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}.

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.

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.

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.

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.

VIS and VUV spectroscopy of 12C17O and deperturbation analysis of the A1Π, υ = 1–5 levels

The reduced T(J) − B_AJ(J + 1) + D_AJ²(J + 1)² term values for the ¹²C¹⁷O A₁Π (υ = 5) level and for the hypothetical unperturbed crossing rovibronic levels of the perturbers.

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.

High-precision laser spectroscopy of the CO A(1)Π - X(1)Σ(+) (2,0), (3,0), and (4,0) bands

High-precision two-photon Doppler-free frequency measurements have been performed on the CO A(1)Π - X(1)Σ(+) fourth-positive system (2,0), (3,0), and (4,0) bands. Absolute frequencies of forty-three transitions, for rotational quantum numbers up to J = 5, have been determined at an accuracy of 1.6 × 10(-3) cm(-1), using advanced techniques of two-color 2  +  1' resonance-enhanced multi-photon ionization, Sagnac interferometry, frequency-chirp analysis on the laser pulses, and correction for AC-Stark shifts. The accurate transition frequencies of the CO A(1)Π - X(1)Σ(+) system are of relevance for comparison with astronomical data in the search for possible drifts of fundamental constants in the early universe. The present accuracies in laboratory wavelengths of Δλ/λ = 2 × 10(-8) may be considered exact for the purpose of such comparisons.

Limits on a gravitational field dependence of the proton-electron mass ratio from H2 in white dwarf stars

Spectra of molecular hydrogen (H2) are employed to search for a possible proton-to-electron mass ratio (μ) dependence on gravity. The Lyman transitions of H2, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions (T∼13 000  K) of their photospheres. We derive sensitivity coefficients Ki which define how the individual H2 transitions shift due to μ dependence. The spectrum of white dwarf star GD133 yields a Δμ/μ constraint of (-2.7±4.7stat±0.2syst)×10(-5) for a local environment of a gravitational potential ϕ∼10(4) ϕEarth, while that of G29-38 yields Δμ/μ=(-5.8±3.8stat±0.3syst)×10(-5) for a potential of 2×10(4) ϕEarth.

Widely tunable laser frequency offset lock with 30 GHz range and 5 THz offset

We demonstrate a simple and versatile method to greatly extend the tuning range of optical frequency shifting devices, such as acousto-optic modulators (AOMs). We use this method to stabilize the frequency of a tunable narrow-band continuous-wave (CW) laser to a transmission maximum of an external Fabry-Perot interferometer (FPI) with a tunable frequency offset. This is achieved through a servo loop which contains an in-loop AOM for simple radiofrequency (RF) tuning of the optical frequency over the full 30 GHz mode-hop-free tuning range of the CW laser. By stabilizing the length of the FPI to a stabilized helium-neon (HeNe) laser (at 5 THz offset from the tunable laser) we simultaneously transfer the ~ 1 MHz absolute frequency stability of the HeNe laser to the entire 30 GHz range of the tunable laser. Thus, our method allows simple, wide-range, fast and reproducible optical frequency tuning and absolute optical frequency measurements through RF electronics, which is here demonstrated by repeatedly recording a 27-GHz-wide molecular iodine spectrum at scan rates up to 500 MHz/s. General technical aspects that determine the performance of the method are discussed in detail.

Fundamental vibration of molecular hydrogen

The fundamental ground tone vibration of H(2), HD, and D(2) is determined to an accuracy of 2×10(-4) cm(-1) from Doppler-free laser spectroscopy in the collisionless environment of a molecular beam. This rotationless vibrational splitting is derived from the combination difference between electronic excitation from the X(1)Σ(g)(+), v=0, and v=1 levels to a common EF(1)Σ(g)(+), v=0 level. Agreement within 1σ between the experimental result and a full ab initio calculation provides a stringent test of quantum electrodynamics in a chemically bound system.

Frequency comb generation by CW laser injection into a quantum-dot mode-locked laser

We report on frequency comb generation at 1.5 μm by injection of a CW laser in a hybridly mode-locked InAs/InP two-section quantum-dot laser (HMLQDL). The generated comb has > 60 modes spaced by ∼ 4.5 GHz and a -20 dBc width of > 100 GHz (23 modes) at > 30 dB signal to background ratio. Comb generation was observed with the CW laser (red) detuned more than 20 nm outside the HMLQDL spectrum, spanning a large part of the gain spectrum of the quantum dot material. It is shown that the generated comb is fully coherent with the injected CW laser and RF frequency used to drive the hybrid mode-locking. This method of comb generation is of interest for the creation of small and robust frequency combs for use in optical frequency metrology, high-frequency (> 100 GHz) RF generation and telecommunication applications.

High-resolution Fourier-transform extreme ultraviolet photoabsorption spectroscopy of 14N15N

The first comprehensive high-resolution photoabsorption spectrum of (14)N(15)N has been recorded using the Fourier-transform spectrometer attached to the Desirs beamline at the Soleil synchrotron. Observations are made in the extreme ultraviolet and span 100 000-109 000 cm(-1) (100-91.7 nm). The observed absorption lines have been assigned to 25 bands and reduced to a set of transition energies, f values, and linewidths. This analysis has verified the predictions of a theoretical model of N(2) that simulates its photoabsorption and photodissociation cross section by solution of an isotopomer independent formulation of the coupled-channel Schrödinger equation. The mass dependence of predissociation linewidths and oscillator strengths is clearly evident and many local perturbations of transition energies, strengths, and widths within individual rotational series have been observed.

QED effects in molecules: test on rotational quantum states of H2

Quantum electrodynamic effects have been systematically tested in the progression of rotational quantum states in the X 1Σ(g)(+), v=0 vibronic ground state of molecular hydrogen. High-precision Doppler-free spectroscopy of the EF 1Σ(g)(+)-X 1Σ(g)(+) (0,0) band was performed with 0.005  cm(-1) accuracy on rotationally hot H2 (with rotational quantum states J up to 16). QED and relativistic contributions to rotational level energies as high as 0.13  cm(-1) are extracted, and are in perfect agreement with recent calculations of QED and high-order relativistic effects for the H2 ground state.

Improved laboratory values of the H2 Lyman and Werner lines for constraining time variation of the proton-to-electron mass ratio

Two distinct high-accuracy laboratory spectroscopic investigations of the H2 molecule are reported. Anchor lines in the EF1Sigmag+-X1Sigmag+ system are calibrated by two-photon deep-UV Doppler-free spectroscopy, while independent Fourier-transform spectroscopic measurements are performed that yield accurate spacings in the B1Sigmau+-EF1Sigmag+ and I1Pig-C1Piu systems. From combination differences accurate transition wavelengths for the B-X Lyman and the C-X Werner lines can be determined with accuracies better than approximately 5 x 10(-9), representing a major improvement over existing values. This metrology provides a practically exact database to extract a possible variation of the proton-to-electron mass ratio based on H2 lines in high-redshift objects. Moreover, it forms a rationale for equipping a future class of telescopes, carrying 30-40 m dishes, with novel spectrometers of higher resolving powers.

Reducing the first-order Doppler shift in a Sagnac interferometer

We demonstrate a technique to reduce first-order Doppler shifts in crossed atomic/molecular and laser beam setups by aligning two counterpropagating laser beams as part of a Sagnac interferometer. Interference fringes on the exit port of the interferometer reveal minute deviations from perfect antiparallelism. Residual Doppler shifts of this method scale with the ratio v/(4d) of the typical atomic/molecular velocity v and the laser beam diameter d. The method is implemented for precision frequency calibration studies at deep-UV wavelengths, both in one- and two-photon excitation schemes: the 6s(2) --> 6s30p(3/2)J=1 line in Yb at 199 nm and the 4p(6) --> 4p(5)p[1/2](0) transition in Kr at lambda=212 nm. The achieved precision of 6 x 10(-10) is limited by the characteristics of the laser system.