The Boltzmann project.

The International Committee for Weights and Measures (CIPM), at its meeting in October 2017, followed the recommendation of the Consultative Committee for Units (CCU) on the redefinition of the kilogram, ampere, kelvin and mole. For the redefinition of the kelvin, the Boltzmann constant will be fixed with the numerical value 1.380 649 × 10-23 J K-1. The relative standard uncertainty to be transferred to the thermodynamic temperature value of the triple point of water will be 3.7 × 10-7, corresponding to an uncertainty in temperature of 0.10 mK, sufficiently low for all practical purposes. With the redefinition of the kelvin, the broad research activities of the temperature community on the determination of the Boltzmann constant have been very successfully completed. In the following, a review of the determinations of the Boltzmann constant k, important for the new definition of the kelvin and performed in the last decade, is given.

Highly accurate intensity factors of pure CO2 lines near 2 µm.

Line intensities for carbon dioxide are measured with a novel spectroscopic approach, assisted by an optical frequency comb synthesizer for frequency calibration purposes. The main feature of the spectrometer consists in the exploitation of optical feedback from a V-shaped high-finesse optical resonator to effectively narrow a distributed feedback diode laser at the wavelength of 2 µm. Laser-gas interaction takes place inside an isothermal cell, which is placed on the transmission from the cavity. High quality, self-calibrated, absorption spectra are observed in pure CO2 samples at different gas pressures, in coincidence with three lines of the R-branch of the ν1 + 2ν2 + ν3 band. Line intensities are determined using a global fitting approach in which a manifold of spectra are simultaneously analyzed across the range of pressures between 5 and 100 Torr, sharing a restricted number of unknown parameters. Various sources of uncertainty have been identified and carefully quantified, thus leading to an overall uncertainty ranging between 0.17% and 0.23%. The measured values are in a very good agreement with recent ab initio predictions.

Characterization of the frequency stability of an optical frequency standard at 1.39 µm based upon noise-immune cavity-enhanced optical heterodyne molecular spectroscopy.

Frequency fluctuations of an optical frequency standard at 1.39 µm have been measured by means of a highly-sensitive optical frequency discriminator based on the fringe-side transmission of a high finesse optical resonator. Built on a Zerodur spacer, the optical resonator exhibits a finesse of 5500 and a cavity-mode width of about 120 kHz. The optical frequency standard consists of an extended-cavity diode laser that is tightly stabilized against the center of a sub-Doppler H(2) (18)O line, this latter being detected by means of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. The emission linewidth has been carefully determined from the frequency-noise power spectral density by using a rather simple approximation, known as ß-line approach, as well as the exact method based on the autocorrelation function of the laser light field. It turns out that the linewidth of the optical frequency standard amounts to about 7 kHz (full width at half maximum) for an observation time of 1 ms. Compared to the free-running laser, the measured width corresponds to a line narrowing by a factor of ~220.

Determination of the Boltzmann constant by means of precision measurements of H2(18)O line shapes at 1.39 µm.

We report on a new implementation of Doppler broadening thermometry based on precision absorption spectroscopy by means of a pair of offset-frequency locked extended-cavity diode lasers at 1.39 µm. The method consists in the highly accurate observation of the shape of the 4(4,1)→4(4,0) line of the H2(18)O ν1+ν3 band, in a water vapor sample at thermodynamic equilibrium. A sophisticated and extremely refined spectral analysis procedure is adopted for the retrieval of the Doppler width as a function of the gas pressure, taking into account the Dicke narrowing effect, the speed dependence of relaxation rates, and the physical correlation between velocity-changing and dephasing collisions. A spectroscopic determination of the Boltzmann constant with a combined (type A and type B) uncertainty of 24 parts over 10(6) is reported. This is the best result obtained so far by means of an optical method. Our determination is in agreement with the recommended CODATA value.

Velocity effects on the shape of pure H2O isolated lines: complementary tests of the partially correlated speed-dependent Keilson-Storer model.

Complementary tests of the partially correlated speed-dependent Keilson-Storer (pCSDKS) model for the shape of isolated transition of pure water vapor [N. H. Ngo et al., J. Chem. Phys. 136, 154310 (2012)] are made using new measurements. The latter have been recorded using a high sensitivity cavity ring down spectrometer, for seven self-broadened H(2)O lines in the 1.6 µm region at room temperature and for pressures from 0.5 to 15 Torr. Furthermore, the H(2) (18)O spectra of [M. D. De Vizia et al., Phys. Rev. A 83, 052506 (2011)] in the 1.38 µm region, measured at 273.15 K and for pressures from 0.3 to 3.75 Torr have also been used for comparison with the model. Recall that the pCSDKS model takes into account the collision-induced velocity changes, the speed dependences of the broadening and shifting coefficients as well as the partial correlation between velocity and rotational-state changes. All parameters of the model have been fixed at values previously determined, except for a scaling factor applied to the input speed-dependent line broadening. Comparisons between predictions and experiments have been made by looking at the results obtained when fitting the calculated and measured spectra by Voigt profiles. The good agreement obtained for all considered lines, at different temperature and pressure conditions, confirms the consistency and the robustness of the model. Limiting cases of the model have been then derived, showing the influence of different contributions to the line shape.

High-precision molecular interrogation by direct referencing of a quantum-cascade-laser to a near-infrared frequency comb.

This work presents a very simple yet effective way to obtain direct referencing of a quantum-cascade-laser at 4.3 µm to a near-IR frequency-comb. Precise tuning of the comb repetition-rate allows the quantum-cascade-laser to be scanned across absorption lines of a CO2 gaseous sample and line profiles to be acquired with extreme reproducibility and accuracy. By averaging over 50 acquisitions, line-centre frequencies are retrieved with an uncertainty of 30 kHz in a linear interaction regime. The extension of this methodology to other lines and molecules, by the use of widely tunable extended-cavity quantum-cascade-lasers, paves the way to a wide availability of high-quality and traceable spectroscopic data in the most crucial region for molecular detection and interrogation.

Observing the intrinsic linewidth of a quantum-cascade laser: beyond the Schawlow-Townes limit.

A comprehensive investigation of the frequency-noise spectral density of a free-running midinfrared quantum-cascade laser is presented for the first time. It provides direct evidence of the leveling of this noise down to a white-noise plateau, corresponding to an intrinsic linewidth of a few hundred hertz. The experiment is in agreement with the most recent theory on the fundamental mechanism of line broadening in quantum-cascade lasers, which provides a new insight into the Schawlow-Townes formula and predicts a narrowing beyond the limit set by the radiative lifetime of the upper level.

Lamb-dip-locked quantum cascade laser for comb-referenced IR absolute frequency measurements.

The frequency of a DFB quantum cascade laser (QCL) emitting at 4.3 microm has been long-term stabilized to the Lamb-dip center of a CO2 ro-vibrational transition by means of first-derivative locking to the saturated absorption signal. Thanks to the non-linear sum-frequency generation (SFG) process with a fiber-amplified Nd:YAG laser, the QCL mid-infrared (IR) radiation has been linked to an optical frequency-comb synthesizer (OFCS) and its absolute frequency counted with a kHz-level precision and an overall uncertainty of 75 kHz.

Primary gas thermometry by means of laser-absorption spectroscopy: determination of the Boltzmann constant.

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) nu1+2nu2(0)+nu3 transition in CO2 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 approximately 1.6 x 10(-4).

Frequency-comb-referenced quantum-cascade laser at 4.4 microm.

We report what we believe to be the first absolute frequency measurement performed using a quantum-cascade laser (QCL) referenced to an optical frequency comb synthesizer (OFCS). A QCL at 4.43 microm has been used for producing near-infrared radiation at 858 nm by means of sum-frequency generation with a Nd:YAG source in a periodically poled lithium niobate nonlinear crystal. The absolute frequency of the QCL source has been measured by detecting the beat note between the sum frequency and a diode laser at the same wavelength, while both the Nd:YAG and the diode laser were referenced to the OFCS. Doppler-broadened line profiles of (13)CO(2) molecular transitions have been recorded with such an absolute frequency reference.

Doppler-free saturated-absorption spectroscopy of CO2 at 4.3 microm by means of a distributed feedback quantum cascade laser.

We report the application of a cw distributed feedback quantum cascade laser to Lamb-dip spectroscopy of CO2 at 4.3 microm. With the laser operating in the free-running mode, we observed the sub-Doppler profile of the P(28) line of the (0,1(1),0)->(0,1(1),1) hot band by implementing a pump-probe scheme and using wavelength modulation spectroscopy for highly sensitive detection of saturated absorption signals. We investigated the main limitations to the observation of a narrow resonance, with particular attention to the effect of the laser current noise. We determined the intrinsic laser emission width, which was found to be approximately 3.4 MHz (FWHM) for an observation time of approximately 200 ms.

Looking into the volcano with a Mid-IR DFB diode laser and Cavity Enhanced Absorption Spectroscopy.

We report on the first application of extended-wavelength DFB diode lasers to Cavity-Enhanced Absorption Spectroscopy in-situ trace measurements on geothermal gases. The emission from the most active fumarole at the Solfatara volcano near Naples (Italy) was probed for the presence of CO and CH(4). After passing through a gas dryer and cooler, the volcanic gas flow (98% CO(2)) was analysed in real time for the concentration of these species, whose relatively strong absorption lines could be monitored simultaneously by a single Distributed Feed-Back (DFB) GaSb-based diode laser emitting around 2.33 mum (4300 cm(-1)) at room temperature. The concentrations were found to be about 3 ppm and 75 ppm, respectively, while actual detection limits for these molecules are around 1 ppb. We discuss the possibility of detecting other species of interest for volcanic emission monitoring.

Assessing soil respiration by means of near-infrared diode laser spectroscopy.

High-resolution diode laser spectroscopy in the near-infrared region is applied to the accurate measurement of soil respiration. In particular, the use of a diode-laser-based spectrometer has allowed the implementation, for the first time, of a static accumulation method capable of measuring soil respiration from continuous measurements of CO(2) concentrations, with minor perturbation on soil respiration as well as on CO(2) transport and emission. The system has been tested in a laboratory experiment by detection of CO(2) production from sandy matrices, inoculated with active soil microbes and supplied with different amounts of decomposable plant material. Respiration rates of all samples were then retrieved using a diffusion model. The results of the laboratory tests are in agreement with those expected on the basis of sample composition. Examples of operation with real soil samples are also reported. We discuss the possible field application of the system, in conjunction with closed static soil chambers.

First field determination of the 13C/12C isotope ratio in volcanic CO2 by diode-laser.

Carbon isotope ratio analysis using a laser-based technique has been performed in the field, on the gaseous emissions from an active volcano. We here describe that 13CO2/12CO2 determinations can be carried out in a quasi-continuous regime using a compact, selective and sensitive diode laser spectrometer at a wavelength of 2 mum. Within the Solfatara crater (near Naples, Italy), in a very harsh environment, we were able to determine relative 13CO2/12CO2 values, on the highest flux fumarole, with an accuracy of 0.5 per thousand. Regular and frequent observations of the carbon isotopes in volcanic gases, which become possible with our methodology, are of the utmost importance for geochemical surveillance of volcanoes.

Isotope analysis of water by means of near infrared dual-wavelength diode laser spectroscopy.

A novel diode laser spectrometer was developed using dualwavelength multiplexing, ensuring ideal conditions for high-precision and simultaneous measurements of the 2H/1H, 17O/16O, and 18O/16O isotope ratios in water. A 1.4-m diode laser probed a H16OH / HO2H line pair near 7198 cm-1, while a similar laser observed H16OH, H17OH, and H18OH rovibrational lines around 7183 cm-1, or a H16OH / H18OH line pair near 7200 cm-1. The 1-sigma standard deviation is 0.2 per thousand for 18O/16O, and 0.5 per thousand for the 2H/1H and 17O/16O isotope ratios. Preliminary experiments with repeated injections of a natural abundance sample point to an accuracy of about 1 per thousand for all three isotope ratios in natural samples.

Determination of the 2H/1H, 17O/16O, and 18O/16O isotope ratios in water by means of tunable diode laser spectroscopy at 1.39 microm.

We demonstrate the feasibility of the accurate and simultaneous measurement of the 2H/1H, 17O/16O, and 18O/16O isotope ratios in water vapor by means of tunable diode laser spectroscopy. The absorptions are due to the v1 + v3 combination band, observed using a room temperature, distributed feedback (DFB) diode laser at 1.39 microm. The precision of the instrument is approximately 3, 1, and 0.5/1000 for the 2H, 17O, and 18O isotope ratios, respectively, and is at present limited by residual optical feedback to the laser. The signal-to-noise, however, is superior to that obtained in a similar experiment using a color center laser at 2.7 microm. Replacing the current laser with a better unit, we are confident that a precision well below 1/1000 is attainable for all three isotope ratios. The diode laser apparatus is ideally suited for applications demanding a reliable, cheap, and/or portable instrument, such as the biomedical doubly labeled water method and atmospheric sensing.

Collisional-Broadened and Dicke-Narrowed Lineshapes of H(2)(16)O and H(2)(18)O Transitions at 1.39 µm.

We present results of a study on the self-broadening and broadening by nitrogen and oxygen of H(2)(16)O and H(2)(18)O lines in the 1.39-µm wavelength region using a distributed feedback semiconductor diode laser. To estimate the broadening coefficients, the absorption lineshapes were analyzed using the ordinary Voigt profile which provided good fits for most of the investigated lines. The broadening coefficients were found to be larger for nitrogen used as a perturber than for oxygen. This agrees with the fact that the quadrupole moment of N(2) is larger than that of O(2). Nevertheless, for lines involving high-rotational quantum number J, relatively smaller broadening coefficients were found and deviations of the measured profiles from the standard Voigt profile were observed. These deviations were ascribed as caused by Dicke-narrowing effect. Corresponding to this effect, collisional-broadening and narrowing coefficients were determined using the Nelkin-Ghatak profile which is suitable for the "hard"-collision model. The optical diffusion coefficients of the water in both nitrogen and oxygen gases were determined from the measurements of the collisional-narrowing coefficients. Copyright 2001 Academic Press.

Spectroscopic observation of the Faraday effect in the far infrared.

The Faraday effect was observed in the far-infrared spectrum of NO(2) for what is believed to be the first time. A systematic investigation of the magneto-optical signal as a function of the uncrossing angle between the polarizers was performed. Differences from similar experiments performed in the infrared and the visible regions were encountered. Moreover, a fit of the experimental data allowed calculation of the difference in the real and the imaginary terms of the refractive index for DM(F)=+1 and DM(F)=-1 multiplets.

Detection of H2O and CO2 with distributed feedback diode lasers: measurement of broadening coefficients and assessment of the accuracy levels for volcanic monitoring.

We reproduced the chemical-physical conditions of fumarolic emission at Phlaegrean Fields, Pozzuoli, Italy, and we measured the CO(2) and H(2)O concentrations using an absorption spectrometer based on two distributed feedback laser diodes at wavelengths of 1.578 and 1.393 microm. We discuss the accuracy levels of the different methods used. Furthermore, we measured the broadening coefficients for H(2)O (self-broadening, 28.2 +/- 0.6 MHz/Torr; CO(2) broadening, 6.0 +/- 0.4 MHz/Torr) and CO(2) (self-broadening, 3.2 +/- 0.1 MHz/Torr; H(2)O broadening, 4.0 +/- 0.1 MHz/Torr). Using the present data, we evaluated a minimum detectable variation of 9% for H(2)O and 1% for CO(2).

Pressure-Broadening Investigation of NO2 in the Near Infrared

In this paper we report the data for self-, oxygen-, and nitrogen-broadening coefficients for 6 NO2 lines belonging to two different bands: the (0 3 0)-(0 0 0) vibrational transition of the A2B2 <-- X2A1 system at 8360 A and the (2 13 1)-(0 0 0) vibrational transition within the X2A1 electronic ground state at 7390 A. These measurements were performed using a differential absorption spectrometer based on semiconductor diode lasers emitting in the near-infrared region. We also report wavelength measurements for 14 lines of the above-cited bands obtained by means of a Michelson wavemeter with an accuracy of one part in 10(7). Copyright 1997 Academic Press. Copyright 1997Academic Press