Ground-state scattering lengths for potassium isotopes determined by double-resonance photoassociative spectroscopy of ultracold39K

We use double-resonance photoassociative spectroscopy of ultracold ${}^{39}\mathrm{K}$ atoms to precisely determine the triplet $a{}^3{\Sigma }_u^{+}$ scattering length for the various isotopes of potassium. Photoassociation of free ${}^{39}\mathrm{K}$ atoms to the pure long-range $0_g^{-}{(v}^{\prime }=0,J^{\prime }=2)$ level is followed by stimulated emission to high-lying levels of the $a{}^3{\Sigma }_u^{+}$ 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 ${}^{39}\mathrm{K},$ $a_t=-33\pm {5a}_0$ ${(1a}_0=0.052\mathrm{}9177\hspace{0.5em}\mathrm{nm}),$ is a factor of $\sim 5$ improvement over previous determinations and establishes that a large ${}^{39}\mathrm{K}$ Bose-Einstein condensate will not be stable.