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

TL;DR

This paper presents a detailed theoretical analysis of the formation of vibrationally cold polar KRb molecules, including multi-channel bound-state calculations, hyperfine structure agreement, and effects of spin-orbit mixing on transition dipole moments and polarizability estimates.

Contribution

The study introduces comprehensive multi-channel calculations and analysis of hyperfine, Zeeman, and spin-orbit effects to better understand and optimize the creation of cold polar molecules.

Findings

Excellent agreement with experimental hyperfine structure data.

Quantitative estimates of transition dipole moments influenced by spin-orbit mixing.

Polarizability estimates for optical trapping near relevant frequencies.

Abstract

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$^1\Sigma^+$ and a$^3\Sigma^+$ 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$^1\Sigma^+$ 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.