Genetics-based deperturbation analysis for the spin-orbit coupled ${\rm A}^1\Sigma^+$ and ${\rm b}^3\Pi_{0^+}$ states of LiRb

We present a deperturbation analysis of the spin-orbit coupled $\rm A^1\Sigma^+$ and $\rm b^3\Pi_{0^+}$ states of LiRb based on the rovibrational energy levels observed previously by photoassociation spectroscopy in bosonic $^7$Li$^{85}$Rb molecule. Using the genetic algorithm, we fit the potential energy curves of the $\rm A^1\Sigma^+$ state and the $\rm b^3\Pi$ state into point-wise form. We then fit these point-wise potentials along with the spin-orbit coupling into expanded Morse oscillator functional form and optimise analytical parameters based on the experimental data. From the fitted results, we calculate the transition dipole moment matrix elements for transitions from the rovibrational levels of the coupled $\rm A^1\Sigma^+$-$\rm b^3\Pi_{0^+}$ state to the Feshbach state and the absolute rovibrational ground state for fermionic $^6$Li$^{87}$Rb molecule. Based on the calculated transition dipole moment matrix elements, several levels of the coupled $\rm A^1\Sigma^+$-$\rm b^3\Pi_{0^+}$ state are predicted to be suitable as the intermediate state for stimulated Raman adiabatic passage transfer from the Feshbach state to the absolute rovibrational ground state. In addition, we also provide a similar estimation for ${\rm B}^1\Pi$-${\rm c}^3\Sigma_1^+$-${\rm b}^3\Pi_1$ state based on available $ab\ initio$ interaction potentials.