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Physical Review A

Determination of 39K scattering lengths using photoassociation spectroscopy of the 0g− state

James P. Burke, Chris H. Greene, John L. Bohn, H. Wang, P. L. Gould, William C. Stwalley

Published Dec 1, 1999• 35 citations
Publisher

Abstract

Threshold scattering properties of ${}^{39}\mathrm{K}$ atoms are extracted from a line-shape analysis of photoassociation data. Specifically, we consider the rovibrational levels ${(v}^{\ensuremath{'}}=0--6)$ populated in the photoassociation process $\mathrm{K}(4S)+\mathrm{K}(4S)+\ensuremath{\Elzxh}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}{\mathrm{K}}_{2}^{*}[{0}_{g}^{\ensuremath{-}}{(v}^{\ensuremath{'}}{,J}^{\ensuremath{'}})].$ The measured spectra exhibit several general trends, including large ${J}^{\ensuremath{'}}=2$ linewidths, large relative ${J}^{\ensuremath{'}}=4$ peak intensities, and odd rotational lines which are weak or missing. The even ${J}^{\ensuremath{'}}$ features signal the presence of a d-wave shape resonance in the ground-state collisions. The combination of spectral features allows us to place the following limits on the ground-state singlet and triplet scattering lengths, ${a}_{s}{=140}_{\ensuremath{-}9}^{+6}$ a.u. and ${a}_{t}=\ensuremath{-}17\ensuremath{-}{0.045(C}_{6}\ensuremath{-}{C}_{6})\ifmmode\pm\else\textpm\fi{}25$ a.u., ${C}_{6}=3800$ a.u.

DOI
10.1103/physreva.60.4417

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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.
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