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Physical Review A

X Σ1+ and a Σ3+ states of the atom pair K+Cs studied by Fourier-transform spectroscopy

R. Ferber, I. P. Klincare, О. Nikolayeva, M. Tamanis, H. Knöckel, E. Tiemann, A. Pashov

Published Dec 1, 2009• 43 citations
Publisher

Abstract

A comprehensive study of the $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ and $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ electronic states of the K and Cs atom pair is presented. Abundant spectroscopic data include 1937 transitions to the $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ state and $13\text{ }724$ transitions to the $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ state for ${^{39}\text{K}\text{ }}^{133}\text{Cs}$ which were obtained by Fourier-transform spectroscopy. From these data potential energy curves were constructed simultaneously for both states $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ and $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ which are coupled by the hyperfine interaction. This allows us to accurately model the potential close to $\text{K}(4s)+\text{Cs}(6s)$ atom-pair asymptote which is required to simulate cold collision processes. Dissociation energies of the $X\text{ }{^{1}\ensuremath{\Sigma}}^{+}$ state as ${D}_{e}^{X}=4069.208(40)\text{ }{\text{cm}}^{\ensuremath{-}1}$ and of the $a\text{ }{^{3}\ensuremath{\Sigma}}^{+}$ state as ${D}_{e}^{a}=267.141(20)\text{ }{\text{cm}}^{\ensuremath{-}1}$ were determined. Scattering lengths are predicted for different KCs isotopologs and Feshbach resonances were calculated for magnetic fields up to 1000 G.

DOI
10.1103/physreva.80.062501

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A comprehensive study of the X 1\ensuremathΣ+X\text{ }{^{1}\ensuremath{\Sigma}}^{+}X 1\ensuremathΣ+ and a 3\ensuremathΣ+a\text{ }{^{3}\ensuremath{\Sigma}}^{+}a 3\ensuremathΣ+ electronic states of the K and Cs atom pair is presented. Abundant spectroscopic data include 1937 transitions to the a 3\ensuremathΣ+a\text{ }{^{3}\ensuremath{\Sigma}}^{+}a 3\ensuremathΣ+ state and 13 72413\text{ }72413 724 transitions to the X 1\ensuremathΣ+X\text{ }{^{1}\ensuremath{\Sigma}}^{+}X 1\ensuremathΣ+ state for 39K 133Cs{^{39}\text{K}\text{ }}^{133}\text{Cs}39K 133Cs which were obtained by Fourier-transform spectroscopy. From these data potential energy curves were constructed simultaneously for both states X 1\ensuremathΣ+X\text{ }{^{1}\ensuremath{\Sigma}}^{+}X 1\ensuremathΣ+ and a 3\ensuremathΣ+a\text{ }{^{3}\ensuremath{\Sigma}}^{+}a 3\ensuremathΣ+ which are coupled by the hyperfine interaction. This allows us to accurately model the potential close to K(4s)+Cs(6s)\text{K}(4s)+\text{Cs}(6s)K(4s)+Cs(6s) atom-pair asymptote which is required to simulate cold collision processes. Dissociation energies of the X 1\ensuremathΣ+X\text{ }{^{1}\ensuremath{\Sigma}}^{+}X 1\ensuremathΣ+ state as DeX=4069.208(40) cm\ensuremath−1{D}_{e}^{X}=4069.208(40)\text{ }{\text{cm}}^{\ensuremath{-}1}DeX​=4069.208(40) cm\ensuremath−1 and of the a 3\ensuremathΣ+a\text{ }{^{3}\ensuremath{\Sigma}}^{+}a 3\ensuremathΣ+ state as Dea=267.141(20) cm\ensuremath−1{D}_{e}^{a}=267.141(20)\text{ }{\text{cm}}^{\ensuremath{-}1}Dea​=267.141(20) cm\ensuremath−1 were determined. Scattering lengths are predicted for different KCs isotopologs and Feshbach resonances were calculated for magnetic fields up to 1000 G.
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 states X 1 Σ + and a 3 Σ + correlated to the ground-state asymptote of Na (3s) and Cs (6s) atoms have been experimentally investigated using high resolution Fourier-transform spectroscopy. The hyperfine splitting of the a 3 Σ + state levels is partially resolved. Transitions to asymptotic vibrational levels of the a 3 Σ + and X 1 Σ + states were recorded simultaneously. The joint evaluation of the data of both the a 3 Σ + and the X 1 Σ + states allows us to determine accurate potential energy curves of both electronic states. Coupled-channels calculations are finally applied for deriving long range dispersion parameters and the exchange contribution of the molecular potentials, yielding a reliable description of cold collisions between Na and Cs atoms in their two different hyperfine ground states. Scattering lengths and Feshbach resonances are predicted for selected quantum states.
The K and Cs atom pair and its $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ electronic molecular states are studied by Fourier-transform spectroscopy with special emphasis on bound states close to the ground state asymptote (4s)K+(6s)Cs(4s)\text{K}+(6s)\text{Cs}(4s)K+(6s)Cs. Significant vibrational mixing due to hyperfine coupling was observed leading to improved potential energy curves for both states. The observed intensity pattern of the hyperfine structure for the last vibrational levels of $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ and $a{\phantom{\rule{0.16em}{0ex}}}^{3}{\ensuremath{\Sigma}}^{+}$ reveals deep insight into the multicomponent wave function of such levels with its influence for modeling the asymptotic behavior of the excited electronic states involved in the reported observations. Examples of derived properties of cold collisions are given and the importance of the present results for efficient production schemes for ultracold KCs is discussed.
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.
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.