Hyperfine, rotational and Zeeman structure of the lowest vibrational levels of the $^{87}$Rb$_2$ $tripletex$ state

We present the results of an experimental and theoretical study of the electronically excited $tripletex$ state of $^{87}$Rb$_2$ molecules. The vibrational energies are measured for deeply bound states from the bottom up to $v=15$ using laser spectroscopy of ultracold Rb$_2$ Feshbach molecules. The spectrum of each vibrational state is dominated by a 47,GHz splitting into a $cog$ and $clg$ component caused mainly by a strong second order spin-orbit interaction. Our spectroscopy fully resolves the rotational, hyperfine, and Zeeman structure of the spectrum. We are able to describe to first order this structure using a simplified effective Hamiltonian.