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.

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.

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.

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 I1µm/I2µm = 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.

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.

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.

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.

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.

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.

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}.

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 1Πu states of Rydberg and valence character while causing their predissociation. New predissociation linewidths and molecular constants are obtained for the states C3Πu(v = 7, 8, 14, 15, 16, 21), G3Πu(v = 0, 1, 4), and F3Πu(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.

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.

Dissociation Energy of the Hydrogen Molecule at 10

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.

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.

Rayleigh-Brillouin Scattering in Binary-Gas Mixtures.

Precise measurements are performed on spectral line shapes of spontaneous Rayleigh-Brillouin scattering in mixtures of the noble gases Ar and Kr, with He. Admixture of a light He atomic fraction results in marked changes of the spectra, although in all experiments He is merely a spectator atom: it affects the relaxation of density fluctuations of the heavy constituent, but its contribution to the scattered light intensity is negligibly small. The results are compared to a theory for the spectral line shape without adjustable parameters, yielding excellent agreement for the case of binary monatomic gases, signifying a step towards modeling and understanding of light scattering in more complex molecular media.

Constraint on a varying proton-electron mass ratio 1.5 billion years after the big bang.

A molecular hydrogen absorber at a lookback time of 12.4 billion years, corresponding to 10% of the age of the Universe today, is analyzed to put a constraint on a varying proton-electron mass ratio, µ. A high resolution spectrum of the J1443+2724 quasar, which was observed with the Very Large Telescope, is used to create an accurate model of 89 Lyman and Werner band transitions whose relative frequencies are sensitive to µ, yielding a limit on the relative deviation from the current laboratory value of Δµ/µ=(-9.5 ± 5.4(stat)± 5.3(syst))×10(-6).

Communication: Test of quantum chemistry in vibrationally hot hydrogen molecules.

Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The v = 12, J = 0 - 3 rovibrational levels of H2 (X(1)Σg (+)), lying only 2000 cm(-1) below the first dissociation limit, were populated by photodissociation of H2S and their level energies were accurately determined by two-photon Doppler-free spectroscopy. A comparison between the experimental results on v = 12 level energies with the best ab initio calculations shows a good agreement, where the present experimental accuracy of 3.5 × 10(-3) cm(-1) is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.