Preparation of ultra-cold (36D<sub>5/2</sub>+ 6S<sub>1/2</sub>) Rydberg molecule and measurement of its permanent electric dipole moment

Abstract

<sec>Ultra-cold long-range Rydberg molecules, consisting of a Rydberg atom and a ground-state atom or another Rydberg atom or ion, have attracted considerable attention due to their exaggerated properties, such as huge size, long chemical bond, large polarization and electric dipole moment, abundant vibrational states and exotic adiabatic potentials. The binding mechanism of Rydberg molecules is a low-energy scattering interaction between the Rydberg electron and the ground state atom for ground-Rydberg molecules or long-range multipole interaction for Rydberg-atom macrodimers and Rydberg-ion molecules, in contrast to covalent bonds, ionic bonds of normal and van der Waals interaction. Owing to its huge size, the dynamic evolution becomes slow compared with normal diatomic molecules and the ultra-long chemical bonds allow being imaged directly by high resolution imaging technology, which makes it convenient to observe the molecular dynamics process chemical reaction process in real time. The investigation of Rydberg molecules will be significant for understanding the mechanism of molecular collision and quantum chemical reaction.</sec><sec>In this work, we study the ultra-cold Rydberg-ground state molecules theoretically and experimentally. Theoretically, we calculate the adiabatic potential energy curve of cesium (36D<sub>5/2</sub>+ 6S<sub>1/2</sub>) Rydberg molecule based on the Fermi model of low energy electron scattering by numerically solving the Hamiltonian of Rydberg molecules. And also, we obtain its characteristic parameters, such as the potential depth, binding energy and equilibrium nuclear distance of Rydberg molecule. Experimentally, the Rydberg-ground molecules are investigated by a photoassociation spectroscopy, where two laser pulses are used to achieve a two-photon transition, and their spectra are obtained by ion detection technology. We successfully observe the Rydberg-ground state molecular spectra that correspond to a scattering triplet and a scattering single-triplet mixture (<sup>S,T</sup>Σ). The measured binding energy of Rydberg-ground state molecules is in good agreement with the theoretical result. In addition, taking the Rydberg-ground state molecules formed by scattering triplet (<sup>T</sup>Σ) for example, we demonstrate the spectrum broadening of Rydberg molecules in a weak electric field, from which we obtain the permanent electric dipole moments <inline-formula><tex-math id="M2">\begin{document}$|\bar{d}|$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M2.png"/></alternatives></inline-formula> of polar Rydberg-ground state molecules about (12.10<inline-formula><tex-math id="M3">\begin{document}$ \pm $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M3.png"/></alternatives></inline-formula>1.65) Debye ((4.76<inline-formula><tex-math id="M4">\begin{document}$ \pm $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20221865_M4.png"/></alternatives></inline-formula>0.65) <i>ea</i><sub>0</sub>). The results are consistent with the theoretical calculations. Our study provides a feasible scheme for the experimental preparation of D-type Rydberg-ground molecules, which is of great significance in studying the binding mechanism and the spectral characteristics of polar Rydberg molecules.</sec>