We use double-resonance photoassociative spectroscopy of ultracold ${}^{39}\mathrm{K}$ atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free ${}^{39}\mathrm{K}$ 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 ${4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=1)$ 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 ${}^{39}\mathrm{K},$ ${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$ ${(1a}_{0}=0.0529177 \mathrm{nm}),$ is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large ${}^{39}\mathrm{K}$ Bose-Einstein condensate will not be stable.We use double-resonance photoassociative spectroscopy of ultracold ${}^{39}\mathrm{K}$ atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free ${}^{39}\mathrm{K}$ 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 ${4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=1)$ 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 ${}^{39}\mathrm{K},$ ${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$ ${(1a}_{0}=0.0529177 \mathrm{nm}),$ is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large ${}^{39}\mathrm{K}$ Bose-Einstein condensate will not be stable.

Physical Review AOct 12, 200062 citations

Photoassociation Spectroscopy of Ultracold Atoms and the Study of Physicists' Molecules

K. M. Jones, Eite Tiesinga, Paul D. Lett +1 more

Reviews of Modern PhysicsMay 22, 20063 citations

We use double-resonance photoassociative spectroscopy of ultracold

{}^{39}\mathrm{K}

atoms to precisely determine the triplet $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free

{}^{39}\mathrm{K}

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

{4s}_{1/2}{(f}_{a}{=1)+4s}_{1/2}{(f}_{b}=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

{}^{39}\mathrm{K},

${a}_{t}=\ensuremath{-}33\ifmmode\pm\else\textpm\fi{}{5a}_{0}$

{(1a}_{0}=0.0529177 \mathrm{nm}),

is a factor of $\ensuremath{\sim}5$ improvement over previous determinations and establishes that a large

{}^{39}\mathrm{K}

Bose-Einstein condensate will not be stable.