Comb-Referenced Doppler-Free Spectrometry of the

We report on precision spectroscopy of the 6s^{2} ^{1}S_{0}→6s6p ^{3}P_{1} intercombination line of mercury in the deep ultraviolet, by means of a frequency-comb referenced, wavelength-modulated, saturated absorption technique. This method allowed us to perform sub-Doppler investigations with an absolute frequency axis at 254 nm, while ensuring a relatively high signal-to-noise ratio. The absolute line center frequencies of the ^{200}Hg and ^{202}Hg bosonic isotopes were measured with a global uncertainty of 8 and 15 kHz (namely, 6.8×10^{-12} and 1.3×10^{-11}, in relative terms), respectively, the statistical and systematic components being significantly reduced as compared to past determinations. This remarkable result was achieved also thanks to an in-depth study of the ac Stark effect. Furthermore, we found the most accurate ^{200}Hg-^{202}Hg isotope shift ever obtained before, namely, 5 295 57 0±15_{stat}±8_{syst} kHz.

On the 12C2H2 near-infrared spectrum: absolute transition frequencies and an improved spectroscopic network at the kHz accuracy level.

Lamb dips of twenty lines in the P, Q, and R branches of the ν1 + ν3 + ν41 vibrational band of 12C2H2, in the spectral window of 7125-7230 cm-1, have been measured using an upgraded comb-calibrated frequency-stabilized cavity ring-down spectrometer, designed for extensive sub-Doppler measurements. Due to the large number of carefully executed Lamb-dip experiments, and to the extrapolation of absolute frequencies to zero pressure in each case, the combined average uncertainty of the measured line-center positions is 15 kHz (5 × 10-7 cm-1) with a 2-σ confidence level. Selection of the twenty lines was based on the theory of spectroscopic networks (SN), ensuring that a large number of transitions, measured previously by precision-spectroscopy investigations, could be connected to the para and ortho principal components of the SN of 12C2H2. The assembled SN contains 331 highly precise transitions, 119 and 121 of which are in the ortho and para principal components, respectively, while the rest remain in floating components. The para- and ortho-12C2H2 energy-level lists, determined during the present study, contain 82 and 80 entries, respectively, with an accuracy similar to that of the lines. Based on the newly assembled lists of para- and ortho-12C2H2 empirical energy levels, a line list, called TenkHz, has been generated. The TenkHz line list contains 282 entries in the spectral range of 5898.97-7258.87 cm-1; thus far, only 149 of them have been measured directly via precision spectroscopy. The TenkHz line list includes 35 intense lines that are missing in the HITRAN2020 database.

Tunable UV spectrometer for Doppler broadening thermometry of mercury.

We realized a UV laser spectrometer at 253.7 nm for Doppler broadening thermometry on the 1S0-3P1 intercombination line in mercury vapors. Our setup is based on the two-stage duplication of a 1014.8 nm diode laser in a fiber-coupled periodically poled lithium niobate waveguide crystal and a beta-barium borate crystal in enhancement cavity, and we exploit injection locking of a 507.4 nm diode laser to boost the available optical power after the first duplication. Our setup addresses spectroscopic features that allow the thermodynamic temperature determination of the atomic sample from the absorption profile with 10-6 accuracy. The realized UV laser source has 1×10-4 relative intensity stability, Gaussian shape, and over 10 GHz mode-hop-free tunable range. These features are crucial for the practical realization of the kelvin in the new International System of Units through a spectroscopic technique.

Absolute frequency stabilization of a QCL at 8.6 µm by modulation transfer spectroscopy.

Modulation transfer spectroscopy is used to demonstrate absolute frequency stabilization of an 8.6-µm-wavelength quantum cascade laser against a sub-Doppler absorption of the CHF3 molecule. The obtained spectral emission properties are thoroughly characterized through a self-referenced optical frequency comb, stabilized against either a GPS-disciplined Rb clock or a 1.54-µm Er-fiber laser locked to a high-finesse ultra-low-expansion optical cavity. Fractional long-term stability and accuracy at a level of 4×10-12 (at 100 s) and 3×10-10, respectively, are demonstrated, along with an emission linewidth as narrow as 10 kHz for observation times of 0.1 s.

Absolute frequency measurements of CHF3 Doppler-free ro-vibrational transitions at 8.6 µm.

We report on absolute measurements of saturated-absorption line-center frequencies of room-temperature trifluoromethane using a quantum cascade laser at 8.6 µm and the frequency modulation spectroscopy method. Absolute calibration of the laser frequency is obtained by direct comparison with a mid-infrared optical frequency comb synthesizer referenced to a radio-frequency Rb standard. Several sub-Doppler transitions falling in the υ5 vibrational band are investigated at around 1158.9 cm-1 with a fractional frequency precision of 8.6·10-12 at 1-s integration time, limited by the Rb-clock stability. The demonstrated frequency uncertainty of 6.6·10-11 is mainly limited by the reproducibility of the frequency measurements.

Linking the thermodynamic temperature to an optical frequency: recent advances in Doppler broadening thermometry.

Laser spectroscopy in the linear regime of radiation-matter interaction is a powerful tool for measuring thermodynamic quantities in a gas at thermodynamic equilibrium. In particular, the Doppler effect can be considered a gift of nature, linking the thermal energy to an optical frequency, namely the line centre frequency of an atomic or molecular spectral line. This is the basis of a relatively new method of primary gas thermometry, known as Doppler broadening thermometry (DBT). This paper reports on the efforts that have been carried out, in the last decade, worldwide, to the end of making DBT competitive with more consolidated and accurate methodologies, such as acoustic gas thermometry and dielectric constant gas thermometry. The main requirements for low-uncertainty DBT, of both theoretical and technical nature, will be discussed, with a special focus on those related to the line shape model and to the frequency scale. A deep comparison among the different molecules that have been selected in successful DBT implementations is also reported. Finally, for the first time, to the best of my knowledge, the influence of refractive index effects is discussed.

Progress towards the determination of thermodynamic temperature with ultra-low uncertainty.

Previous research effort towards the determination of the Boltzmann constant has significantly improved the supporting theory and the experimental practice of several primary thermometry methods based on the measurement of a thermodynamic property of a macroscopic system at the temperature of the triple point of water. Presently, experiments are under way to demonstrate their accuracy in the determination of the thermodynamic temperature T over an extended range spanning the interval between a few kelvin and the copper freezing point (1358 K). We discuss how these activities will improve the link between thermodynamic temperature and the temperature as measured using the International Temperature Scale of 1990 (ITS-90) and report some preliminary results obtained by dielectric constant gas thermometry and acoustic gas thermometry. We also provide information on the status of other primary methods, such as Doppler broadening thermometry, Johnson noise thermometry and refractive index gas thermometry. Finally, we briefly consider the implications of these advancements for the dissemination of calibrated temperature standards.

Direct phase-locking of a 8.6-µm quantum cascade laser to a mid-IR optical frequency comb: application to precision spectroscopy of N2O.

We developed a high-precision spectroscopic system at 8.6 µm based on direct heterodyne detection and phase-locking of a room-temperature quantum-cascade-laser against an harmonic, 250-MHz mid-IR frequency comb obtained by difference-frequency generation. The ∼30 dB signal-to-noise ratio of the detected beat-note together with the achieved closed-loop locking bandwidth of ∼500 kHz allows for a residual integrated phase noise of 0.78 rad (1 Hz-5 MHz), for an ultimate resolution of ∼21 kHz, limited by the measured linewidth of the mid-IR comb. The system was used to perform absolute measurement of line-center frequencies for the rotational components of the ν2 vibrational band of N2O, with a relative precision of 3×10(-10).

Frequency-comb-assisted precision laser spectroscopy of CHF3 around 8.6 µm.

We report a high-precision spectroscopic study of room-temperature trifluoromethane around 8.6 µm, using a CW quantum cascade laser phase-locked to a mid-infrared optical frequency comb. This latter is generated by a nonlinear down-conversion process starting from a dual-branch Er:fiber laser and is stabilized against a GPS-disciplined rubidium clock. By tuning the comb repetition frequency, several transitions falling in the υ5 vibrational band are recorded with a frequency resolution of 20 kHz. Due to the very dense spectra, a special multiple-line fitting code, involving a Voigt profile, is developed for data analysis. The combination of the adopted experimental approach and survey procedure leads to fractional accuracy levels in the determination of line center frequencies, down to 2 × 10(-10). Line intensity factors, pressure broadening, and shifting parameters are also provided.

Absolute frequency stabilization of an extended-cavity diode laser by means of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy.

We implemented an optical frequency standard based on noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) at 1.39 µm. The emission frequency of an extended-cavity diode laser was actively stabilized against the center of the 4(4,1)→4(4,0) transition of the H(2)(18)O ν1+ν3 band, under optical saturation conditions. The nonlinear regime of laser-gas interaction was reached by using an optical cavity with a finesse of about 8700. By filling it with an 18O-enriched water sample at a pressure of a few Pa, the Lamb dip could be observed with a full width at half-maximum of about 2 MHz. Absolute frequency stabilization was obtained by locking the cavity resonance to the center of the sub-Doppler signal, which was provided by the NICE-OHMS technique under the dispersion regime of operation. An Allan deviation analysis demonstrated a relative frequency stability of ∼5×10(-13) for an integration time of 1 s. For longer integration times, the flicker frequency noise floor set the stability at the level of 4×10(-14).

Narrow-linewidth quantum cascade laser at 8.6 µm.

We report on a narrow-linewidth distributed-feedback quantum cascade laser at 8.6 µm that is optical-feedback locked to a high-finesse V-shaped cavity. The spectral purity of the quantum cascade laser is fully characterized using a high-sensitivity optical frequency discriminator, leading to a 1 ms linewidth of less than 4 kHz and a minimum laser frequency noise spectral density as low as 0.01 Hz2/Hz for Fourier frequencies larger than 100 kHz. The cumulative standard deviation of the laser intensity is better than 0.1% over an integration bandwidth from 2 Hz to 100 MHz.

Line-narrowing effects in the near-infrared spectrum of water and precision determination of spectroscopic parameters.

A dual laser absorption spectrometer operating at 1.39 µm was employed to acquire high-quality absorption spectra in coincidence with the 44,1 → 44,0 line of the H2 (18)O ν1 + ν3 band, at the temperature of the triple point of water. A rather sophisticated global fitting procedure was developed and used to simultaneously fit spectra across the explored pressure range, roughly between 1 and 4 Torr. Adopting the speed-dependent Galatry profile with a hypergeometric dependence of the collisional width and shift on the absorbers' velocity, we could take into account narrowing effects ascribed to collision-induced velocity changes and speed-dependence of relaxation rates. The global approach allowed us to implement and exploit some relevant physical constraints at the aim of reducing significantly statistical correlation issues among free parameters. Consequently, we demonstrated the possibility of determining pressure broadening and shifting parameters with high precision and accuracy, at the level of one part over 10(3). Furthermore, even being in the Doppler regime, it was possible to determine the effective frequency of velocity-changing collisions for self-colliding H2 (18)O molecules.

Coherent phase lock of a 9 µm quantum cascade laser to a 2 µm thulium optical frequency comb.

We demonstrate coherent phase locking of a room-temperature continuous-wave quantum cascade laser (QCL) at 9.1 µm to a Tm-fiber laser frequency comb centered at 2 µm, with an integrated residual phase error of 0.9 rad (30 mHz to 1.5 MHz). This resulted in a QCL linewidth reduction from 525 to 25 kHz at 1 ms observation time, limited by the linewidth of the free-running frequency comb.

Offset-frequency locking of extended-cavity diode lasers for precision spectroscopy of water at 1.38 µm.

We describe a continuous-wave diode laser spectrometer for water-vapour precision spectroscopy at 1.38 µm. The spectrometer is based upon the use of a simple scheme for offset-frequency locking of a pair of extended-cavity diode lasers that allows to achieve unprecedented accuracy and reproducibility levels in measuring molecular absorption. When locked to the master laser with an offset frequency of 1.5 GHz, the slave laser exhibits residual frequency fluctuations of 1 kHz over a time interval of 25 minutes, for a 1-s integration time. The slave laser could be continuously tuned up to 3 GHz, the scan showing relative deviations from linearity below the 10{-6} level. Simultaneously, a capture range of the order of 1 GHz was obtained. Quantitative spectroscopy was also demonstrated by accurately determining relevant spectroscopic parameters for the 22,1→22,0line of the H2(18)O v1+v3 band at 1384.6008 nm.

Absolute frequency stabilization of an extended-cavity diode laser against Doppler-free H(2)O17 absorption lines at 1.384 microm.

We report the frequency stabilization of a cw extended-cavity diode laser against saturated absorption lines of the H(2)O17 isotopologue of water vapor at around 1.384 microm. The saturation of rotovibrational transitions is achieved by filling a high-finesse optical resonator with H(2)O17 at low pressure and by locking the laser frequency to the resonator by using the Pound-Drever-Hall technique. Absolute frequency stabilization is obtained, locking the cavity resonance to the center of the sub-Doppler line by means of the wavelength modulation method. A relative frequency stability of sigma(y)(tau)=10(-13)(0.1tau(-2)+0.9)(1/2) is demonstrated for integration times in the range 4 ms

The line shape problem in the near-infrared spectrum of self-colliding CO2 molecules: experimental investigation and test of semiclassical models.

An intensity-stabilized diode laser absorption spectrometer was developed and used to perform a highly accurate study of the line shape of CO(2) absorption lines, in the spectral region around 5000 cm(-1), belonging to the nu(1) + 2nu(2)(0) + nu(3) combination band, at a temperature of 296.00 K. Standard and complex semiclassical models, including Dicke narrowing and speed-dependent broadening effects, were applied, tested, and compared in the pressure range between 0.7 and 4 kPa, in order to single out the model best reproducing the absorption profile and, hence, the physical situation of self-colliding CO(2) molecules. Line intensity factors and self-broadening coefficients were determined. The 1-sigma overall accuracy of our determinations is at a level of 0.1%, which is, to our knowledge, the highest ever reached.

Measuring the 13C/12C isotope ratio in atmospheric CO2 by means of laser absorption spectrometry: a new perspective based on a 2.05-microm diode laser.

The potential use of high sensitivity laser absorption spectroscopy for measuring the 13C/12C isotope ratio in atmospheric CO2 has been demonstrated, using a GaSb-based diode laser at 2.05 microm. In this spectral region, the overlapping between relatively strong 12CO2 and 13CO2 absorption features gives rise to several line pairs which are well suitable for a spectroscopic determination of the isotope ratio. Preliminary results have demonstrated that a short-term precision better than 1 per thousand can be easily obtained, for a CO2 concentration of 1000 ppm. We extensively discuss the influence of a possible non-linearity in the detectors' response on the delta-value and suggest an instrumental development that would allow to eliminate this effect.

Oxygen isotope ratio measurements in CO(2) by means of a continuous-wave quantum cascade laser at 4.3 mum.

A mid-infrared laser spectrometer was developed for simultaneous high-precision (18)O/(16)O and (17)O/(16)O isotope ratio measurements in carbon dioxide. A continuous-wave, liquid-nitrogen cooled, distributed feedback quantum cascade laser, working at a wavelength of 4.3 microm, was used to probe (12)C(16)O(2), (16)O(12)C(18)O, and (16)O(12)C(17)O lines at ~2311.8 cm(-1). High sensitivity was achieved by means of wavelength modulation spectroscopy with second-harmonic detection. The experimental reproducibility in the short and long terms was deeply investigated through the accurate analysis of a large number of spectra. In particular, we found a short term precision of 0.5 per thousand and 0.6 per thousand, respectively, for (18)O/(16)O and (17)O/(16)O isotope ratios. The occurrence of systematic deviations is also discussed.

Highly accurate determinations of CO(2) line strengths using intensity-stabilized diode laser absorption spectrometry.

An intensity-stabilized laser absorption spectrometer, which incorporates a mirror-extended cavity diode laser, a temperature-stabilized gas cell, and a Michelson interferometer, was developed and applied to a highly accurate investigation of line intensity factors within the nu(1)+2nu(2) (0)+nu(3) combination band of carbon dioxide, around 2 microm wavelength, at a temperature of 296.0 K. This relatively complex apparatus enables one to observe the absorption line shape with high precision and accuracy in such a way that it is possible to retrieve the integrated absorbance with a relative uncertainty better than 0.1%. The absorption spectra were interpolated with the uncorrelated strong-collision model of Rautian and Sobel'man in order to take into account Dicke narrowing effects, thus obtaining an agreement at a level of a few parts per 10(-5). We report line strength values for the R(2)-R(18) transitions with an unprecedented level of accuracy, in the range between 0.1% and 0.15%. Finally, we discuss the possibility of providing a first experimental test of the theoretical model for molecular line strengths based on the Herman-Wallis expansion.