# Level structure of deeply bound levels of the $c^3\Sigma_g^+$ state of $^{87}\text{Rb}_2$

## TL;DR

This study combines spectroscopic measurements and theoretical modeling to elucidate the hyperfine, rotational, and Zeeman structures of specific vibrational levels of the $c^3\Sigma_g^+$ state in $^{87} ext{Rb}_2$, providing detailed molecular parameters and potential energy curves.

## Contribution

It introduces a comprehensive experimental and theoretical analysis of the $c^3\Sigma_g^+$ state, including the first determination of the anisotropic hyperfine constant and potential energy curve fitting for vibrational levels 0 to 13.

## Key findings

- Accurate hyperfine and rotational constants for vibrational levels 0, 7, 13.
- First measurement of the anisotropic hyperfine constant.
- Potential energy curve segment for the $c^3\Sigma_g^+$ state derived from coupled-channel calculations.

## Abstract

We spectroscopically investigate the hyperfine, rotational and Zeeman structure of the vibrational levels $\text{v}'=0$, $7$, $13$ within the electronically excited $c^3\Sigma_g^+$ state of $^{87}\text{Rb}_2$ for magnetic fields of up to $1000\,\text{G}$. As spectroscopic methods we use short-range photoassociation of ultracold Rb atoms as well as photoexcitation of ultracold molecules which have been previously prepared in several well-defined quantum states of the $a^3\Sigma_u^+$ potential. As a byproduct, we present optical two-photon transfer of weakly bound Feshbach molecules into $a^3\Sigma_u^+$, $\text{v}=0$ levels featuring different nuclear spin quantum numbers. A simple model reproduces well the molecular level structures of the $c^3\Sigma_g^+$ vibrational states and provides a consistent assignment of the measured resonance lines. Furthermore, the model can be used to predict the relative transition strengths of the lines. From fits to the data we extract for each vibrational level the rotational constant, the effective spin-spin interaction constant, as well as the Fermi contact parameter and (for the first time) the anisotropic hyperfine constant. In an alternative approach, we perform coupled-channel calculations where we fit the relevant potential energy curves, spin-orbit interactions and hyperfine functions. The calculations reproduce the measured hyperfine level term frequencies with an average uncertainty of $\pm9\:$MHz, similar as for the simple model. From these fits we obtain a section of the potential energy curve for the $c^3\Sigma_g^+$ state which can be used for predicting the level structure for the vibrational manifold $\text{v}'=0$ to $13$ of this electronic state.