, kB, using the Doppler Broadening Technique. The main systematic effects affecting the measurement are discussed. A revised error budget is presented in which the global uncertainty on systematic effects is reduced to 2.3 ppm. This corresponds to a reduction of more than one order of magnitude compared to our previous Boltzmann constant measurement. Means to reach a determination of kB at the part per million accuracy level are outlined.

Abstract:
In this paper, we describe an experiment performed at the Laboratoire de Physique des Lasers and dedicated to an optical measurement of the Boltzmann constant. With the proposed innovative technique, determining 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 sqrt(kT) and thus to a determination of the Boltzmann constant. The laser source is an ultra-stable CO2 laser with a wavelength . The absorption cell is placed in a thermostat keeping the temperature at 273.15 K within 1.4 mK. We were able to measure with a relative uncertainty as small as 3.8x10-5, which represents an improvement of an order of magnitude for an integration time comparable to our previous measurement published in 2007 [1]

Abstract:
We have recorded the Doppler profile of a well-isolated rovibrational line in the \nu2 band of 14NH3. 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, kB, by laser spectroscopy. A relative uncertainty of 2x10-4 has been obtained. The present determination should be significantly improved in the near future and contribute to a new definition of the kelvin.

Abstract:
In this paper, we present the latest results on the measurement of the Boltzmann constant kB, by laser spectroscopy of ammonia at 10 ?m. The Doppler absorption profile of a ro-vibrational line of an NH3 gas sample at thermal and pressure equilibrium is measured as accurately as possible. The absorption cell is placed inside a large 1m3 thermostat filled with an ice-water mixture, which sets the temperature very close to 273.15 K. Analysing this profile, which is related to the Maxwell-Boltzmann molecular speed distribution, leads to a determination of the Boltzmann constant via a measurement of the Doppler width (proportional tosqrt(kBT)). A spectroscopic determination of the Boltzmann constant with an uncertainty as low as 37 ppm is obtained. Recent improvements with a new passive thermostat lead to a temperature accuracy, stability and homogeneity of the absorption cell better than 1 ppm over a day.

Abstract:
The Planck constant $h$ is one of the most significant constants in quantum physics. Recently, the precision measurement of the numeral value of $h$ has been a hot issue due to its important role in establishment for both a new SI and a revised fundamental physical constant system. Up to date, two approaches, the watt balance and counting atoms, have been employed to determine the Planck constant at a level of several parts in $10^8$. In this paper, the principle and progress on precision measurement of the Planck constant using watt balance and counting atoms at national metrology institutes are reviewed. Further improvements for the Planck constant determination and possible developments of a revised physical constant system in future are discussed.

Abstract:
A Doppler broadening thermometry (DBT) instrument is built based on cavity ring-down spectroscopy (CRDS) for precise determination of the Boltzmann constant. Compared with conventional direct absorption methods, the high-sensitivity of CRDS allows to reach a satisfied precision at lower sample pressures, which also reduces the influence due to collisions. By recording the spectrum of C$_2$H$_2$ at 787 nm, we demonstrate a statistical uncertainty of 6 ppm (part per million) in the determined linewidth values by several hours' measurement at a sample pressure of 1.5 Pa. The influence on the spectroscopy-determined temperatures has been investigated, including the "hidden" weak lines overlapped with the selected transition for DBT measurements. The reproducibility has also been examined to be better than 10 ppm, and it indicates that the instrument is feasible for DBT measurement toward a precision at the ppm level.

Abstract:
The Boltzmann constant was measured by comparing the Johnson noise of a resistor at the triple point of water with a quantum-based voltage reference signal generated with a superconducting Josephson-junction waveform synthesizer. The measured value of k = 1.380651(18) \times 10^-23 J/K is consistent with the current CODATA value and the combined uncertainties. This is our first measurement of k with this electronic technique, and the first noise thermometry measurement to achieve a relative combined uncertainty of 13 parts in 10^6. We describe the most recent improvements to our Johnson Noise Thermometer that enabled the statistical uncertainty contribution to be reduced to seven parts in 10^6, as well as the further reduction of spurious systematic errors and EMI effects. The uncertainty budget for this measurement is discussed in detail.

Abstract:
We report on a new optical implementation of primary gas thermometry based on laser absorption spectrometry in the near infrared. The method consists in retrieving the Doppler broadening from highly accurate observations of the line shape of the R(12) $\nu_{1} + 2 \nu_{2}^{\phantom{1}0} + \nu_{3}$ transition in CO$_{2}$ gas at thermodynamic equilibrium. Doppler width measurements as a function of gas temperature, ranging between the triple point of water and the gallium melting point, allowed for a spectroscopic determination of the Boltzmann constant with a relative accuracy of $\sim1.6\times10^{-4}$.

Abstract:
We report in this paper the progresses on the determination of the Boltzmann constant using the acoustic gas thermometer (AGT) of fixed-length cylindrical cavities. First, we present the comparison of the molar masses of pure argon gases through comparing speeds of sound of gases. The procedure is independent from the methodology by Gas Chromatography-Mass Spectrometry (GC-MS). The experimental results show good agreement between both methods. The comparison offers an independent inspection of the analytical results by GC-MS. Second, we present the principle of the novel differential-cylindrical procedure based on the AGT of two fixed-length cavities. The deletion mechanism for some major perturbations is analyzed for the new procedure. The experimental results of the differential-cylindrical procedure demonstrate some major improvements on the first, second acoustic and third virial coefficients, and the excess half-widths. The three acoustic virial coefficients agree well with the stated-of-the-art experimental and theoretical (the ab initio calculation) results. The new method is characterized by much less correction-dependence. The differential-cylindrical procedure results in the preliminary determination of the Boltzmann constant of 1.380 650 6*10^-23 with the relative standard uncertainty of 2.3*10^-6. The new value is in 1.3*10^-6 above the adjusted Boltzmann constant given in CODATA 2010. The resultant gas constant R =8.314 473 J/mol/K with the same the relative standard uncertainty.