Coherent Control of the Rotational Degree of Freedom of a Two-Ion Coulomb Crystal

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.