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arXiv:2406.13157 · Physical Review A

Genetics-based deperturbation analysis for the spin-orbit-coupled A 1 Σ + and b 3 Π 0 + states of LiRb

Yide Yin, Xuhui Bai, Xuechun Li, Jie Yu, Gao‐Ren Wang, Yong‐Chang Han, Xinyu Luo

Published Oct 11, 2024• 2 citations
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Abstract

We present a deperturbation analysis of the spin-orbit-coupled $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ and $b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{{0}^{+}}$ states of LiRb based on the rovibrational energy levels observed previously by photoassociation spectroscopy in the bosonic $^{7}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}^{85}\mathrm{Rb}$ molecule. Using the genetic algorithm (GA), we optimize the pointwise ab initio potential energy curves of the $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state and the $b{\phantom{\rule{0.16em}{0ex}}}^{3}\mathrm{\ensuremath{\Pi}}$ state based on spectroscopic data. Then we fit the pointwise potentials obtained by the GA and the ab initio spin-orbit-coupling term with the expanded Morse oscillator (EMO) function. Finally, we optimize the parameters of the EMO function using the sequential least-squares quadratic programming algorithm with the guidance of the experimental data and pointwise potentials obtained by the GA. From the fitted results, we calculate the transition dipole moment matrix elements for transitions from the rovibrational levels of the coupled $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\text{--}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{{0}^{+}}$ state to the Feshbach state and the absolute rovibrational ground state for the fermionic $^{6}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}^{87}\mathrm{Rb}$ molecule. Based on the calculated transition dipole moment matrix elements, several levels of the coupled $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}\text{--}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{{0}^{+}}$ 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 the $B{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\text{--}c{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{1}^{+}\text{--}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{1}$ state based on available ab initio interaction potentials.

DOI
10.1103/physreva.110.042812

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We performed a diabatization of the mutually perturbed $1^{1}\mathrm{\ensuremath{\Pi}}$ and $2^{1}\mathrm{\ensuremath{\Pi}}$ states of KRb based on both electronic structure calculation and direct coupled-channel deperturbation analysis of experimental energies. The potential energy curves (PECs) of the diabatic states and their scalar coupling were constructed from the ab initio adiabatic PECs by analytically integrating the radial $\ensuremath{\langle}{\ensuremath{\psi}}_{1}^{ad}|\ensuremath{\partial}/\ensuremath{\partial}R|{\ensuremath{\psi}}_{2}^{ad}\ensuremath{\rangle}$ matrix element obtained by a finite-difference method. The diabatic potentials and electronic coupling function were refined by the least squares fitting of the rovibronic term values of the $1{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}\ensuremath{\sim}2{\phantom{\rule{0.16em}{0ex}}}^{1}\mathrm{\ensuremath{\Pi}}$ complex. The empirical PECs combined with the coupling function as well as the diabatized spin-orbit coupling and transition dipole matrix elements are crucial to discovering efficient photoassociation pathways for production of ultracold ground-state KRb molecules.
Abstract We adopt the genetic algorithm to fit the potential energy curve for B1Π state of 85Rb133Cs molecule based on the data of rovibrational energy levels, which were observed previously by Fourier-transform spectroscopy and photoassociation spectroscopy. We explore the effect of different hyperparameter settings on the evolutionary process and final results to optimise the performance of the algorithm. Finally, the fitting procedure can reproduce the rovibrational levels with an error less than 0.06 cm−1 compared to the experimental data.
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