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

Ramsey-type microwave spectroscopy on CO (a3Πa^3\Pi)

Using a Ramsey-type setup, the lambda-doublet transition in the $J=1,\, \Omega=1$ level of the $a^3\Pi$ state of CO was measured to be 394 064 870(10) Hz. In our molecular beam apparatus, a beam of metastable CO is prepared in a single quantum level by expanding CO into vacuum and exciting the molecules using a narrow-band UV laser system. After passing two microwave zones that are separated by 50 cm, the molecules are state-selectively deflected and detected 1 meter downstream on a position sensitive detector. In order to keep the molecules in a single $m_J^B$ level, a magnetic bias field is applied. We find the field-free transition frequency by taking the average of the $m_J^B = +1 \rightarrow m_J^B = +1$ and $m_J^B = -1 \rightarrow m_J^B = -1$ transitions, which have an almost equal but opposite Zeeman shift. The accuracy of this proof-of-principle experiment is a factor of 100 more accurate than the previous best value obtained for this transition

A 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, $\mu$. 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 $\mu$, yielding a limit on the relative deviation from the current laboratory value of $\Delta\mu/\mu=(-9.5\pm5.4_{\textrm{stat}} \pm 5.3_{\textrm{sys}})\times 10^{-6}$.Comment: Accepted for publication in PRL. Includes supplemental materia

Rayleigh-Brillouin light scattering spectroscopy of nitrous oxide (N2_2O)

High signal-to-noise and high-resolution light scattering spectra are measured for nitrous oxide (N$_2$O) gas at an incident wavelength of 403.00 nm, at 90$^\circ$ scattering, at room temperature and at gas pressures in the range $0.5-4$ bar. The resulting Rayleigh-Brillouin light scattering spectra are compared to a number of models describing in an approximate manner the collisional dynamics and energy transfer in this gaseous medium of this polyatomic molecular species. The Tenti-S6 model, based on macroscopic gas transport coefficients, reproduces the scattering profiles in the entire pressure range at less than 2\% deviation at a similar level as does the alternative kinetic Grad's 6-moment model, which is based on the internal collisional relaxation as a decisive parameter. A hydrodynamic model fails to reproduce experimental spectra for the low pressures of 0.5-1 bar, but yields very good agreement ($< 1$\%) in the pressure range $2-4$ bar. While these three models have a different physical basis the internal molecular relaxation derived can for all three be described in terms of a bulk viscosity of $\eta_b \sim (6 \pm 2) \times 10^{-5}$ Pa$\cdot$s. A 'rough-sphere' model, previously shown to be effective to describe light scattering in SF$_6$ gas, is not found to be suitable, likely in view of the non-sphericity and asymmetry of the N-N-O structured linear polyatomic molecule

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