Precision Measurement of Vibrational Quanta in Tritium Hydride

Saturated absorption measurements of transitions in the (2-0) band of radioactive tritium hydride are performed with the ultrasensitive noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy intracavity absorption technique in the range 1460-1510 nm. The hyperfine structure of rovibrational transitions of tritium hydride, in contrast to that of hydrogen deuteride, exhibits a single isolated hyperfine component, allowing for the accurate determination of hyperfineless rovibrational transition frequencies, resulting in R(0)=203 396 426 692(22)  kHz and R(1)=205 380 033 644(21)  kHz. This corresponds to an accuracy 3 orders of magnitude better than previous measurements in tritiated hydrogen molecules. Observation of an isolated component in P(1) with reversed signal amplitude contradicts models for line shapes in hydrogen deuteride based on crossover resonances.

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.

FT-spectroscopy of the 12C18O rare isotopologue and deperturbation analysis of the A1Π(v = 3) level

Research on 12C18O was carried out using two complementary Fourier-transform methods: (1) vacuum-ultraviolet absorption spectroscopy, with an accuracy ca. 0.03 cm-1 on the DESIRS beamline (SOLEIL synchrotron) and (2) visible emission spectroscopy with an accuracy of about 0.005-0.007 cm-1 by means of the Bruker IFS 125HR spectrometer (University of Rzeszów). The maximum rotational quantum number of the energy levels involved in the observed spectral lines was Jmax = 54. An effective Hamiltonian and the term-value fitting approach were implemented for the precise analysis of the A1Π(v = 3) level in 12C18O. It was performed by means of the PGOPHER code. The data set consisted of 571 spectral lines belonging to the A1Π-X1Σ+(3, 0), B1Σ+-A1Π(0, 3), C1Σ+-A1Π(0, 3) bands and several lines involving states that perturb the A1Π(v = 3) level as well as to the previously analysed B1Σ+-X1Σ+(0, 0) and C1Σ+-X1Σ+(0, 0) transitions. A significantly extended quantum-mechanical description of the A1Π(v = 3) level in 12C18O was provided. It consists of the 5 new unimolecular interactions of the spin-orbit and rotation-electronic nature, which had not been taken into account previously in the literature. The ro-vibronic term values of the A1Π(v = 3, Jmax = 55), a'3Σ+(v = 13), D1Δ(v = 4) and I1Σ-(v = 5) levels were determined with precision improved by a factor of 10 relative to the previously known values.

Lamb Dip of a Quadrupole Transition in H_{2}

The saturated absorption spectrum of the hyperfineless S(0) quadrupole line in the (2-0) band of H_{2} is measured at λ=1189  nm, using the NICE-OHMS technique under cryogenic conditions (72 K). It is the first time that a Lamb dip of a molecular quadrupole transition has been recorded. At low (150-200 W) saturation powers a single narrow Lamb dip is observed, ruling out an underlying recoil doublet of 140 kHz. Studies of Doppler-detuned resonances show that the redshifted recoil component can be made visible for low pressures and powers, and prove that the narrow Lamb dip must be interpreted as the blue recoil component. A transition frequency of 252 016 361 164 (8) kHz is extracted, which is off by -2.6 (1.6) MHz from molecular quantum electrodynamical calculations therewith providing a challenge to theory.

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 K_c quantum number, where K_c 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 K_a ≥ 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) ∼ [D¹Δ(v = 1), I¹Σ^-(v = 1), I¹Σ^-(v = 2)] and spin-orbit interaction parameters for A¹Π(v = 1) ∼ [d³Δ(v = 6), e³Σ^-(v = 3), a'³Σ⁺(v = 11)]; the spin-orbit/spin-electronic/L-uncoupling a³Π(v = 12) ∼ d³Δ(v = 5) and spin-orbit a³Π(v = 12) ∼ [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) ∼ [e³Σ^-(v = 2, 3), d³Δ(v = 5, 6)] ∼ A¹Π(v = 1) spin-orbit/spin-electronic/L-uncoupling interaction and a³Π(v = 12) ∼ [I¹Σ^-(v = 2), D¹Δ(v = 1)] ∼ 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.

Cross-calibration of a combined electrostatic and time-of-flight analyzer for energy- and charge-state-resolved spectrometry of tin laser-produced plasma

We present the results of the calibration of a channeltron-based electrostatic analyzer operating in time-of-flight mode (ESA-ToF) using tin ions resulting from laser-produced plasma, over a wide range of charge states and energies. Specifically, the channeltron electron multiplier detection efficiency and the spectrometer resolution are calibrated, and count rate effects are characterized. With the obtained overall response function, the ESA-ToF is shown to accurately reproduce charge-integrated measurements separately and simultaneously obtained from a Faraday cup (FC), up to a constant factor the finding of which enables absolute cross-calibration of the ESA-ToF using the FC as an absolute benchmark. Absolute charge-state-resolved ion energy distributions are obtained from ns-pulse Nd:YAG-laser-produced microdroplet tin plasmas in a setting relevant for state-of-the-art extreme ultraviolet nanolithography.

Shape Resonances in H_{2} as Photolysis Reaction Intermediates

Shape resonances in H_{2}, produced as reaction intermediates in the photolysis of H_{2}S precursor molecules, are measured in a half-collision approach. Before disintegrating into two ground state H atoms, the reaction is quenched by two-photon Doppler-free excitation to the F electronically excited state of H_{2}. For J=13, 15, 17, 19, and 21, resonances with lifetimes in the range of nano- to milliseconds were observed with an accuracy of 30 MHz (1.4 mK). The experimental resonance positions are found to be in excellent agreement with theoretical predictions when nonadiabatic and quantum electrodynamical corrections are included. This is the first time such effects are observed in collisions between neutral atoms. From the potential energy curve of the H_{2} molecule, now tested at high accuracy over a wide range of internuclear separations, the s-wave scattering length for singlet H(1s)+H(1s) scattering is determined at a=0.2735_{31}^{39} a_{0}.

Deceleration and Trapping of SrF Molecules

We report on the electrostatic trapping of neutral SrF molecules. The molecules are captured from a cryogenic buffer-gas beam source into the moving traps of a 4.5-m-long traveling-wave Stark decelerator. The SrF molecules in X^{2}Σ^{+}(v=0,N=1) state are brought to rest as the velocity of the moving traps is gradually reduced from 190  m/s to zero. The molecules are held for up to 50 ms in multiple electric traps of the decelerator. The trapped packets have a volume (FWHM) of 1  mm^{3} and a velocity spread of 5(1)  m/s, which corresponds to a temperature of 60(20) mK. Our result demonstrates a factor 3 increase in the molecular mass that has been Stark decelerated and trapped. Heavy molecules (mass>100  amu) offer a highly increased sensitivity to probe physics beyond the standard model. This work significantly extends the species of neutral molecules of which slow beams can be created for collision studies, precision measurement, and trapping experiments.

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, W_d and W_s, 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 W_d and W_s 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 W_d and 8.29 ± 0.12 kHz for W_s.

A supersonic laser ablation beam source with narrow velocity spreads

A supersonic beam source for SrF and BaF molecules is constructed by combining the expansion of carrier gas (a mixture of 2% SF₆ and 98% argon) from an Even-Lavie valve with laser ablation of a barium/strontium metal target at a repetition rate of 10 Hz. Molecular beams with a narrow translational velocity spread are produced at relative values of Δv/v = 0.053(11) and 0.054(9) for SrF and BaF, respectively. The relative velocity spread of the beams produced in our source is lower in comparison with the results from other metal fluoride beams produced in supersonic laser ablation sources. The rotational temperature of BaF is measured to be 3.5 K. The source produces 6 × 10⁸ and 10⁷ molecules per steradian per pulse in the X²Σ⁺ (ν = 0, N = 1) state of BaF and SrF molecules, respectively, a state amenable to Stark deceleration and laser cooling.

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.

Photolysis Production and Spectroscopic Investigation of the Highest Vibrational States in H2 (X1Σg+ v = 13, 14)

Rovibrational quantum states in the X1Σg+ electronic ground state of H2 are prepared in the v = 13 vibrational level up to its highest bound rotational level J = 7, and in the highest bound vibrational level v = 14 (for J = 1) by two-photon photolysis of H2S. These states are laser-excited in a subsequent two-photon scheme into F1Σg+ outer well states, where the assignment of the highest (v,J) states is derived from a comparison of experimentally known levels in F1Σg+, combined with ab initio calculations of X1Σg+ levels. The assignments are further verified by excitation of F1Σg+ population into autoionizing continuum resonances, which are compared with multichannel quantum defect calculations. Precision spectroscopic measurements of the F-X intervals form a test for the ab initio calculations of ground state levels at high vibrational quantum numbers and large internuclear separations, for which agreement is found.

Extreme ultraviolet light from a tin plasma driven by a 2-µm-wavelength laser

An experimental study of laser-produced plasmas is performed by irradiating a planar tin target by laser pulses, of 4.8 ns duration, produced from a KTP-based 2-µm-wavelength master oscillator power amplifier. Comparative spectroscopic investigations are performed for plasmas driven by 1-µm- and 2-µm-wavelength pulsed lasers, over a wide range of laser intensities spanning 0.5 - 5 × 10¹¹ W/cm ². Similar extreme ultraviolet (EUV) spectra in the 5.5-25.5 nm wavelength range and underlying plasma ionicities are obtained when the intensity ratio is kept fixed at I_1µm/I_2µm = 2.4(7). Crucially, the conversion efficiency (CE) of 2-µm-laser energy into radiation within a 2% bandwidth centered at 13.5 nm relevant for industrial applications is found to be a factor of two larger, at a 60 degree observation angle, than in the case of the denser 1-µm-laser-driven plasma. Our findings regarding the scaling of the optimum laser intensity for efficient EUV generation and CE with drive laser wavelength are extended to other laser wavelengths using available literature data.

Crisis and catharsis in atomic physics

Precise measurement of an atomic hydrogen transition resolves the proton size puzzle

Chirp-compensated pulsed titanium-sapphire laser system for precision spectroscopy

Active frequency-chirp control for a narrowband pulsed titanium-sapphire laser oscillator-amplifier laser system is demonstrated using an intra-cavity electro-optic modulator, resulting in improved spectral resolution and stability. Beat-note measurements of its output to a continuous-wave laser locked to an optical frequency comb yields an Allan deviation of 5×10^-11 (at 10 s). Correction of residual chirp from a comparison with the fourth-harmonic upconverted pulsed output to a molecular H₂ two-photon resonance delivers a value for the uncertainty contribution due to frequency chirp below the 1.5×10^-10 level.

Proton-electron mass ratio from laser spectroscopy of HD+ at the part-per-trillion level

Recent mass measurements of light atomic nuclei in Penning traps have indicated possible inconsistencies in closely related physical constants such as the proton-electron and deuteron-proton mass ratios. These quantities also influence the predicted vibrational spectrum of the deuterated molecular hydrogen ion (HD+) in its electronic ground state. We used Doppler-free two-photon laser spectroscopy to measure the frequency of the v = 0→9 overtone transition (v, vibrational quantum number) of this spectrum with an uncertainty of 2.9 parts per trillion. By leveraging high-precision ab initio calculations, we converted our measurement to tight constraints on the proton-electron and deuteron-proton mass ratios, consistent with the most recent Penning trap determinations of these quantities. This results in a precision of 21 parts per trillion for the value of the proton-electron mass ratio.

Time- and space-resolved optical Stark spectroscopy in the afterglow of laser-produced tin-droplet plasma

The afterglow emission from Nd:YAG-laser-produced microdroplet-tin plasma is investigated, with a focus on analyzing Stark effect phenomena and the dynamical evolution of the plasma. Time- and space-resolved optical imaging spectroscopy is performed on 11 lines from Sn i-iv ions, in the 315-425-nm wavelength range. Stark shift-to-width ratios serve as the basis for unambiguous experimental tests of atomic physics theory predictions. Experiment and theory, where available, are found to be in poor agreement, and are in disagreement regarding the sign of the ratio in several cases. Spectroscopic measurements of the Stark widths in tandem with Saha-Boltzmann fits to Sn i and Sn ii lines, establish the evolution of the local temperature and density of the plasma afterglow, 20-40 ns after the end of the 15-ns-long temporally box-shaped laser pulse. A clear cool-down from ∼2 to 1 eV is observed of the plasma in this time window, having started at ∼30 eV when emitting extreme-ultraviolet (EUV) light. An exponential reduction of the density of the plasma from ∼10^{18}-10^{17}e^{-} cm^{-3} is observed in this same time window. Our work is relevant for understanding the dynamics of the decaying, expanding plasma in state-of-the-art EUV nanolithography machines.

Prominent radiative contributions from multiply-excited states in laser-produced tin plasma for nanolithography

Extreme ultraviolet (EUV) lithography is currently entering high-volume manufacturing to enable the continued miniaturization of semiconductor devices. The required EUV light, at 13.5 nm wavelength, is produced in a hot and dense laser-driven tin plasma. The atomic origins of this light are demonstrably poorly understood. Here we calculate detailed tin opacity spectra using the Los Alamos atomic physics suite ATOMIC and validate these calculations with experimental comparisons. Our key finding is that EUV light largely originates from transitions between multiply-excited states, and not from the singly-excited states decaying to the ground state as is the current paradigm. Moreover, we find that transitions between these multiply-excited states also contribute in the same narrow window around 13.5 nm as those originating from singly-excited states, and this striking property holds over a wide range of charge states. We thus reveal the doubly magic behavior of tin and the origins of the EUV light.

Extreme ultraviolet (EUV) light is entering use in nanolithography. Here the authors discuss experimental and theoretical results about the prominent role of multiply-excited states in highly charged tin ions in the mechanism of EUV light emission from laser-produced plasma.

Precision measurement of the fundamental vibrational frequencies of tritium-bearing hydrogen molecules: T2, DT, HT

High-resolution coherent Raman spectroscopic measurements of all three tritium-containing molecular hydrogen isotopologues T2, DT and HT were performed to determine the ground electronic state fundamental Q-branch (v = 0 → 1, ΔJ = 0) transition frequencies at accuracies of 0.0005 cm-1. An over hundred-fold improvement in accuracy over previous experiments allows the comparison with the latest ab initio calculations in the framework of non-adiabatic perturbation theory including nonrelativisitic, relativisitic and QED contributions. Excellent agreement is found between experiment and theory, thus providing a verification of the validity of the NAPT-framework for these tritiated species. While the transition frequencies were corrected for ac-Stark shifts, the contributions of non-resonant background as well as quantum interference effects between resonant features in the nonlinear spectroscopy were quantitatively investigated, also leading to corrections to the transition frequencies. Methods of saturated CARS with the observation of Lamb dips, as well as the use of continuous-wave radiation for the Stokes frequency were explored, that might pave the way for future higher-accuracy CARS measurements.

Characterization of a Novel Temperature Lidar Receiver by Means of Laboratory Rayleigh-Brillouin Scattering Measurements

A new receiver setup based on an imaging Fizeau interferometer measuring the Rayleigh Brillouin scattering (RBS) spectra to retrieve tropospheric temperature profiles is introduced. The optical layout of the proposed receiver design is discussed and its functionality is demonstrated by means of accurate and controlled laboratory RBS measurements. The proposed temperature receiver is based on a Fizeau interferometer and a 32 channel PMT array which can resolve the RBS spectrum without applying any scanning procedures. In order to avoid any incidence angle fluctuations on the Fizeau interferometer caused by for instance atmospheric turbulence, the application of a fiver coupled telescope was investigated. It is shown that a 50 µm fiber (NA=0.12) provides both, sufficient coupling efficiency and sufficiently low divergence in order to keep the Finesse of the interferometer. The performance of the novel lidar receiver is verified by means of accurate laboratory RBS measurements.

The spin-forbidden vacuum-ultraviolet absorption spectrum of 14N15N

Photoabsorption spectra of ¹⁴N¹⁵N were recorded at high resolution with a vacuum-ultraviolet Fourier-transform spectrometer fed by synchrotron radiation in the range of 81-100 nm. The combination of high column density (3 × 10¹⁷ cm^-2) and low temperature (98 K) allowed for the recording of weak spin-forbidden absorption bands' exciting levels of triplet character. The triplet states borrow intensity from ¹Π_u states of Rydberg and valence character while causing their predissociation. New predissociation linewidths and molecular constants are obtained for the states C³Π_u(v = 7, 8, 14, 15, 16, 21), G³Π_u(v = 0, 1, 4), and F³Π_u(v = 0). The positions and widths of these levels are shown to be well-predicted by a coupled-Schrödinger equation model with empirical parameters based on experimental data on ¹⁴N₂ and ¹⁵N₂ triplet levels.

Determination of the Interval between the Ground States of Para- and Ortho-H_{2}

Nuclear-spin-symmetry conservation makes the observation of transitions between quantum states of ortho- and para-H_{2} extremely challenging. Consequently, the energy-level structure of H_{2} derived from experiment consists of two disjoint sets of level energies, one for para-H_{2} and the other for ortho-H_{2}. We use a new measurement of the ionization energy of para-H_{2} [E_{I}(H_{2})/(hc)=124 417.491 098(31)  cm^{-1}] to determine the energy separation [118.486 770(50)  cm^{-1}] between the ground states of para- and ortho-H_{2} and thus link the energy-level structure of the two nuclear-spin isomers of this fundamental molecule. Comparison with recent theoretical results [M. Puchalski et al., Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003] enables the derivation of an upper bound of 1.5 MHz for a hypothetical global shift of the energy-level structure of ortho-H_{2} with respect to that of para-H_{2}.

Lamb-dips and Lamb-peaks in the saturation spectrum of HD

The saturation spectrum of the R(1) transition in the (2-0) band in hydrogen deuteride (HD) is found to exhibit a composite line shape, involving a Lamb-dip and a Lamb-peak. We propose an explanation for such behavior based on the effects of crossover resonances in the hyperfine substructure, which is made quantitative in a density matrix calculation. This resolves an outstanding discrepancy on the rovibrational R(1) transition frequency, which is now determined at 217,105,181,901 (50) kHz and in agreement with current theoretical calculations.

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 η_b/η_s = 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.

Dissociation Energy of the Hydrogen Molecule at 10^{-9} Accuracy

The ionization energy of ortho-H_{2} has been determined to be E_{I}^{o}(H_{2})/(hc)=124 357.238 062(25)  cm^{-1} from measurements of the GK(1,1)-X(0,1) interval by Doppler-free, two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave, near-infrared laser spectroscopy. E_{I}^{o}(H_{2}) was used to derive the dissociation energy of H_{2}, D_{0}^{N=1}(H_{2}), at 35 999.582 894(25)  cm^{-1} with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.

Relativistic and QED Effects in the Fundamental Vibration of T_{2}

The hydrogen molecule has become a test ground for quantum electrodynamical calculations in molecules. Expanding beyond studies on stable hydrogenic species to the heavier radioactive tritium-bearing molecules, we report on a measurement of the fundamental T_{2} vibrational splitting (v=0→1) for J=0-5 rotational levels. Precision frequency metrology is performed with high-resolution coherent anti-Stokes Raman spectroscopy at an experimental uncertainty of 10-12 MHz, where sub-Doppler saturation features are exploited for the strongest transition. The achieved accuracy corresponds to a 50-fold improvement over a previous measurement, and it allows for the extraction of relativistic and QED contributions to T_{2} transition energies.

Sub-Doppler Frequency Metrology in HD for Tests of Fundamental Physics

Weak transitions in the (2,0) overtone band of the hydrogen deuteride molecule at λ=1.38  μm were measured in saturated absorption using the technique of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Narrow Doppler-free lines were interrogated with a spectroscopy laser locked to a frequency comb laser referenced to an atomic clock to yield transition frequencies [R(1)=217105181895(20)  kHz; R(2)=219042856621(28)  kHz; R(3)=220704304951(28)  kHz] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the smallest neutral molecule, and they open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions.

Deep-Ultraviolet Frequency Metrology of H_{2} for Tests of Molecular Quantum Theory

Molecular hydrogen and its isotopic and ionic species are benchmark systems for testing quantum chemical theory. Advances in molecular energy structure calculations enable the experimental verification of quantum electrodynamics and potentially a determination of the proton charge radius from H_{2} spectroscopy. We measure the ground state energy in ortho-H_{2} relative to the first electronically excited state by Ramsey-comb laser spectroscopy on the EF^{1}Σ_{g}^{+}-X^{1}Σ_{g}^{+}(0,0) Q1 transition. The resulting transition frequency of 2 971 234 992 965(73) kHz is 2 orders of magnitude more accurate than previous measurements. This paves the way for a considerably improved determination of the dissociation energy (D_{0}) for fundamental tests with molecular hydrogen.

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.

Precision measurements and test of molecular theory in highly excited vibrational states of H2 (v = 11)

Accurate E F 1 Σ g + - X 1 Σ g + transition energies in molecular hydrogen were determined for transitions originating from levels with highly excited vibrational quantum number, v = 11, in the ground electronic state. Doppler-free two-photon spectroscopy was applied on vibrationally excited H 2 ∗ , produced via the photodissociation of H2S, yielding transition frequencies with accuracies of 45 MHz or 0.0015 cm-1. An important improvement is the enhanced detection efficiency by resonant excitation to autoionizing 7 p π electronic Rydberg states, resulting in narrow transitions due to reduced ac-Stark effects. Using known EF level energies, the level energies of X(v = 11, J = 1, 3-5) states are derived with accuracies of typically 0.002 cm-1. These experimental values are in excellent agreement with and are more accurate than the results obtained from the most advanced ab initio molecular theory calculations including relativistic and QED contributions.

A testing time for antimatter

Precision measurement of antiprotonic helium provides a test of physical laws

Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD(.)

The simplest molecules in nature, molecular hydrogen ions in the form of H2(+) and HD(+), provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD(+) by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws.