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Physica Scripta

Potential energy curve for B1Π state of 85Rb133Cs obtained via genetic algorithm

Yide Yin, Ziang Li, Xuhui Bai, Ting Gong, Zhonghua Ji, Yanting Zhao, Yong‐Chang Han, Jie Yu, Gao‐Ren Wang

Published Feb 20, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ad2b3e

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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.
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 7Li85Rb^{7}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}^{85}\mathrm{Rb}7Li85Rb 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 6Li87Rb^{6}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}^{87}\mathrm{Rb}6Li87Rb 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.
We present the formation of ultracold (85)Rb(133)Cs molecules in the (5)0(+) electronic state by photoassociation and their detection via resonance-enhanced two-photon ionization. Up to v = 47 vibrational levels including the lowest v = 0 vibrational and lowest J = 0 levels are identified with rotationally resolved high resolution photoassociation spectra. Precise Dunham coefficients are determined for the (5)0(+) state with high accuracy, then the Rydberg-Klein-Rees potential energy curve is derived. The electric dipole moments with respect to the vibrational numbers of the (5)0(+) electronic state of (85)Rb(133)Cs molecule are also measured in the range between 1.9 and 4.8 D. These comprehensive studies on previously unobserved rovibrational levels of the (5)0(+) state are helpful to understand the molecular structure and discover suitable transition pathways for transferring ultracold atoms to deeply bound rovibrational levels of the electronic ground state.
We investigate the production of cold 85Rb133Cs molecules in the lowest vibronic level of the ground electronic state via the B1Π1 short-range state. The photoassociation (PA) spectra of the B1Π1 state, including newly observed transition to 2 vibronic levels, are obtained by high sensitivity time-of-flight mass spectrometry. Based on these PA spectra, the harmonic and anharmonic constants of vibronic states are obtained, resulting in predicted vibronic energies with an uncertainty of 1–2 cm−1. The B1Π1 (v = 3) state is found to have the maximum production rate for ground-state molecules with a value of 3(1) × 104 s−1, which is 3 times larger than the value via the previously studied 23Π0+ (v = 10, J = 0) state with two-photon cascade decay. The populations of J = 0, 1, and 2 rotational levels of X1Σ+ (v = 0) state molecules formed via the B1Π1 (v = 3, J = 1) state are measured to be around 20%, 40%, and 20%. To quantify the coupling strength between the B1Π1 (v = 3) state and X1Σ+ (v = 0) state, the transition dipole moment between them is measured to be 7.2(2) × 10−3ea0, which is also 3 times larger than the value between the 23Π0+(v=10) state and X1Σ+ (v = 0) state, meaning the B1Π1 (v = 3) state has a stronger coupling with the X1Σ+ (v = 0) state. Our detailed measurements provide relevant parameters for investigation on direct stimulated Raman adiabatic passage transfer between the atomic scattering state and molecular bound state for 85Rb133Cs molecules.
We establish a theoretical model to analyze the photoassociative spectroscopy of 85Rb 133Cs molecules in the (3)3Σ+ state. The vibrational energy, spin-spin coupling constant, and hyperfine interaction constant of the (3)3Σ+ state are determined based on nine observed vibrational levels. Consequently, the Rydberg-Klein-Rees potential energy curve of the (3)3Σ+ state is obtained and compared with the ab initial potential energy curve. Our model can be adopted to analyze the photoassociative spectroscopy of other heteronuclear alkali-metal diatomic molecules in the (3)3Σ+ state.
We present an accurate potential energy curve of the B (1)Pi state in the LiCs molecule for which vibrational levels between v(') = 0 and v(') = 35 (bound by 11.4 GHz) were measured by photoassociation spectroscopy in an ultracold ensemble of (7)Li and (133)Cs atoms. By the combination of conventional spectroscopic data of the B-X system and the new photoassociation measurements a very precise value of the dissociation energy of the ground state X (1)Sigma(+) of LiCs was determined to be D(0) = 5783.495(5) cm(-1).
Analyzing the photoassociation spectra of ultracold 85^{85}85Rb133^{133}133Cs molecule in (3)3Σ+(3)^3Σ^+(3)3Σ+ state
We establish a theoretical model to analyze the photoassociative (PA) spectroscopy of (3)3Σ+(3)^3Σ^+(3)3Σ+ state of 85^{85}85Rb133^{133}133Cs molecule. The term energy, spin-spin coupling constants and hyperfine interaction constant of nine vibrational levels in the (3)3Σ+(3)^3Σ^+(3)3Σ+ state are determined. Based on the fitted term energy and rotation constant, the potential energy curve of (3)3Σ+(3)^3Σ^+(3)3Σ+ state is obtained by using the RKR method which is compared with the ab initial potential curve.