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 H$_2$ ($X^1\Sigma_g^+$), lying only $2000$ cm$^{-1}$ below the first dissociation limit, were populated by photodissociation of H$_2$S 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 \textit{ab initio} calculations shows good agreement, where the present experimental accuracy of $3.5 \times10^{-3}$ cm$^{-1}$ is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.Comment: 5 pages, 4 figures, and 2 table

B\,^1\Sigma^{+}_{u} and EF\,^{1}\Sigma^{+}_{g} level energies of D2_{2}

Accurate absolute level energies of the B\,^1\Sigma^{+}_{u}, $v=0-8, N$ and EF\,^{1}\Sigma^{+}_{g}, $v=0-21, N$ rovibrational quantum states of molecular deuterium are derived by combining results from a Doppler-free two-photon laser excitation study on several lines in the $EF\,{}^{1}\Sigma_{g}^{+}-X\,{}^{1}\Sigma_{g}^{+}$ (0,0) band, with results from a Fourier-transform spectroscopic emission study on a low-pressure hydrogen discharge. Level energy uncertainties as low as 0.0005 cm$^{-1}$ are obtained for some low-lying E\,^{1}\Sigma^{+}_{g} inner-well rovibrational levels, while uncertainties for higher-lying rovibrational levels and those of the F\,^{1}\Sigma^{+}_{g} outer-well states are nominally 0.005 cm$^{-1}$. Level energies of B\,^1\Sigma^{+}_{u} rovibrational levels, for $v \leq 8$ and $N \leq 10$ are determined at an accuracy of 0.001 cm$^{-1}$. Computed wavelengths of D$_2$ Lyman transitions in the B\,^1\Sigma^{+}_{u}-X\,^{1}\Sigma^{+}_{g} ($v,0$) bands are also tabulated for future applications.Comment: appears in Journal of Molecular Spectroscopy (2014

High-precision laser spectroscopy of the CO A1Π^1\Pi - X1Σ+^1\Sigma^+ (2,0), (3,0) and (4,0) bands

High-precision two-photon Doppler-free frequency measurements have been performed on the CO A$^1\Pi$ - X$^1\Sigma^+$ 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 $1.6\times10^{-3}$ 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$^1\Pi$ - X$^1\Sigma^+$ 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 $\Delta\lambda/\lambda = 2 \times 10^{-8}$ may be considered exact for the purpose of such comparisons.Comment: 13 pages, 6 figures, The Journal of Chemical Physics (2015) accepte

QED effects in molecules: test on rotational quantum states of H2_2

Quantum electrodynamic effects have been systematically tested in the progression of rotational quantum states in the $X ^{1}\Sigma_{g}^{+}, v=0$ vibronic ground state of molecular hydrogen. High-precision Doppler-free spectroscopy of the $EF ^{1}\Sigma_{g}^{+} - X ^{1}\Sigma_{g}^{+}$ (0,0) band was performed with 0.005 cm$^{-1}$ accuracy on rotationally-hot H$_2$ (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 H$_2$ ground state.Comment: 4 pages, 3 figures, to be published in Physical Review Letter

Constraints on extra dimensions from precision molecular spectroscopy

Accurate investigations of quantum level energies in molecular systems are shown to provide a test ground to constrain the size of compactified extra dimensions. This is made possible by the recent progress in precision metrology with ultrastable lasers on energy levels in neutral molecular hydrogen (H$_2$, HD and D$_2$) and the molecular hydrogen ions (H$_2^+$, HD$^+$ and D$_2^+$). Comparisons between experiment and quantum electrodynamics calculations for these molecular systems can be interpreted in terms of probing large extra dimensions, under which conditions gravity will become much stronger. Molecules are a probe of space-time geometry at typical distances where chemical bonds are effective, i.e. at length scales of an \AA. Constraints on compactification radii for extra dimensions are derived within the Arkani-Hamed-Dimopoulos-Dvali framework, while constraints for curvature or brane separation are derived within the Randall-Sundrum framework. Based on the molecular spectroscopy of D$_2$ molecules and HD$^+$ ions, the compactification size for seven extra dimensions (in connection to M-theory defined in 11 dimensions) of equal size is shown to be limited to $R_7 < 0.6 \mu$m. While limits on compactification sizes of extra dimensions based on other branches of physics are compared, the prospect of further tightening constraints from the molecular method is discussed

CARS spectroscopy of the (v=0→1v=0\to1) band in T2\rm{T_2}

Molecular hydrogen is a benchmark system for bound state quantum calculation and tests of quantum electrodynamical effects. While spectroscopic measurements on the stable species have progressively improved over the years, high resolution studies on the radioactive isotopologues $\rm{T_2}$, $\rm{HT}$ and $\rm{DT}$ have been limited. Here we present an accurate determination of $\rm{T_2}$ $Q(J = 0 - 5)$ transition energies in the fundamental vibrational band of the ground electronic state, by means of high resolution Coherent Anti-Stokes Raman Spectroscopy. With the present experimental uncertainty of $0.02\,\rm{cm^{-1}}$, which is a fivefold improvement over previous measurements, agreement with the latest theoretical calculations is demonstrated.Comment: 9 pages, 3 figure

Study of the Born-Oppenheimer Approximation for Mass-Scaling of Cold Collision Properties

Asymptotic levels of the A $^1\Sigma_u^+$ state of the two isotopomers $^{39}{\rm K}_2$ and $^{39}{\rm K}^{41}{\rm K}$ up to the dissociation limit are investigated with a Doppler-free high resolution laser-spectroscopic experiment in a molecular beam. The observed level structure can be reproduced correctly only if a mass dependent correction term is introduced for the interaction potential. The applied relative correction in the depth of the potential is $10^{-6}$, which is in the order of magnitude expected for corrections of the Born-Oppenheimer approximation. A similar change in ground state potentials might lead to significant changes of mass-scaled properties describing cold collisions like the s-wave scattering length.Comment: 8 pages, 6 figure

The B2Π−^2\Pi-X2Π^2\Pi electronic origin band of 13^{13}C6_6H

The rotationally resolved spectrum of the B$^2\Pi-$X$^2\Pi$ electronic origin band transition of $^{13}$C$_6$H is presented. The spectrum is recorded using cavity ring-down spectroscopy in combination with supersonic plasma jets by discharging a $^{13}$C$_2$H$_2$/He/Ar gas mixture. A detailed analysis of more than a hundred fully-resolved transitions allows for an accurate determination of the spectroscopic parameters for both the ground and electronically excited state of $^{13}$C$_6$H.Comment: 4 pages, 1 figure, 2 table