Determination of Potassium Cold Collision Parameters by an Analysis of Feshbach Resonances

Sergey Alyabyshev, Roman V. Krems

Arturo Bambini, S. Geltman

In this paper we briefly review the basic steps that allow the calculation of the scattering length in the collision of two alkali-metal atoms in a well defined magnetic polarization state, and in the presence of a static magnetic field. Calculations are actually done for the low-field seeking state $F=1, {\ensuremath{\mu}}_{F}=\ensuremath{-}1$ of bosonic potassium atoms. The electrostatic potentials obtained through Rydberg-Klein-Rees data are connected to a dispersive, long range tail in which the dominant dipole-dipole ${C}_{6}$ term may take different values within a specified range. We show the occurrence of Feshbach resonances in the ultra cold collision of two identical atoms, belonging either to the bosonic species ${}^{39}\mathrm{K}$ or ${}^{41}\mathrm{K}.$ Our results demonstrate that there is a range of ${C}_{6}$ values for which the collision of two ${}^{39}\mathrm{K}$ atoms displays a single resonance, while for other values of ${C}_{6}$ no resonance occurs. On the other hand, Feshbach resonances are present in the collision of two ${}^{41}\mathrm{K}$ atoms for almost all values of the dispersion coefficient ${C}_{6}$ in that range. We also show the origin of the different types of Feshbach resonances that occur in the cold collision of two ${}^{41}\mathrm{K}$ atoms. The detection of such resonances can help establish the actual value of the dispersive coefficient.

Matthew D. Frye, Jeremy M. Hutson

Andrea Simoni, Alexandra Viel

Stephan Falke, H. Knöckel, J. Friebe +3 more

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.

Francesca Ferlaino, Chiara D’Errico, G. Roati +4 more