Polarizability tensor invariants of H2, HD, and D2

Magic wavelength for a rovibrational transition in molecular hydrogen

Molecular hydrogen, among other simple calculable atomic and molecular systems, possesses a huge advantage of having a set of ultralong living rovibrational states that make it well suited for studying fundamental physics. Further experimental progress will require trapping cold H₂ samples. However, due to the large energy of the first electronic excitation, the conventional approach to finding a magic wavelength does not work for H₂. We find a rovibrational transition for which the AC Stark shift is largely compensated by the interplay between the isotropic and anisotropic components of polarizability. The residual AC Stark shift can be completely eliminated by tuning the trapping laser to a specific “magic wavelength” at which the weak quadrupole polarizability cancels the residual dipole polarizability.

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.

Vibration overtone hyperpolarizability measured for H2

The second hyperpolarizability (γ) of the H₂ molecule was measured by gas-phase electric field induced second harmonic generation at the frequencies of the one-photon resonance for the 3-0 Q(J) overtone transitions (v, J = 0, J → 3, J for J = 0, 1, 2, and 3). The magnitude of the resonant contribution to γ was measured with 2% accuracy using the previously determined non-resonant γ for calibration. Pressure broadening and frequency shift for the transitions were also measured. A theoretical expression for the resonant vibrational γ contribution in terms of transition polarizabilities is compared to the observations. The measured γ resonance strength is 4%-14% larger than the results obtained from this theoretical expression evaluated using ab initio transition polarizabilities.

Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state

In this work, we provide values for the quadrupole moment Θ, the hexadecapole moment Φ, the dipole polarizability α, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability γ, and the dipole-dipole-quadrupole hyperpolarizability B for the hydrogen molecule in the ground singlet state, evaluated by finite-field configuration interaction singles and doubles (CISD) and coupled-cluster singles and doubles (CCSD) methods for 26 different H-H separations r, ranging from 0.567 a.u. to 10.0 a.u. Results obtained with various large correlation-consistent basis sets are compared at the vibrationally averaged bond length r₀ in the ground state. Results over the full range of r values are presented at the CISD/d-aug-cc-pV6Z level for all of the independent components of the property tensors. In general, our values agree well with previous ab initio results of high accuracy for the ranges of H-H distances that have been treated in common. To our knowledge, for H₂ in the ground state, our results are the first to be reported in the literature for Φ for r > 7.0 a.u., γ and B for r > 6.0 a.u., and C and E for any H-H separation outside a narrow range around the potential minimum. Quantum Monte Carlo values of Θ have been given previously for H-H distances out to 10.0 a.u., but the statistical error is relatively large for r > 7.0 a.u. At the larger r values in this work, α_xx and α_zz show the expected functional forms, to leading order in r^-1. As r increases further, Θ and Φ vanish, while α, γ, and the components of B converge to twice the isolated-atom values. Components of C and E diverge as r increases. Vibrationally averaged values of the properties are reported for all of the bound states (vibrational quantum numbers υ = 0-14) with rotational quantum numbers J = 0-3.