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International Symposium on Molecular Spectroscopy (ISMS)

SPECTROSCOPY OF H2+ AND HD+ NEAR THE DISSOCIATION THRESHOLD: SHAPE AND FESHBACH RESONANCES

Frédéric Merkt, Maximilian Beyer

Published Jun 20, 2016• 0 citations
Publisher

Abstract

\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.30]{maby_ortho_h2-01.eps} \end{wrapfigure} We use high Rydberg states to measure the properties of H$_2^+$ and HD$^+$ in the vicinity of their dissociation limits H$^+$+H, H$^+$+D and H+D$^+$, with particular emphasis on quasibound rovibrational levels above the dissociation threshold of the X$^+$ $^2\Sigma_g^+$ ground state. Although the existence of these quasibound levels has been predicted a long time ago, they have never been observed. Positions and widths of the lowest resonances have not been calculated either. Given the role that such states play in the three-body and radiative recombination of H(1s) and H$^+$ to form H$_2^+$, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels (shape resonances) of H$_2^+$, located close to the top of the centrifugal barriers and which decay by quantum-mechanical tunneling. For HD$^+$ we present measurements of rovibrational levels of the A$^+$ $^2\Sigma_u^+$ state, located between the two dissociation limits. Because of the g-u-symmetry breaking in HD$^+$, these levels are coupled to the H$^+$+D continuum by nonadiabatic interactions (Feshbach resonances). The experimental results will be compared with the positions and widths we calculate for these levels using a potential model for the X$^+$ and the A$^+$ state of H$_2^+$ and HD$^+$ which includes adiabatic, nonadiabatic, relativistic and radiative corrections to the Born-Oppenheimer potential energies.

DOI
10.15278/isms.2016.mf10

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\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.30]{maby_ortho_h2-01.eps} \end{wrapfigure} We use high Rydberg states to measure the properties of H2+_2^+2+​ and HD+^++ in the vicinity of their dissociation limits H+^+++H, H+^+++D and H+D+^++, with particular emphasis on quasibound rovibrational levels above the dissociation threshold of the X+^++ 2Σg+^2\Sigma_g^+2Σg+​ ground state. Although the existence of these quasibound levels has been predicted a long time ago, they have never been observed. Positions and widths of the lowest resonances have not been calculated either. Given the role that such states play in the three-body and radiative recombination of H(1s) and H+^++ to form H2+_2^+2+​, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels (shape resonances) of H2+_2^+2+​, located close to the top of the centrifugal barriers and which decay by quantum-mechanical tunneling. For HD+^++ we present measurements of rovibrational levels of the A+^++ 2Σu+^2\Sigma_u^+2Σu+​ state, located between the two dissociation limits. Because of the g-u-symmetry breaking in HD+^++, these levels are coupled to the H+^+++D continuum by nonadiabatic interactions (Feshbach resonances). The experimental results will be compared with the positions and widths we calculate for these levels using a potential model for the X+^++ and the A+^++ state of H2+_2^+2+​ and HD+^++ which includes adiabatic, nonadiabatic, relativistic and radiative corrections to the Born-Oppenheimer potential energies.
Ab initio calculations of the energy level structure of H2+ that include relativistic and radiative corrections to nonrelativistic energies and the diagonal part of the hyperfine interaction have predicted the existence of four bound rovibrational levels [(v = 0, N = 0 − 2) and (v = 1, N = 0)] of the first electronically excited (A+ Σu+2) state of H2+, the (v = 1, N = 0) level having a calculated binding energy of only Eb = 1.082 219 8(4)·10−9 Eh and leading to an extremely large scattering length of 750(5) a0 for the H+ + H collision [J. Carbonell et al., J. Phys. B: At., Mol. Opt. Phys. 37, 2997 (2004)]. We present an investigation of the nonadiabatic coupling between the first two electronic states (X+ Σg+2 and A+ Σu+2) of H2+ induced by the Fermi-contact term of the hyperfine-coupling Hamiltonian. This interaction term, which mixes states of total spin quantum number G = 1/2, is rigorously implemented in a close-coupling approach to solve the spin-rovibronic Schrödinger equation. We show that it mixes states of gerade and ungerade electronic symmetry, that it shifts the positions of all weakly bound rovibrational states of H2+, and that it affects both the positions and widths of its shape resonances. The calculations demonstrate that the G = 1/2 hyperfine component of the A+ (v = 1, N = 0) state does not exist and that, for G = 1/2, the s-wave scattering lengths of the H+ + H(1s) collision are −578(6) a0 and −43(4) a0 for the F = 0 and F = 1 hyperfine components of the H(1s) atom, respectively. The binding energy of the G = 3/2 hyperfine component of the A+ (v = 1, N = 0) state is not significantly affected by the hyperfine interaction and the corresponding scattering length for the H+ + H(1s, F = 1) collision is 757(7) a0.
Cross sections for He+H2\mathrm{He}+{\mathrm{H}}_{2}He+H2​ collisions are reported for rovibrational states near dissociation at translational energies less than $1000\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. In contrast to our previously reported cross sections for lower-lying initial rotational states, the excited rotational states near dissociation give rise to shape resonances for energies between 0.001 and $1\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. The emergence of these resonances with increasing rotational level is opposite to the trend found for He+CO\mathrm{He}+\mathrm{C}\mathrm{O}He+CO where the shape resonance strength decreases with rotational level for low-lying states. Quasiresonant energy transfer and low energy excitation thresholds are also discussed and it is found that there are 11 rovibrationally excited states that are stable against collision at ultracold temperatures.
The susceptibility of ultracold gases to precise manipulation via external fields makes them ideal systems to study fundamental quantum mechanical phenomena. Various regimes, which are not possible to reach in condensed matter or nuclear physics, can be probed with these quantum gases. Especially the tunability of the interactions and confining potentials make that these ultracold gases offer unique possibilities to explore and study universal behavior. The tunability of the dominant two-body interactions in dilute ultracold atomic gases stems from the presence of Feshbach resonances. Via these resonances pairs of ultracold atoms can be associated to form ultracold molecules. In fact, measurements of Feshbach resonance positions can be used to reveal part of the underlying molecular structure. Vica versa, accurate molecular Born-Oppenheimer potentials can be used as input for full numerical coupled-channels calculations to reliably predict Feshbach resonances. For most of the heteronuclear mixtures currently studied however, the relevant molecular potentials are not accurate enough. As the coupled-channels method is often too elaborate and too time consuming to be used to fit the measured data to enable the construction of more accurate potentials, a need for accurate models which complement this established method is created. In this thesis we have developed a simplified model for resonant scattering of two ultracold atoms which fulfills this need. The asymptotic bound-state model (ABM) is a hierarchical model which can be systematically increased in complexity and accuracy. In its most simple form, the ABM only needs two parameters to predict the position and strength of Feshbach resonances: Two binding energies corresponding to the least bound state of the two molecular potentials involved. We demonstrate that this model, although it is solely based on bound states, can incorporate threshold effects. Additionally, the model can be extended to include: Multiple vibrational levels, overlapping resonances, and magnetic dipole-dipole interactions. This versatile model allows for a description of Feshbach resonances in a large variety of systems without accurate knowledge of the relevant molecular Born-Oppenheimer potentials. Being computationally light, the ABM can be used to analyze measurements of Feshbach resonances and hereby expose the basic underlying molecular structure. Additionally, the ABM is well suited to map out all available Feshbach resonances in a system. This ability is particularly useful when an optimal resonance is required for a certain experiment. For the 6Li-40K mixture we have utilized this ability to experimentally observe a strong Feshbach resonance which offers promising perspectives to reach the strongly interacting universal regime in a mass-imbalanced Fermi gas. By analyzing the various inelastic decay processes and the accuracy of the ab initio Born-Oppenheimer potentials, we predict a strong resonance in a mixture of metastable bosonic and fermionic helium atoms. For the homonuclear (bosonic as well as fermionic) helium gas we do not find strong resonances. For an ultracold gas of 40K atoms, an elaborate combined theoretical and experimental effort is presented to map out the Feshbach resonance structure. On the experimental side we observed 36 Feshbach resonances, 31 of which where observed for the first time. These observations are in excellent agreement with coupled-channels calculations which use unmodified Born-Oppenheimer potentials as input. On the theoretical side, we present a comparison between different simplified models of resonance scattering and the full numerical coupled-channels calculations. We have developed the resonant state model (RSM) to describe the resonant scattering of two ultracold atoms. This model is founded on resonant states, the natural (eigen) frequencies of the two-body system, and their non-trivial properties. Threshold effects are implicitly build into the RSM. The RSM can describe the effect of the continuum of scattering states, states which are neglected in the ABM, on the position and strength of a Feshbach resonance by only a few resonant states. Especially when a low-energy resonance is embedded in the continuum of scattering states, the effect of these states on the Feshbach resonance cannot be neglected. The RSM can be viewed as the natural generalization of the ABM. As the RSM can be based on just a few resonant states, it retains the computational simplicity of the ABM. Using the tunability of two-body interactions induced by a Feshbach resonance, we describe a crossover for a rotating Fermi gas between two strongly-correlated many-body states. We demonstrate that the correlation induced long-range interaction will shift the crossover with respect to the non-rotating case.
Partial wave resonances are quasi-bound states that are formed by tunneling through the centrifugal barrier. Such states are important to collisions that deviate from the Langevin limit where direct collision path is suppressed due to quantum symmetry or a potential barrier. In such a case, quantum resonances play a major role in the dynamics at low temperatures where scattering process can be described mainly by the resonance contribution. Here we present the first observation of the lowest-lying partial wave resonance in the Penning ionization collisions between metastable neon and rovibrationally ground state HD molecules. We observe the resonance at an energy of $k_B\times$22mK taking advantage of the phase space correlation similar to atomic delta kick cooling. We show that the ppp-wave resonance position is particularly sensitive to the leading term of the van der Waals interaction. We also measure shape resonance at a higher angular momentum state, l=6l=6l=6, allowing us to disentangle and probe the short and the long parts of the intermolecular interaction.
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}.
Full-dimensional quantum scattering calculations are reported for ro-vibrational transitions in HD+HD collisions using a highly accurate interaction potential for the H2_22​-H2_22​ system. Several near-resonant ro-vibrational transitions are identified that conserve the overall rotational angular momentum and nearly conserve the internal energy of the collision partners. Key anisotropic terms that drive the rotational transitions and angular momentum partial waves that contribute to low energy resonant features in the energy dependence of the cross sections are identified. The computed results are in agreement with total cross sections reported in previous experimental results, including resonant features in the energy dependence of the cross section. In particular, low-energy cross sections show a strong resonant feature associated with an l=3l=3l=3 partial wave in the incident channel. Rate coefficients for several inelastic rotational and ro-vibrational transitions are reported for temperatures ranging from 0.10.10.1 K to 200200200 K and they display a maximum between 111 K-101010 K reflecting the important contributions from the l=3l=3l=3 shape resonance that occurs around 2.5 K.