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arXiv:0804.2949 · Physical Review A

Potassium ground-state scattering parameters and Born-Oppenheimer potentials from molecular spectroscopy

Stephan Falke, H. Knöckel, J. Friebe, Matthias Riedmann, E. Tiemann, Christian Lisdat

Published Jul 11, 2008• 91 citations
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Abstract

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 ${^{39}\text{K}}_{2}$ 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 ${\text{I}}_{2}$ lines or by absolute measurements using a fs-frequency comb. The determined level energies were used together with Feshbach resonances from cold collisions of $^{39}\text{K}$ and $^{40}\text{K}$ 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.

DOI
10.1103/physreva.78.012503

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We present precision measurements with MHz uncertainty of the energy gap between asymptotic and well bound levels in the electronic ground state X 1\ensuremathΣg+X\text{ }{^{1}\ensuremath{\Sigma}}_{\text{g}}^{+}X 1\ensuremathΣg+​ of the 39K2{^{39}\text{K}}_{2}39K2​ molecule. The molecules are prepared in a highly collimated particle beam and are interrogated in a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type excitation scheme of optical transitions to long range levels close to the asymptote of the ground state, using the electronically excited state A 1\ensuremathΣu+{A\text{ }^{1}\ensuremath{\Sigma}}_{\text{u}}^{+}A 1\ensuremathΣu+​ 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.
We report results from close-coupling calculations for homonuclear ultracold collisions between potassium atoms, using the most up-to-date Born-Oppenheimer potential curves. The present study includes both of the bosonic isotopes 39K^{39}\mathrm{K}39K and 41K^{41}\mathrm{K}41K. The sss-wave scattering lengths as functions of the magnetic field strength for collisions between atoms in identical and different hyperfine states are obtained. Several Feshbach resonances are located and characterized for both isotopes. Comparison with experiments, where such data are available, show excellent agreement. We also study weakly bound molecular states of the K2{\mathrm{K}}_{2}K2​ molecule in close relation to the calculated Feshbach resonances. Another objective of the present work is to study inelastic collisions in which the hyperfine states of the colliding atoms are changed. From this type of calculation we obtain transition rates as functions of the magnetic field strength. Finally, we discuss how such transition rates might be of importance for experimental work.
Asymptotic levels of the AAA $^{1}\ensuremath{\Sigma}_{u}^{+}$ 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 ${10}^{\ensuremath{-}6}$, 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.
A comprehensive study of the electronic states at the 4s+5s4s+5s4s+5s asymptote in KRb\mathrm{KRb}KRb is presented. Abundant spectroscopic data on the $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ state were collected by Fourier-transform spectroscopy, which allows one to determine an accurate experimental potential energy curve up to 14.8A˚14.8\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}14.8A˚. The existing data set [C. Amiot et al., J. Chem. Phys. 112, 7068 (2000)] on the ground state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ was extended by several additional levels lying close to the atomic asymptote. In a coupled channels fitting routine complete molecular potentials for both electronic states were fitted. Along with the line frequencies of the molecular transitions, recently published positions of Feshbach resonances in 40K^{40}\mathrm{K}40K and 87Rb^{87}\mathrm{Rb}87Rb mixtures [F. Ferlaino et al., Phys. Rev. A 74, 039903 (2006)] were included in the fit. This makes the derived potential curves capable for an accurate description of observed cold collision features so far. Predictions of scattering lengths and Feshbach resonances in other isotopic combinations are reported.
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.
We use double-resonance photoassociative spectroscopy of ultracold 39K{}^{39}\mathrm{K}39K atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free 39K{}^{39}\mathrm{K}39K atoms to the pure long-range ${0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}=0,{J}^{\ensuremath{'}}=2)$ level is followed by stimulated emission to high-lying levels of the $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potential. The binding energies of levels within 5 GHz below the lowest ground-state 4s1/2(fa=1)+4s1/2(fb=1){4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=1)4s1/2​(fa​=1)+4s1/2​(fb​=1) hyperfine asymptote are measured by both trap loss and ionization detection. The locations of these near-threshold hyperfine-coupled molecular levels allow us to constrain the triplet potential and thereby determine the triplet scattering length. The result for 39K,{}^{39}\mathrm{K},39K, ${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$ (1a0=0.0529177nm),{(1a}_{0}=0.0529177 \mathrm{nm}),(1a0​=0.0529177nm), is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large 39K{}^{39}\mathrm{K}39K Bose-Einstein condensate will not be stable.