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arXiv:0706.2290 · Physical Review A

Born-Oppenheimer approximation for mass scaling of cold-collision properties

Stephan Falke, E. Tiemann, Christian Lisdat

Published Jul 31, 2007• 7 citations
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Abstract

Asymptotic levels of the $A$ $^{1}\ensuremath{\Sigma}_{u}^{+}$ state of the two isotopomers $^{39}\mathrm{K}_{2}$ and $^{39}\mathrm{K}^{41}\mathrm{K}$ 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 ${10}^{\ensuremath{-}6}$, 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.

DOI
10.1103/physreva.76.012724

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Asymptotic levels of the AAA 1\ensuremathΣu+^{1}\ensuremath{\Sigma}_{u}^{+}1\ensuremathΣu+​ state of the two isotopomers 39K2^{39}\mathrm{K}_{2}39K2​ and 39K41K^{39}\mathrm{K}^{41}\mathrm{K}39K41K 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\ensuremath−6{10}^{\ensuremath{-}6}10\ensuremath−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 sss-wave scattering length.
We present precision measurements with MHz uncertainty of the energy gap between asymptotic and well bound levels in the electronic ground state $X\text{ }{^{1}\ensuremath{\Sigma}}_{\text{g}}^{+}$ of the 39K2{^{39}\text{K}}_{2}39K2​ molecule. The molecules are prepared in a highly collimated particle beam and are interrogated in a $\ensuremath{\Lambda}$-type excitation scheme of optical transitions to long range levels close to the asymptote of the ground state, using the electronically excited state ${A\text{ }^{1}\ensuremath{\Sigma}}_{\text{u}}^{+}$ as the intermediate one. The transition frequencies are measured either by comparison with I2{\text{I}}_{2}I2​ lines or by absolute measurements using a fs-frequency comb. The determined level energies were used together with Feshbach resonances from cold collisions of 39K^{39}\text{K}39K and 40K^{40}\text{K}40K reported from other authors to fit ground state potentials. Precise scattering lengths are determined and tests of the validity of the Born-Oppenheimer approximation for the description of cold collisions at this level of precision are performed.
This thesis is concerned with long range behavior of the interaction potential of two neutral atoms.Two aspects are of special interest: First, how the long range behavior changes if one of the atoms is replaced by another isotope.Second, how to model the influence of a laser field on long range interaction.Several high precision spectroscopy experiments on particle beams are carried out.The transition frequencies of the D lines of 39,40,41 K are measured with frequency comb generated by a self-referenced femtosecond laser, which is locked to a Cs-clock.Discrepancies in the literature are removed and new values for the hyperfine structures of the 4p 1/2 and 4p 3/2 state and the isotope shift of both D lines are derive.On a beam of potassium dimers the A 1 Σ + u state of K 2 is studied up to the dissociation limit complementing and extending photoassociation spectroscopy of ultracold ensembles.Local perturbation due to the spin-orbit coupling with the b 3 Π u state are identified.Molecular hyperfine structure of levels close to the asymptote is observed and modeled by atomic parameter only.Improved values of the atomic radiative lifetime of the states 4p 1/2 and 4p 3/2 are derived from the long range parameter C 3 of the molecule.Also, an improved value for the dissociation energy of the X 1 Σ + g ground state is obtained and recipes for the investigation of cold collision via spectroscopy of the molecular structure at the ground state asymptotes are derived.For the first time asymptotic levels of two isotopomers of K 2 are studied and a comparison of asymptotic spectra of two isotopomers 39 K 2 and 39 K 41 K shows that corrections to the Born-Oppenheimer potential are needed.Optical coupling between asymptotic ground state levels and long range levels of an excited state has been suggested as tool for influencing cold collisions.Here, we model lineshapes for an experiment which investigates such a coupling systematically in Na 2 by laser spectroscopy in a beam.A fit program for the lineshape is used to compare experimental and theoretical values and to check the validity of the applied model from multichannel quantum defect theory.The dependency on the detuning of the coupling laser is reproduced but other details failed.To allow similar studies are reported for alkali metals on the simpler quantum system from alkali earth elements the development of an oven for a continuous beam of Ca 2 for Doppler-free spectroscopy is discussed including a major change of design and first experiences are reported.The heating of the oven is, unlike those for the beams applied above, outside the vacuum tank because of the high temperatures needed for the oven.
High-resolution Fourier transform spectroscopy was used to record fluorescence progressions of KLi formed in a heat pipe. Lithium isotope effects were used to derive the adiabatic correction to the Born-Oppenheimer potential for the electronic ground state over a wide range of internuclear separations. With a short extrapolation from the experimentally determined potential functions of the coupled states $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ and $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ toward their common atomic asymptote, we have improved the modeling of recently observed Feshbach resonances for the fermionic atom pair 6Li^{6}\text{L}\text{i}6Li and 40K^{40}\text{K}40K. Predictions for cold collisions between different isotopologues are presented using mass scaling with or without Born-Oppenheimer corrections. Predictions for Feshbach resonance positions differ by up to 0.5 G within reach of current experimental verification.
State-of-the-art ab initio techniques have been applied to compute the potential-energy curves for the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and excited ${}^{1}{\ensuremath{\Pi}}_{g}(4s3d)$ states of the calcium dimer in the Born-Oppenheimer approximation. The weakly bound ground state was calculated by symmetry-adapted perturbation theory, while the strongly bound excited state was computed using a combination of the linear-response theory within the coupled-cluster singles and doubles framework for the core-valence electronic correlation and of the full configuration interaction for the valence-valence correlation. The ground-state potential has been corrected by considering the relativistic terms resulting from the first-order many-electron Breit theory, and the retardation corrections. The magnetic electronic transition dipole moment governing the ${}^{1}{\ensuremath{\Pi}}_{g}{\ensuremath{\leftarrow}}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ transitions has been obtained as the first residue of the polarization propagator computed with the coupled-cluster method restricted to single and double excitations. The computed energies and transition moments have been analytically fitted and used in the dynamical calculations of the rovibrational energy levels, ground-state scattering length, photoassociation intensities at ultralow temperatures, and spontaneous emission coefficients from the ${}^{1}{\ensuremath{\Pi}}_{g}(4s3d)$ to the $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ state. The spectroscopic constants of the theoretical ground-state potential are in a good agreement with the experimental values derived from the Fourier-transform spectra [O. Allard et al., Eur. Phys. J. D (to be published)]. The theoretical s-wave scattering length for the ground state is a=44bohrs,a=44\mathrm{bohrs},a=44bohrs, suggesting that it should be possible to obtain a stable Bose-Einstein condensate of calcium atoms. Finally, the computed photoassociation intensities and spontaneous emission coefficients suggest that it should be possible to obtain cold calcium molecules by photoassociation of cold atoms to the first ${}^{1}{\ensuremath{\Pi}}_{g}$ state followed by a spontaneous emission to the ground state.
We report on deviations beyond the Born-Oppenheimer approximation in potassium interatomic potentials. Identifying three previously unknown d-wave Feshbach resonances, we significantly improve the understanding of the K39 interatomic potentials. Combining these observations with the most recent data on known inter- and intraisotope Feshbach resonances, we show that Born-Oppenheimer corrections can be determined from atomic collisional properties alone and that significant differences between the homo- and heteronuclear cases appear.
The experimental characterization of the electronic states correlated to the asymptote of ground state Na (3S) and Rb (5S) atoms was expanded by spectroscopic data on $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state levels using a high resolution Fourier transform spectroscopy technique. The hyperfine splitting of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state levels was partially resolved and analyzed for both Na85Rb\mathrm{Na}\phantom{\rule{0.2em}{0ex}}^{85}\mathrm{Rb}Na85Rb and Na87Rb\mathrm{Na}\phantom{\rule{0.2em}{0ex}}^{87}\mathrm{Rb}Na87Rb isotopomers. Transitions to high lying levels of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ and $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ states were recorded simultaneously which enables one to determine long range parameters of the molecular potentials. Coupled channels calculations based on the Fourier grid method were finally applied for deriving accurate potential energy curves of the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ and $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ states capable of a reliable description of cold collisions between Na and Rb atoms in their ground states. Scattering lengths and Feshbach resonances were calculated for some quantum states.