All paths lead to hubs in the spectroscopic networks of water isotopologues H216O and H218O.

Network theory has fundamentally transformed our comprehension of complex systems, catalyzing significant advances across various domains of science and technology. In spectroscopic networks, hubs are the quantum states involved in the largest number of transitions. Here, utilizing network paths probed via precision metrology, absolute energies have been deduced, with at least 10-digit accuracy, for almost 200 hubs in the experimental spectroscopic networks of H216O and H218O. These hubs, lying on the ground vibrational states of both species and the bending fundamental of H216O, are involved in tens of thousands of observed transitions. Relying on the same hubs and other states, benchmark-quality line lists have been assembled, which supersede and improve, by three orders of magnitude, the accuracy of the massive amount of data reported in hundreds of papers dealing with Doppler-limited spectroscopy. Due to the omnipresence of water, these ultraprecise line lists could be applied to calibrate high-resolution spectra and serve ongoing and upcoming space missions.

Extreme ultraviolet broadband imaging spectrometer using dispersion-matched zone plates.

We present simultaneous 1D imaging and broadband spectroscopy of a laser-produced plasma (LPP) source of extreme ultraviolet light, using a tapered zone plate that is matched to the dispersion of a transmission grating. We describe the design and fabrication of the zone plates in the 5-80 nm wavelength regime with designed spatial resolution of ∼10 µm and spectral resolution of ∼0.8 nm. Subsequently, we benchmark the imaging spectrometer with a solid tin target LPP. Plane wave propagation simulations qualitatively match the experimental results and confirm the device performance.

High-energy parametric oscillator and amplifier pulsed light source at 2-µm.

A laser system generating high-energy pulses at 2-µm wavelength with pulse widths tunable from 10-24 ns is described. It comprises an optical parametric oscillator that generates mJ-level signal seed radiation and an optical parametric amplifier that boosts the output to 800 mJ of combined signal and idler when pumped with 2 J pulses of 1064-nm laser light. The system operated with KTP crystals and running at 10 Hz repetition rate is characterized in the spatial, temporal, and spectral domains. The effect of saturation leads to an output pulse approaching flat-top spatial and box-shaped temporal profiles, as desired in various applications. The amplified pulses can be imaged down to sub-100 µm diameters, making this laser system a suitable driver for plasma sources of extreme ultraviolet light.

Parity-pair-mixing effects in nonlinear spectroscopy of HDO.

A non-linear spectroscopic study of the HDO molecule is performed in the wavelength range of 1.36-1.42 µm using noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy (NICE-OHMS). More than 100 rovibrational Lamb dips are recorded, with an experimental precision of 2-20 kHz, related to the first overtone of the O-H stretch fundamental of HD16O and HD18O. Significant perturbations, including distortions, shifts, and splittings, have been observed for a number of Lamb dips. These spectral perturbations are traced back to an AC-Stark effect, arising due to the strong laser field applied in all saturation-spectroscopy experiments. The AC-Stark effect mixes parity pairs, that is pairs of rovibrational states whose assignment differs solely in the Kc quantum number, where Kc is part of the standard J K a,K c asymmetric-top rotational label. Parity-pair mixing seems to be especially large for parity pairs with Ka ≥ 3, whereby their energy splittings become as small as a few MHz, resulting in multi-component asymmetric Lamb-dip profiles of gradually increasing complexity. These complex profiles often include crossover resonances. This effect is well known in saturation spectroscopy, but has not been reported in combination with parity-pair mixing. Parity-pair mixing is not seen in H2 16O and H2 18O, because their parity pairs correspond to ortho and para nuclear-spin isomers, whose interaction is prohibited. Despite the frequency shifts observed for HD16O and HD18O, the absolute accuracy of the detected transitions still exceeds that achievable by Doppler-limited techniques.

VUV-VIS FT spectroscopy of the rare 13C18O isotopologue of carbon monoxide: Analysis of the A1Π(v = 1) multiply-perturbed level.

Ro-vibronic spectra of the 13C18O carbon monoxide isotopologue were obtained with (i) emission spectroscopy in the visible region using a Bruker IFS 125HR spectrometer (University of Rzeszów) and (ii) vacuum-ultraviolet absorption spectroscopy using the wave-front-division spectrometer on the DESIRS beamline of the SOLEIL synchrotron. A deperturbation analysis of the 13C18O A1Π(v = 1) level was conducted from 598 observed transitions from the B1Σ+ - A1Π(0, 1), C1Σ+ - A1Π(0, 1), A1Π - X1Σ+(1, 0), B1Σ+ - X1Σ+(0, 0), C1Σ+ - X1Σ+(0, 0), I1Σ- - X1Σ+(2, 0) bands and five further nominally forbidden bands. An effective Hamiltonian and term-value fitting analysis was implemented. Consequently, 135 parameters were floated: 23 molecular parameters, including molecular constants for A1Π(v = 1), I1Σ-(v = 2), d3Δ(v = 6), e3Σ-(v = 3) and D1Δ(v = 1); rotation-electronic (L-uncoupling) mixing of A1Π(v = 1) âˆ¼ [D1Δ(v = 1), I1Σ-(v = 1), I1Σ-(v = 2)] and spin-orbit interaction parameters for A1Π(v = 1) âˆ¼ [d3Δ(v = 6), e3Σ-(v = 3), a'3Σ+(v = 11)]; the spin-orbit/spin-electronic/L-uncoupling a3Π(v = 12) âˆ¼ d3Δ(v = 5) and spin-orbit a3Π(v = 12) âˆ¼ [D1Δ(v = 1), I1Σ-(v = 2)] perturbation parameters; as well as 112 ro-vibronic term values of B1Σ+(v = 0) up to J = 50 and C1Σ+(v = 0) up to J = 60. The significant, indirect a3Π(v = 12) âˆ¼ [e3Σ-(v = 2, 3), d3Δ(v = 5, 6)] âˆ¼ A1Π(v = 1) spin-orbit/spin-electronic/L-uncoupling interaction and a3Π(v = 12) âˆ¼ [I1Σ-(v = 2), D1Δ(v = 1)] âˆ¼ A1Π(v = 1) spin-orbit/L-uncoupling interaction were detected and analysed. Thus, this study, using modern experimental methods and deperturbation analysis, leads to a much improved description in terms of molecular constants and interaction parameters, compared to previous studies of the A1Π(v = 1) energy region in the 13C18O isotopologue. This research is a continuation of the studies on the A1Π state and its numerous perturbers in the CO isotopologues made by our team.

Hyperfine-Resolved Near-Infrared Spectra of H217O.

Huge efforts have recently been taken in the derivation of accurate compilations of rovibrational energies of water, one of the most important reference systems in spectroscopy. Such precision is desirable for all water isotopologues, although their investigation is challenged by hyperfine effects in their spectra. Frequency-comb locked noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy (NICE-OHMS) allows for achieving high sensitivity, resolution, and accuracy. This technique has been employed to resolve the subtle hyperfine splittings of rovibrational transitions of H217O in the near-infrared region. Simulation and interpretation of the H217O saturation spectra have been supported by coupled-cluster calculations performed with large basis sets and accounting for high-level corrections. Experimental 17O hyperfine parameters are found in excellent agreement with the corresponding computed values. The need of including small hyperfine effects in the analysis of H217O spectra has been demonstrated together with the ability of the computational strategy employed for providing quantitative predictions of the corresponding parameters.

Systematic study and uncertainty evaluation of P, T-odd molecular enhancement factors in BaF.

A measurement of the magnitude of the electric dipole moment of the electron (eEDM) larger than that predicted by the Standard Model (SM) of particle physics is expected to have a huge impact on the search for physics beyond the SM. Polar diatomic molecules containing heavy elements experience enhanced sensitivity to parity (P) and time-reversal (T)-violating phenomena, such as the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleons and the electrons, and are thus promising candidates for measurements. The NL-eEDM collaboration is preparing an experiment to measure the eEDM and S-PS interaction in a slow beam of cold BaF molecules [P. Aggarwal et al., Eur. Phys. J. D 72, 197 (2018)]. Accurate knowledge of the electronic structure parameters, Wd and Ws, connecting the eEDM and the S-PS interaction to the measurable energy shifts is crucial for the interpretation of these measurements. In this work, we use the finite field relativistic coupled cluster approach to calculate the Wd and Ws parameters in the ground state of the BaF molecule. Special attention was paid to providing a reliable theoretical uncertainty estimate based on investigations of the basis set, electron correlation, relativistic effects, and geometry. Our recommended values of the two parameters, including conservative uncertainty estimates, are 3.13 ±0.12×1024Hzecm for Wd and 8.29 ± 0.12 kHz for Ws.

Rayleigh-Brillouin scattering in binary mixtures of disparate-mass constituents: SF_{6}-He,SF_{6}-D_{2}, and SF_{6}-H_{2}.

The spectral distribution of light scattered by microscopic thermal fluctuations in binary mixture gases was investigated experimentally and theoretically. Measurements of Rayleigh-Brillouin spectral profiles were performed at a wavelength of 532 nm and at room temperature, for mixtures of SF_{6}-He,SF_{6}-D_{2}, and SF_{6}-H_{2}. In these measurements, the pressure of the gases with heavy molecular mass (SF_{6}) is set at 1 bar, while the pressure of the lighter collision partner was varied. In view of the large polarizability of SF_{6} and the very small polarizabilities of He, H_{2}, and D_{2}, under the chosen pressure conditions these low mass species act as spectators and do not contribute to the light scattering spectrum, while they influence the motion and relaxation of the heavy SF_{6} molecules. A generalized hydrodynamic model was developed that should be applicable for the particular case of molecules with heavy and light disparate masses, as is the case for the heavy SF_{6} molecule, and the lighter collision partners. Based on the kinetic theory of gases, our model replaces the classical Navier-Stokes-Fourier relations with constitutive equations having an exponential memory kernel. The energy exchange between translational and internal modes of motion is included and quantified with a single parameter z that characterizes the ratio between the mean elastic and inelastic molecular collision frequencies. The model is compared with the experimental Rayleigh-Brillouin scattering data, where the value of the parameter z is determined in a least-squares procedure. Where very good agreement is found between experiment and the generalized hydrodynamic model, the computations in the framework of classical hydrodynamics strongly deviate. Only in the hydrodynamic regime both models are shown to converge.

Spectroscopic-network-assisted precision spectroscopy and its application to water.

Frequency combs and cavity-enhanced optical techniques have revolutionized molecular spectroscopy: their combination allows recording saturated Doppler-free lines with ultrahigh precision. Network theory, based on the generalized Ritz principle, offers a powerful tool for the intelligent design and validation of such precision-spectroscopy experiments and the subsequent derivation of accurate energy differences. As a proof of concept, 156 carefully-selected near-infrared transitions are detected for H216O, a benchmark system of molecular spectroscopy, at kHz accuracy. These measurements, augmented with 28 extremely-accurate literature lines to ensure overall connectivity, allow the precise determination of the lowest ortho-H216O energy, now set at 23.794 361 22(25) cm-1, and 160 energy levels with similarly high accuracy. Based on the limited number of observed transitions, 1219 calibration-quality lines are obtained in a wide wavenumber interval, which can be used to improve spectroscopic databases and applied to frequency metrology, astrophysics, atmospheric sensing, and combustion chemistry.

High accuracy theoretical investigations of CaF, SrF, and BaF and implications for laser-cooling.

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [NL-eEDM Collaboration, Eur. Phys. J. D 72, 197 (2018)]. Knowledge of the molecular properties of BaF is thus needed to plan the measurements and, in particular, to determine the optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require the incorporation of both high-order correlation and relativistic effects in the calculations. In this work, theoretical investigations of the ground and lowest excited states of BaF and its lighter homologs, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster and multireference configuration interaction methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the A2Π1/2→X2Σ1/2 + transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the B2Σ1/2 +→X2Σ1/2 + transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the nondiagonal nature of the FCFs in this system. Special attention is given to the properties of the A'2Δ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and excited states of the three molecules and the transition dipole moments (TDMs) between the different states. Finally, using the calculated FCFs and TDMs, we determine that the A2Π1/2→X2Σ1/2 + transition is suitable for transverse cooling in BaF.

Bulk viscosity of CO2 from Rayleigh-Brillouin light scattering spectroscopy at 532 nm.

Rayleigh-Brillouin scattering spectra of CO2 were measured at pressures ranging from 0.5 to 4 bars and temperatures from 257 to 355 K using green laser light (wavelength 532 nm, scattering angle of 55.7°). These spectra were compared to two line shape models, which take the bulk viscosity as a parameter. One model applies to the kinetic regime, i.e., low pressures, while the second model uses the continuum, hydrodynamic approach and takes the rotational relaxation time as a parameter, which translates into the bulk viscosity. We do not find a significant dependence of the bulk viscosity with pressure or temperature. At pressures where both models apply, we find a consistent value of the ratio of bulk viscosity over shear viscosity ηb/ηs = 0.41 ± 0.10. This value is four orders of magnitude smaller than the common value that is based on the damping of ultrasound and signifies that in light scattering only relaxation of rotational modes matters, while vibrational modes remain "frozen."

Benchmarking Theory with an Improved Measurement of the Ionization and Dissociation Energies of H_{2}.

The dissociation energy of H_{2} represents a benchmark quantity to test the accuracy of first-principles calculations. We present a new measurement of the energy interval between the EF ^{1}Σ_{g}^{+}(v=0,N=1) state and the 54p1_{1} Rydberg state of H_{2}. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy D_{0}^{N=1} of ortho-H_{2} that has, for the first time, reached a level of uncertainty that is 3 times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of 35 999.582 834(11) cm^{-1} is in remarkable agreement with the theoretical result of 35 999.582 820(26) cm^{-1} obtained in calculations including high-order relativistic and quantum-electrodynamics corrections, as reported in the following Letter [M. Puchalski, J. Komasa, P. Czachorowski, and K. Pachucki, Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003]. This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of H_{2} in the context of the current controversy on the charge radius of the proton.

Active Two-Dimensional Steering of Radiation from a Nanoaperture.

We experimentally demonstrate control over the direction of radiation of a beam that passes through a square nanoaperture in a metal film. The ratio of the aperture size and the wavelength is such that only three guided modes, each with different spatial symmetries, can be excited. Using a spatial light modulator, the superposition of the three modes can be altered, thus allowing for a controlled variation of the radiation pattern that emanates from the nanoaperture. Robust and stable steering of 9.5° in two orthogonal directions was achieved.

Molecular Fountain.

The resolution of any spectroscopic or interferometric experiment is ultimately limited by the total time a particle is interrogated. Here we demonstrate the first molecular fountain, a development which permits hitherto unattainably long interrogation times with molecules. In our experiments, ammonia molecules are decelerated and cooled using electric fields, launched upwards with a velocity between 1.4 and 1.9 m/s and observed as they fall back under gravity. A combination of quadrupole lenses and bunching elements is used to shape the beam such that it has a large position spread and a small velocity spread (corresponding to a transverse temperature of <10 µK and a longitudinal temperature of <1 µK) when the molecules are in free fall, while being strongly focused at the detection region. The molecules are in free fall for up to 266 ms, making it possible, in principle, to perform sub-Hz measurements in molecular systems and paving the way for stringent tests of fundamental physics theories.

A systematic study of Rayleigh-Brillouin scattering in air, N2, and O2 gases.

Spontaneous Rayleigh-Brillouin scattering experiments in air, N2, and O2 have been performed for a wide range of temperatures and pressures at a wavelength of 403 nm and at a 90° scattering angle. Measurements of the Rayleigh-Brillouin spectral scattering profile were conducted at high signal-to-noise ratio for all three species, yielding high-quality spectra unambiguously showing the small differences between scattering in air, and its constituents N2 and O2. Comparison of the experimental spectra with calculations using the Tenti S6 model, developed in the 1970s based on linearized kinetic equations for molecular gases, demonstrates that this model is valid to high accuracy for N2 and O2, as well as for air. After previous measurements performed at 366 nm, the Tenti S6 model is here verified for a second wavelength of 403 nm, and for the pressure-temperature parameter space covered in the present study (250-340 K and 0.6-3 bars). In the application of the Tenti S6 model, based on the transport coefficients of the gases, such as thermal conductivity κ, internal specific heat capacity c(int) and shear viscosity η, as well as their temperature dependencies taken as inputs, values for the more elusive bulk viscosity η(b) for the gases are derived by optimizing the model to the measurements. It is verified that the bulk viscosity parameters obtained from previous experiments at 366 nm are valid for wavelengths of 403 nm. Also for air, which is treated as a single-component gas with effective gas transport coefficients, the Tenti S6 treatment is validated for 403 nm as for the previously used wavelength of 366 nm, yielding an accurate model description of the scattering profiles for a range of temperatures and pressures, including those of relevance for atmospheric studies. It is concluded that the Tenti S6 model, further verified in the present study, is applicable to LIDAR applications for exploring the wind velocity and the temperature profile distributions of the Earth's atmosphere. Based on the present findings at 90° scattering and the determination of η(b) values, predictions can be made on the spectral profiles for a typical LIDAR backscatter geometry. These Tenti S6 predictions for Rayleigh-Brillouin scattering deviate by some 7% from purely Gaussian profiles at realistic sub-atmospheric pressures occurring at 3-5 km altitude in the Earth's atmosphere.

Analysis of Rayleigh-Brillouin spectral profiles and Brillouin shifts in nitrogen gas and air.

On the basis of experimental Rayleigh-Brillouin scattering data in gaseous nitrogen and air, simulations are performed to describe the observed frequency profiles in analytical form. The experimental data pertain to a λ = 366 nm scattering wavelength, a 90° scattering angle, pressures of 1 and 3 bar, and temperatures in the range 250 - 340 K. Two different models are used to represent the RB-profiles, to distinguish the RB-peaks, and to obtain the Brillouin shift associated with the acoustic waves generated in a gaseous medium. Calculations in the framework of V3 and G3 models, exhibiting composite profiles of three distinct peaks of Voigt or Gaussian functions, are compared to observation. Fitting results show that the V3 model yields an improvement over the G3 model. This mathematical model provides an even better representation of the observed profiles than the Tenti S6 model, which is considered to be the optimum representation in terms of physical parameters. For the derivation of Brillouin shifts, both models perform well at high gas pressure, while at lower pressures, the V3 model yields a higher accuracy than the G3 model.

Perspective: tipping the scales: search for drifting constants from molecular spectra.

Transitions in atoms and molecules provide an ideal test ground for constraining or detecting a possible variation of the fundamental constants of nature. In this perspective, we review molecular species that are of specific interest in the search for a drifting proton-to-electron mass ratio µ. In particular, we outline the procedures that are used to calculate the sensitivity coefficients for transitions in these molecules and discuss current searches. These methods have led to a rate of change in µ bounded to 6 × 10(-14)/yr from a laboratory experiment performed in the present epoch. On a cosmological time scale, the variation is limited to âˆ£Δµ∕µâˆ£ < 10(-5) for look-back times of 10-12× 10(9) years and to âˆ£Δµ∕µâˆ£ < 10(-7) for look-back times of 7× 10(9) years. The last result, obtained from high-redshift observation of methanol, translates into µÌ‡/µ=(1.4±1.4)×10(-17)/yr if a linear rate of change is assumed.