Direct determination of the Boltzmann constant by an optical method

A mathematical model of biofilm growth and spread within plant xylem: Case study of Xylella fastidiosa in olive trees

Xylem-limited bacterial pathogens cause some of the most destructive plant diseases. Though imposed measures to control these pathogens are generally ineffective, even among susceptible taxa, some hosts can limit bacterial loads and symptom expression. Mechanisms by which this resistance is achieved are poorly understood. In particular, it is still unknown how differences in vascular structure may influence biofilm growth and spread within a host. To address this, we developed a novel theoretical framework to describe biofilm behaviour within xylem vessels, adopting a polymer-based modelling approach. We then parameterised the model to investigate the relevance of xylem vessel diameters on Xylella fastidiosa resistance among olive cultivars. The functionality of all vessels was severely reduced under infection, with hydraulic flow reductions of 2-3 orders of magnitude. However, results suggest wider vessels act as biofilm incubators; allowing biofilms to develop over a long time while still transporting them through the vasculature. By contrast, thinner vessels become blocked much earlier, limiting biofilm spread. Using experimental data on vessel diameter distributions, we were able to determine that a mechanism of resistance in the olive cultivar Leccino is a relatively low abundance of the widest vessels, limiting X. fastidiosa spread.

Computer-Aided Reconstruction and Application of Bacillus halodurans S7 Xylanase with Heat and Alkali Resistance

β-1,4-Endoxylanase is the most critical hydrolase for xylan degradation during lignocellulosic biomass utilization. However, its poor stability and activity in hot and alkaline environments hinder its widespread application. In this study, BhS7Xyl from Bacillus halodurans S7 was improved using a computer-aided design through isothermal compressibility (βT) perturbation engineering and by combining three thermostability prediction algorithms (ICPE-TPA). The best variant with remarkable improvement in specific activity, heat resistance (70 °C), and alkaline resistance (both pH 9.0 and 70 °C), R69F/E137M/E145L, exhibited a 4.9-fold increase by wild-type in specific activity (1368.6 U/mg), a 39.4-fold increase in temperature half-life (458.1 min), and a 57.6-fold increase in pH half-life (383.1 min). Furthermore, R69F/E137M/E145L was applied to the hydrolysis of agricultural waste (corncob and hardwood pulp) to efficiently obtain a higher yield of high-value xylooligosaccharides. Overall, the ICPE-TPA strategy has the potential to improve the functional performance of enzymes under extreme conditions for the high-value utilization of lignocellulosic biomass.

The Free Energy of Nucleosomal DNA Based on the Landau Model and Topology

The free energy of nucleosomal DNA plays a key role in the formation of nucleosomes in eukaryotes. Some work on the free energy of nucleosomal DNA have been carried out in experiments. However, the relationships between the free energy of nucleosomal DNA and its conformation, especially its topology, remain unclear in theory. By combining the Landau theory, the Hopfion model and experimental data, we find that the free energy of nucleosomal DNA is at the lower level. With the help of the energy minimum principle, we conclude that nucleosomal DNA stays in a stable state. Moreover, we discover that small perturbations on nucleosomal DNA have little effect on its free energy. This implies that nucleosomal DNA has a certain redundancy in order to stay stable. This explains why nucleosomal DNA will not change significantly due to small perturbations.

Linear Probing of Molecules at Micrometric Distances from a Surface with Sub-Doppler Frequency Resolution

We report on precision spectroscopy of subwavelength confined molecular gases. This was obtained by rovibrational selective reflection of NH_{3} and SF_{6} gases using a quantum cascade laser at λ≈10.6  μm. Our technique probes molecules at micrometric distances (≈λ/2π) from the window of a macroscopic cell with submegahertz resolution, allowing molecule-surface interaction spectroscopy. We exploit the linearity and high resolution of our technique to gain novel spectroscopic information on the SF_{6} greenhouse gas, useful for enriching molecular databases. The natural extension of our work to thin cells will allow compact frequency references and improved measurements of the Casimir-Polder interaction with molecules.

Sideband amplitude modulation absorption spectroscopy of CH4 at 1170 nm

We report on the method of the sideband amplitude modulation (SAM) to achieve high-sensitivity spectroscopy with a fiber electro-optic modulator (fiber-EOM). This method increases the signal to noise ratio (SNR) by a factor of forty, comparing with conventional absorption spectroscopy. It is a temporal balanced detection to eliminate the intensity noise of the light source, and capable of preserving an undistorted Doppler profile for further quantitative analysis. Taking advantage of the newly developed fiber-EOM, SAM is applicable for various spectroscopies with a simple experimental setup. We performed SAM on CH₄3ν₃ overtone band at 1170 nm using an external cavity Quantum dot laser. We demonstrated that one of the absorption lines buried in the other ten times stronger nearby lines was clearly extracted. SAM shows great potential on the molecular spectroscopy, where the spectrum is complicated and quantitative analysis is required.

Prediction of line shape parameters and their temperature dependences for CO2-N2 using molecular dynamics simulations

We show in this paper that requantized classical molecular dynamics simulations (rCMDSs) are capable of predicting various refined spectral-shape parameters of absorption lines of CO₂ broadened by N₂ with high precision. Combining CMDSs and a requantization procedure, we computed the auto-correlation function of the CO₂ dipole moment responsible for the absorption transition. Its Fourier-Laplace transform directly yields the spectrum. Calculations were made for two temperatures, 200 and 296 K, at 1 atm and for a large range of Doppler widths, from the near-Doppler to the collision-dominant regimes. For each temperature and each line, the spectra calculated for various Doppler widths were simultaneously fit with the Hartmann-Tran (HT) profile. This refined profile, which takes into account the effects of the speed dependent collisional line broadening, the Dicke narrowing, and the collisional line mixing, was recommended as a reference model to be used in high-resolution spectroscopy (instead of the simplified Voigt model). The HT parameters retrieved from the rCMDS-calculated spectra were then directly compared with those deduced from high-precision measurements [J. S. Wilzewski et al., J. Quant. Spectrosc. Radiat. Transfer 206, 296-305 (2018)]. The results show a very good agreement, even for those parameters whose influence on the spectra is very small. Good agreement is also obtained between measured and predicted temperature dependences of these parameters. This demonstrates that rCMDS is an excellent tool, highly competitive with respect to high quality measurements for precise line-shape studies.

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.

Conjugating precision and acquisition time in a Doppler broadening regime by interleaved frequency-agile rapid-scanning cavity ring-down spectroscopy

We propose a novel approach to cavity-ring-down-spectroscopy (CRDS) in which spectra acquired with a frequency-agile rapid-scanning (FARS) scheme, i.e., with a laser sideband stepped across the modes of a high-finesse cavity, are interleaved with one another by a sub-millisecond readjustment of the cavity length. This brings to time acquisitions below 20 s for few-GHz-wide spectra composed of a very high number of spectral points, typically 3200. Thanks to the signal-to-noise ratio easily in excess of 10 000, each FARS-CRDS spectrum is shown to be sufficient to determine the line-centre frequency of a Doppler broadened line with a precision of 2 parts over 10¹¹, thus very close to that of sub-Doppler regimes and in a few-seconds time scale. The referencing of the probe laser to a frequency comb provides absolute accuracy and long-term reproducibility to the spectrometer and makes it a powerful tool for precision spectroscopy and line-shape analysis. The experimental approach is discussed in detail together with experimental precision and accuracy tests on the (30 012) ← (00 001) P12e line of CO₂ at ∼1.57 μm.

Direct-comb molecular spectroscopy by heterodyne detection with continuous-wave laser for high sensitivity

We have demonstrated direct-comb molecular spectroscopy in which an individual-comb mode is resolved by heterodyne detection with a continuous-wave (cw) laser. This simple, fast, and sensitive technique was demonstrated for atomic spectroscopy in [ Appl. Phys. Lett.101, 051105 ( 2012)], but is more suitable for molecular spectroscopy. Four rotation-vibration transitions of methane have simultaneously been recorded in a Doppler-limited resolution using a spectrally broadened comb based on an Er-doped fiber laser and a cw 1651-nm distributed-feedback laser diode. Even though the power level of the comb modes and the sample absorption are weaker than those of the previous studies, in this work the cw laser frequency is stabilized to one of the comb modes, and the data are thereby averaged for extended periods of time, resulting an improvement in sensitivity.

Low uncertainty Boltzmann constant determinations and the kelvin redefinition

At its 25th meeting, the General Conference on Weights and Measures (CGPM) approved Resolution 1 'On the future revision of the International System of Units, the SI', which sets the path towards redefinition of four base units at the next CGPM in 2018. This constitutes a decisive advance towards the formal adoption of the new SI and its implementation. Kilogram, ampere, kelvin and mole will be defined in terms of fixed numerical values of the Planck constant, elementary charge, Boltzmann constant and Avogadro constant, respectively. The effect of the new definition of the kelvin referenced to the value of the Boltzmann constant k is that the kelvin is equal to the change of thermodynamic temperature T that results in a change of thermal energy kT by 1.380 65×10(-23) J. A value of the Boltzmann constant suitable for defining the kelvin is determined by fundamentally different primary thermometers such as acoustic gas thermometers, dielectric constant gas thermometers, noise thermometers and the Doppler broadening technique. Progress to date of the measurements and further perspectives are reported. Necessary conditions to be met before proceeding with changing the definition are given. The consequences of the new definition of the kelvin on temperature measurement are briefly outlined.

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.

Accurate lineshape spectroscopy and the Boltzmann constant

Spectroscopy has an illustrious history delivering serendipitous discoveries and providing a stringent testbed for new physical predictions, including applications from trace materials detection, to understanding the atmospheres of stars and planets, and even constraining cosmological models. Reaching fundamental-noise limits permits optimal extraction of spectroscopic information from an absorption measurement. Here, we demonstrate a quantum-limited spectrometer that delivers high-precision measurements of the absorption lineshape. These measurements yield a very accurate measurement of the excited-state (6P1/2) hyperfine splitting in Cs, and reveals a breakdown in the well-known Voigt spectral profile. We develop a theoretical model that accounts for this breakdown, explaining the observations to within the shot-noise limit. Our model enables us to infer the thermal velocity dispersion of the Cs vapour with an uncertainty of 35 p.p.m. within an hour. This allows us to determine a value for Boltzmann's constant with a precision of 6 p.p.m., and an uncertainty of 71 p.p.m.

Doppler broadening thermometry of acetylene and accurate measurement of the Boltzmann constant

In this paper, we present accurate measurements of the fundamental Boltzmann constant based on a line-shape analysis of acetylene spectra in the ν1 + ν3 band recorded using a tunable diode laser. Experimental spectra recorded at low pressures (0.25 - 9 Torr), have been analyzed using a Speed Dependent Voigt model that takes into account the molecular speed dependence effects. This line-shape model reproduces the experimental data with good accuracy and allows us to determine precise line-shape parameters for the P(25) transition of the ν1 + ν3 band. From the recorded spectra we obtained the Doppler-width and then determined the Boltzmann constant, k(B).

Ultrasensitive, self-calibrated cavity ring-down spectrometer for quantitative trace gas analysis

A cavity ring-down spectrometer is built for trace gas detection using telecom distributed feedback (DFB) diode lasers. The longitudinal modes of the ring-down cavity are used as frequency markers without active-locking either the laser or the high-finesse cavity. A control scheme is applied to scan the DFB laser frequency, matching the cavity modes one by one in sequence and resulting in a correct index at each recorded spectral data point, which allows us to calibrate the spectrum with a relative frequency precision of 0.06 MHz. Besides the frequency precision of the spectrometer, a sensitivity (noise-equivalent absorption) of 4×10^-11  cm^-1  Hz^-1/2 has also been demonstrated. A minimum detectable absorption coefficient of 5×10^-12  cm^-1 has been obtained by averaging about 100 spectra recorded in 2  h. The quantitative accuracy is tested by measuring the CO₂ concentrations in N₂ samples prepared by the gravimetric method, and the relative deviation is less than 0.3%. The trace detection capability is demonstrated by detecting CO₂ of ppbv-level concentrations in a high-purity nitrogen gas sample. Simple structure, high sensitivity, and good accuracy make the instrument very suitable for quantitative trace gas analysis.

Optical feedback frequency stabilized cavity ring-down spectroscopy

We introduce optical feedback frequency stabilized cavity ring-down spectroscopy (OFFS-CRDS), a near-shot-noise-limited technique that combines kilohertz resolution with an absorption detection sensitivity of 5×10(-13) cm(-1) Hz(-1/2). Its distributed feedback laser source is stabilized to a highly stable V-shaped reference cavity by optical feedback and fine-tuned by means of single-sideband modulation. The stability of this narrow laser is transferred to a ring-down (RD) cavity using a new fibered Pound-Drever-Hall (PDH) locking scheme without a dedicated electro-optic phase modulator, yielding several hundred RD events per second. We demonstrate continuous coverage of more than 7 nm with a baseline noise of 5×10(-12) cm(-1) and a dynamic range spanning six decades. With its resonant intracavity light intensity on the order of 1 kW/cm2, the spectrometer was used for observing a Lamb dip in a transition of carbon dioxide involving four vibrational quanta. Saturating such a weak transition at 160 μW input power, OFFS-CRDS paves the way to Doppler-free molecular overtone spectroscopy for precision measurements of hyperfine structures and pressure shifts.

Cavity mode-width spectroscopy with widely tunable ultra narrow laser

We explore a cavity-enhanced spectroscopic technique based on determination of the absorbtion coefficient from direct measurement of spectral width of the mode of the optical cavity filled with absorbing medium. This technique called here the cavity mode-width spectroscopy (CMWS) is complementary to the cavity ring-down spectroscopy (CRDS). While both these techniques use information on interaction time of the light with the cavity to determine absorption coefficient, the CMWS does not require to measure very fast signals at high absorption conditions. Instead the CMWS method require a very narrow line width laser with precise frequency control. As an example a spectral line shape of P7 Q6 O₂ line from the B-band was measured with use of an ultra narrow laser system based on two phase-locked external cavity diode lasers (ECDL) having tunability of ± 20 GHz at wavelength range of 687 to 693 nm.

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.

Optical feedback stabilized laser tuned by single-sideband modulation

We report a subkilohertz-linewidth distributed-feedback diode laser that is optical-feedback locked to a highly stable V-shaped cavity with drift rates below 20 Hz/s. This source is continuously tunable over 1 THz around 1590 nm by selecting a cavity mode and using an innovative single-sideband modulation scheme, which allows for frequency shifting over up to 40 GHz with millihertz accuracy. This robust setup achieves high performance without advanced vibration isolation and will be a powerful tool for metrological applications, in particular a redetermination of the Boltzmann constant by molecular spectroscopy.

Absolute frequency list of the ν3-band transitions of methane at a relative uncertainty level of 10(-11)

We determine the absolute frequencies of 56 rotation-vibration transitions of the ν(3) band of CH(4) from 88.2 to 90.5 THz with a typical uncertainty of 2 kHz corresponding to a relative uncertainty of 2.2 × 10(-11) over an average time of a few hundred seconds. Saturated absorption lines are observed using a difference-frequency-generation source and a cavity-enhanced absorption cell, and the transition frequencies are measured with a fiber-laser-based optical frequency comb referenced to a rubidium atomic clock linked to the international atomic time. The determined value of the P(7) F(2)((2)) line is consistent with the International Committee for Weights and Measures recommendation within the uncertainty.

Application of cavity ring-down spectroscopy to the Boltzmann constant determination

The Boltzmann constant can be optically determined by measuring the Doppler width of an absorption line of molecules at gas phase. We propose to apply a near infrared cavity ring-down (CRD) spectrometer for this purpose. The superior sensitivity of CRD spectroscopy and the good performance of the near-ir lasers can provide ppm (part-per-million) accuracy which will be competitive to present most accurate result obtained from the speed of sound in argon measurement. The possible influence to the uncertainty of the determined Doppler width from different causes are investigated, which includes the signal-to-noise level, laser frequency stability, detecting nonlinearity, and pressure broadening effect. The analysis shows that the CRD spectroscopy has some remarkable advantages over the direct absorption method proposed before. The design of the experimental setup is presented and the measurement of C2H2 line near 0.8 μm at room temperature has been carried out as a test of the instrument.

Laser-locked, continuously tunable high resolution cavity ring-down spectrometer

A continuous-wave cavity ring-down spectrometer with sub-MHz precision has been built using the sideband of a frequency stabilized laser as the tunable light source. The sideband is produced by passing the carrier laser beam through an electro-optic modulator (EOM) and then selected by a short etalon on resonance. The carrier laser frequency is locked to a longitude mode of a thermo-stabilized Fabry-Perot interferometer (FPI) with a long-term absolute frequency stability of 0.2 MHz (5 × 10(-10)). Broad and precise spectral scanning is accomplished, respectively, by selecting a different longitudinal mode of the FPI and by tuning the radio-frequency driving the EOM. The air broadened water absorption line at 12,321 cm(-1) was studied to test the performance of the spectrometer.

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.

Transmission properties of hollow-core photonic bandgap fibers in relation to molecular spectroscopy

The transmission properties of five types of hollow-core photonic bandgap fibers (HC-PBFs) are characterized in the telecom wavelength range around 1.5 microm. The variations in optical transmission are measured as a function of laser frequency over a 2 GHz scan range as well as a function of time over several hours. The influence of these variations on spectroscopy of molecules in a HC-PBF is simulated.

Ultrasensitive near-infrared cavity ring-down spectrometer for precise line profile measurement

A cavity ring-down (CRD) spectrometer is built with a continuous-wave Ti:sapphire ring laser. Using a pair of R approximately 0.999 95 high-reflective mirrors, the noise-equivalent minimum detectable absorption loss reaches 7 x 10(-11)/cm over the spectral range of 780-830 nm. A thermal-stabilized Fabry-Perot interferometer is applied to calibrate the CRD spectrum with an accuracy of 1 x 10(-4) cm(-1). The quantitative measurement is carried out for the line profile measurements of some overtone absorption lines of C(2)H(2) near 787 nm. Doppler determined line shape has been observed with milli-Torr acetylene gas in the ring-down cavity. The instrumental line width is estimated from the line profile fitting to be <1 x 10(-4) cm(-1). It demonstrates that the CRD spectrometer with extremely high sensitivity is also very suitable for quantitative measurements including precise line profile studies in the near-infrared.

A frequency-stabilized difference frequency generation laser spectrometer for precise line profile studies in the midinfrared

A midinfrared laser spectrometer is built up based on the difference frequency generation (DFG) of a Nd:YAG (yttrium aluminum garnet) laser and a tunable Ti:sapphire (Ti:Sa) laser. Tuning the Ti:Sa laser and operating properly with the periodically poled lithium niobate crystal, the DFG emission is tunable in the spectral range of 2.3-5.0 microm. The 1064 nm Nd:YAG laser frequency is stabilized to the 10(-6) cm(-1) level on a Doppler-broadened I(2) absorption line at 532 nm. As a result, the DFG emission frequency is stabilized within 1x10(-4) cm(-1). The measurement of an absorption line of CH(4) near 3 mum demonstrates that the DFG spectrometer is very suitable for the molecular absorption line profile studies in the midinfrared region.

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).