Multi-channel modelling of the formation of vibrationally cold polar KRb molecules

We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar ${}^{40}$K${}^{87}$Rb molecules \cite{nphys08,science08}. Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold ${}^{40}$K and ${}^{87}$Rb atoms. Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X${}^1{\mathrm{\Sigma }}^{+}$ and a${}^3{\mathrm{\Sigma }}^{+}$ vibrational levels. We find excellent agreement with the hyperfine structure observed in experimental data. In addition, we studied the spin-orbit mixing in the intermediate state of the Raman transition. This allowed us to investigate its effect on the vibrationally-averaged transition dipole moment to the lowest ro-vibrational level of the X${}^1{\mathrm{\Sigma }}^{+}$ state. Finally, we obtained an estimate of the polarizability of the initial and final ro-vibrational states of the Raman transition near frequencies relevant for optical trapping of the molecules.