  We demonstrate the preparation and coherent control of the angular momentum
state of a two-ion crystal. The ions are prepared with an average angular
momentum of $7780\hbar$ freely rotating at 100~kHz in a circularly symmetric
potential, allowing us to address rotational sidebands. By coherently exciting
these motional sidebands, we create superpositions of states separated by up to
four angular momentum quanta. Ramsey experiments show the expected dephasing of
the superposition which is dependent on the number of quanta separating the
states. These results demonstrate coherent control of a collective motional
state described as a quantum rotor in trapped ions. Moreover, our work offers
an expansion of the utility of trapped ions for quantum simulation,
interferometry, and sensing.
